Techniques of Water-Resources Investigations
of the Uni
tes Geological Survey
l
A MODU
FINITE-DIFFE
By Mich el G. McDonald
Arl n W. Harbaugh
pen-file
and
U.S. Geological
Report 83-875
Book 6
MODELING
TECHNIQUES
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DEPARTMENT OF THE INTERIOR
DONALD
PAUL HODEL, Secretary
U.S. GEOLOGICAL
SURVEY
Dallas 1. Peck, Director
A copy of the source program of the Modular Model
is available at cost, from:
Chief, Office of Ground Water, MS 411, National Center,
U.S. Geological Survey, Reston, Virginia 22092
UNITED
STATES GOVERNMENT
PRINTING
OFFICE, WASHINGTON
For sale by the Books and Open-File Reports Section, U.S. Geological Survey,
Federal Center, Box 25425, Denver, CO 80225
: 1988
PREFACE
The series of manuals on techniques describes procedures for planning and
executingspecializedwork in water-resourcesinvestigations.The material is grouped
under major subject headingscalled books and further subdivided into sections and
chapters. Section A of Book 6 is on ground-water modeling.
Provisional drafts of chapters are distributed to field offices of the U.S. Geological
Survey for their use. These drafts are subject to revision becauseof experiencein use
or because of advancement in knowledge, techniques, or equipment. After the
technique describedin a chapter is sufficiently developed,the chapter is published and
is for sale by the Books and Open-File Reports Section, US. Geological Survey,
Federal Center, Box 25425, Denver, Colorado 80225.
Reference to trade names, commercial products, manufacturers, or distributors in
this manual constitutes neither endorsement by the U.S. Geological Survey nor
recommendationfor use.
...
III
TECHNIQUES
OF WATER-RESOURCES INVESTIGATIONS
UNITED STATES GEOLOGICAL SURVEY
OF THE
The U.S. Geological Survey publishes a series of manuals describing procedures for planning and conducting
specializedwork in water-resourcesinvestigations.The manualspublished to date are listed below and may be ordered
by mail from the U.S. Geoiogical Survey Books and Open-File Reports, Federal Center, Box 25425,Denver,Colorado
80225an authorized agent of the Superintendent of Documents, Government Printing Office).
Prepaymentis required. Remittance should be sentby check or money order payableto U.S. Geological Survey.Prices
are not included in the listing below as they are subject to change. Current prices can be obtained by writing to the
USGS, Books and Open File Reports. Prices include cost of domestic surface transportation. l%r transmittal outside the
U.S.A. (except to Canada and Mexico) a surcharge of 25 percent of the net bill should be included to cover surface
transportation. When ordering any of thesepublications, pleasegive the title, book number, chapter number, and “U.S.
Geological Survey Techniques of Water-ResourcesInvestigations.”
TWI 1-Dl.
TWI 1.D2.
Water temperature-influential factors, field measurement, and data presentation, by H.H. Stevens,Jr., J.F. Flcke, and GE Smoot,
1975,65 pages.
Guidelines for collection and field analysii of ground-water samples for selected unstable constituents, by W.W. Wood. 1976. 24
Application of surface geophysics to ground water investigations, by A.A.R. Zohdy, G.P. Eaton, and D.R. Mabey. 1974.116 pages.
Application of borehole geophysics to water-resources investigations, by W.S. Keys and L.M. MacCaly. 1971. 126 pages.
General field and office procedures for indirect discharge measurement, by M.A. Benson and Tate Dahymple. 1967.30 pages
Measurement of peak discharge by the slope-area method, by Tate Dabymple and MA. Benson. 1967.12 pages
Measurement of peak discharge.at culverts by indirect methods, by G.L. Bcdhaine. 1968. 60 pages.
Measurement of peak discharge at width contractions by indirect methods, by H.F. Matthai. 1967. 44 pages
Measurement of peak discharge at dams by indirect methods, by Harry Hulsing. 1967.29 pages.
General procedure for gaging streams, by R.W. Carter and Jacob Davidian. 1968.13 pages
Stage measurements at gaging stations, by T.J. Buchanan and W.P. Somers. 1968.28 pages
Discharge measurements at gaging stations, by TJ. Buchanan and W.P. Somers. 1969.65 pages.
Measurement of time of travel and dispersion in streams by dye tracing, by E.P. Hubbard, F.A. Kilpatrick, L.A. Martens, and
J.F. Wilson, Jr. 1982.44 pages
l-WI 3-AlO. Discharge ratings at gaging stations, by EJ. Kennedy. 1984.59 pages.
TWI 3-All. Measurement of discharge by moving-boat method, by G.F. Smoot and CC. Novak. 1969. 22 pages.
TWI 3-A12. Fluorometric procedures for dye tracing. Revised, by James F. Wilson, Jr., Ernest D. Cobb, and Frederick A. Kilpatrick. 1986.41
TWI
TWI
TWI
TWI
TWI
TWI
TWI
TWI
TWI
TWI
TWI
2-Dl.
2-El.
3-Al.
3-A2.
3-A3.
3-A4.
3-As.
3-A6.
3-A7.
3-A8.
3-A9.
TWI
TWI
TWI
TWI
TWI
TWI
TWI
3-A13.
3-A14.
3-A15
3-A16
3-A17.
3-Bl.
3-B2.
TWI 3-B3.
TWI 3-BS.
TWI 3-B6.
TWI
TWI
TWI
TWI
TWI
TWI
TWI
TWI
TWI
TWI
3x1.
3x2.
3x3.
4-Al.
4-A2.
4-Bl.
4-B2.
4-B3.
4-Dl.
S-Al.
TWI 542.
Iv
Computation of continuous records of streamflow, by Edward J. Kennedy. 1983.53 pages.
Use of flumes in measuring discharge, by EA. Kilpatrick, and V.R. Schneider. 1983.46 pages.
Computation of water-surface profiles in open channels, by Jacob Davidian. 1984. 48 pages
Measurement of discharge using tracers, by F.A. Kilpatrick and E.D. Cobb. 1985.52 pages.
Acoustic velocity meter systems, by Antonius Laenen. 1985. 38 pages.
Aquifer-test design, observation, and data analysii by R.W. Stallman. 1971. 26 pages
Introduction to ground-water hydraulics, a programmed text for self-instruction, by G.D. Bennett. 1976. 172 pages. Spanish
translation TWL 3-B2 also available.
Type cures for selected problems of flow to wells in confined aquifers, by J.E. Reed. 1980. 106 p.
Definition of boundaxy and initial conditions in the analysis of saturated ground-water flow systems-an introduction, by 0. Lehn
Franke, Thomas E. Reilly, and Gordon D. Bennett. 1987. 15 pages.
The principle of superposition and its application in ground-water hydraulics, by Thomas E. Reilly, 0. Lehn Franke, and Gordon D.
Bennett.1987. 28 pages.
Fluvial sediment concepts, by H.P. Guy. 1970.55 pages.
Field methods of measurement of fluvial sediment, by H.P. Guy and V.W. Norman. 1970. 59 pages.
Computation of fluvial-sediment discharge, by George Portertield. 1972. 66 pages.
Some statistical tools in hydrology, by H.C. Riw. 1968. 39 pages.
Frequency curves, by H.C. Riggs, 1968. 15 pages.
Low-flow investigations, by H.C. Riggs. 1972. 18 pages
Storage analyses for water supply, by H.C. Riggs and C.H. Hardison. 1973.20 pages
Regional analyses of streamflow characteristics, by H.C. Riggs. 1973. 15 pages.
Computation of rate and volume of stream depletion by wells, by C.T. Jenkins. 1970. 17 page&
Methods for determination of inorganic substancesin water and fluvial sediments, by M.W. Skougstad and others, editors. 1979.626
pages.
Determination of minor elements in water by emission spectroscopy, by P.R. Bamett and E.C. Mallory, Jr. 1971. 31 pages.
TWI 543.
TWI S-A4
TWI 545.
TWI 5-A6.
lwI 5x1.
TWI 6-Al.
TWI 7x1.
TWI 7x2.
TWI 7-C%
TWI 8-Al.
TWI 842.
TWI 8-B2.
Methods for the determination of organic substancesin water and fluvial sediments, edited by R.L. Wershaw, M.J. Fishman, R.R.
Grabbe, and L.E. Lowe. 1987.80 pages This manual is a revision of “Methods for Analysii of Organic Substancesin Water” by
Donald F. Goerlitz and Eugene Brown, Book 5, Chapter A3, published in 1972.
Methods for collection and analysis of aquatic biological and microbiological samples, edited by P.E. Greeson, T.A. Ehlke, G.A.
Irwin, B.W. Lium, and K.V. Slack. 1977. 332 pages.
Methods for determination of radioactive substances in water and fluvial sediments, by L.L. Thatcher, VJ. Janzer, and K.W.
Edwards. 1977.95 pages.
Quality assurance practices for the chemical and biological analyses of water and fluvial sediments, by L.C. Friedman and D.E.
Erdmann. 1982. 181 pages.
Laboratory theory and methods for sediment analysis, by H.P. Guy. 1969.58 pages.
A modular threedimensional finitedifference ground-water flow model, by Michael G. McDonald and Arlen W. Harbaugh. 1988.
586 pages.
Finite difference model for aquifer simulation in two dimensions with results of numerical experiments, by P.C. Txxxcott, G.F.
Pinder, and S.P. Larson. 1976. 116 pages.
Computer model of two-dimensional solute transport and dispersion in ground water, by L.F. Konikow and J.D. Bredehoeft. 1978.
90 pages.
A model for simulation of flow in singular and interconnected channels, by R.W. Schaffranek, R.A. Baltzer, and DE Goldberg.
1981.110 pages.
Methods of measuring water levels in deep wells, by M.S. Garber and EC. Koopman. 1968. 23 pages.
Installation and setice manual for U.S. Geological Survey monometers, by J.D. Craig. 1983. 57 pages.
Calibration and maintenance of vertical-axis type current meters, by G.F. Smoot and C.E. Novak. 1968.15 pages.
CONTENTS
Page
Abstract ..............................................................
Introduction
..............................................
Chapter 1.
Purpose .............................................................
Organization
of This Report .........................................
Acknowledgement .....................................................
Chapter 2. Derivation
of the Finite-Difference
Equation..............2
Mathematical
Model ..................................................
Discretization
Convention ...........................................
Finite-Difference
Equation ..........................................
Iteration
...........................................................
Formulation
of equations
for solution ...............................
Types of Model Cell and Simulation
of Boundaries....................2-2
Conceptual
Aspects of Vertical
Discretization.......................2-2
Chapter 3.
Program Design ............................................
Overall
Structure ...................................................
Array Boundaries and Aquifer
Boundaries .............................
Volumetric
Budget ...................................................
Space Allocation
....................................................
Three-Dimensional
Subscripts
for Model Arrays.......................3-2
Input Structure .....................................................
Output Structure ....................................................
...............................
Main Program........................
FORTRAN Listing
of the Main Program. ...............................
...............................
Chapter 4.
Basic Package.............
Conceptualization
and Implementation
...............................
Selection
of Major Options and Des i gnation of Input Files.........4...............................
The IBOUND Array..................
Initial
Conditions
................................................
Discretization
of Time ............................................
output ............................................................
Budget Calculations
in the Basic Package ..........................
Input
Instructions
..................................................
ll-
1
2
l- 2
ll-
3
7
- 1
2- 1
2- 2
2- 5
2-20
2-25
7
9
3- 1
33-1;
3-16
3-22
3
3-24
3-28
3-29
3-32
4- 1
4- 1
1
. 4- 2
44444-
2
5
5
8
9
4-13
Sample Input ......................................................
4-14
Input Instructions
for Output Control ...............................
4-17
Sample Input for Output Control ...................................
4-18
Module Documentation ................................................
4-19
BASlDF ............................................................
4-23
BASlAL .............................................................
BASlRP . . . . . . . .‘I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27
4-31
BASlST ............................................................
4-35
BASlAD ............................................................
4-39
BASlFM ............................................................
4-42
BASlOC ............................................................
4-46
BASlOT ............................................................
4-51
SBASlD ............................................................
4-55
SBASlH ............................................................
SABSlI ............................................................
vii
4-59
Page
SBASlT ............................................................
SBASlV ............................................................
Chapter 5. Block-Centered
Flow Package ...............................
................................
Conceptualization
and Implementation
Basic Conductance Equations .......................................
Horizontal
Conductance Under Confined Conditions..................5
Horizontal
Conductance Under Water Table Conditions...............5
Vertical
Conductance Formulation ..................................
Vertical
Flow Calculation
Under Dewatered Conditions..............5-19
Storage Formulation ...............................................
Storage Term Conversion ...........................................
Applicability
and Limitations
of Optional
Formulations............5-3
Data Requirements .................................................
Input Instructions
..................................................
Sample Input ......................................................
Module Documentation ................................................
BCFlAL ............................................................
BCFlRP ............................................................
BCFlFM ............................................................
BCFlBD ............................................................
SBCFlN ............................................................
SBCFlH ............................................................
SBCFlC ............................................................
SBCF1B............................................................
SBCFlF ............................................................
Chapter 6. River Package .............................................
................................
Conceptualization
and Implementation
..................................................
Input Instructions
Sample Input ......................................................
Module Documentation ................................................
RIVlAL ............................................................
RIVlRP ............................................................
4-63
4-66
5- 1
5- 1
5- 2
- 6
- 9
5-11
5-24
5-26
0
5-30
5-37
5-41
5-42
5-44
5-50
5-56
5-62
5-68
5-73
5-77
5-81
5-86
6- 1
6- 1
6-14
6-16
6-17
6-18
6-22
RIVlFM ............................................................
6-26
RIVlBD ............................................................
6-30
7- 1
7- 1
7- 6
7- 8
7- 9
7-10
7-14
7-18
7-22
8- 1
8- 1
8- 3
8- 4
8- 5
8- 6
8-10
8-14
8-17
Chapter 7. Recharge Package ..........................................
................................
Conceptualization
and Implementation
..................................................
Input Instructions
Sample Input ......................................................
Module Documentation ................................................
RCH1AL ............................................................
RCHlRP ............................................................
RCHlFM............................................................
...........................
RCHlBD ..................................
Chapter 8. Well Package ..............................................
................................
Conceptualization
and Implementation
Input Instructions
..................................................
Sample Input ......................................................
Module Documentation ................................................
WELlAL ............................................................
WELlRP ............................................................
WELlFM............................................................
WELlBD ............................................................
...
Vlll
Page
Chapter 9. Drain
Conceptualization
Package ..............................................
.................................
and Implementation
Input Instructions ...................................................
Sample Input .......................................................
9- 1
9- 1
;-- ;
9-10
Module Documentation .................................................
9-11
DRNlAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9-15
DRNlRP .............................................................
9-19
DRNlFM.............................................................
9-23
DRNlBD .............................................................
lo- 1
Package ...............................
Chapter 10. Evapotranspiration
lo- 1
Conceptualization
and Implementation ................................
Input Instructions ..................................................
Sample Input ......................................................
Module Documentation ................................................
EVTlAL ............................................................
EVTlRP ............................................................
EVTlFM ............................................................
EVTlBD............................................................
Chapter 11. General-Head Boundary Package ............................
................................
Conceptualization
and Implementation
Input Instructions ..................................................
Sampl e Input ......................................................
Module Documentation ................................................
GHBlAL ............................................................
GHBlRP............................................................
GHBlFM............................................................
GHBlBD............................................................
Implicit
Procedure Package......................12
Chapter 12. Strongly
Conceptualization
and Implementation ................................
General Theory ....................................................
Transfer
of Arrays ................................................
..............................................
Order of Calculation
Iteration Parameters ..............................................
Input Instructions ..................................................
Sample Input ......................................................
Module Documentation
................................................
lo- 8
10-10
10-11
10-12
lo-16
10-20
lo-24
ll- 1
ll- 1
ll- 5
ll- 7
ll- 8
ll- 9
11-13
11-17
11-21
- 1
12- 1
12- 1
12-20
12-21
12-23
12-30
12-31
12-32
SIPlAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-33
12-37
SI PlRP ............................................................
12-41
SIPlAP ............................................................
12-56
SSIPlP ............................................................
12-59
SSIPlI ............................................................
Overrelaxation
Package..................13
- 1
Chapter 13. Slice-Successive
13- 1
Conceptualization
and Implementation ................................
13-10
Input Instructions ..................................................
13-11
Module Documentation ................................................
SORlAL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-12
SORlRP............................................................
SORlAP ............................................................
SSORlB ............................................................
Utility
Modules ..........................................
Chapter 14.
Input Instructions
for Array Readers ................................
UBUDSV..*.......*.................................................
ix
13-16
13-19
13-29
14- 1
14- 4
14- 6
Page
14- 9
14-12
14-17
14-22
14-26
ULASAV............................................................
ULAPRS............................................................
ULAPRW............................................................
UCOLNO............................................................
UZDREL............................................................
UZDINT............................................................
UlDREL ............................................................
References ............................................................
........................................
Appendix A--Program Portability
Appendix B--Space Requirements
in the X Array ..........................
Appendix C--Continuation
of a Previous Run .............................
Appendix D--Sample Problem .............................................
Appendix E--Abbreviated
Input Instructions .............................
x
14-30
14-35
14-39
A- 1
B- 1
c- 1
D- 1
E- 1
ILLUSTRATIONS
Page
Figure
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
22.
23.
24.
25.
26.
27.
28.
29.
30.
A discretized
hypothetical
aquifer
system................2
- 3
Grids showing the difference
between block-centered
and point-centered
formulations........................2
- 6
Cell i,j,k
and the six adjacent
cells....................2
- 8
Flow into cell i,j,k
from cell i.j-l.k...................Z
- 9
Conceptual
representation
of leakage through a
2-14
riverbed
into a cell ...................................
2-17
................................
Hydrograph for cell i,j,k
Iterative
calculation
of a head distribution.............Z-2
2
Discretized
aquifer
showing boundaries
and cell
2-28
designations
...........................................
Schemes of vertical
discretization.......................Z-3
0
Possible
pattern
of flow in a cross section
consisting
of two high conductivity
units
separated by a low conductivity
unit...................Z-3
2
A cross section
in which a low conductivity
unit
is represented
by six model layers.....................Z-3
3
A cross section
in which a low conductivity
unit is
represented
by the conductance between model layers....Z-3
5
32
................................
Overall
program structure
Organization
of modules by procedures
and packages.......3
- 6
Primary modules organized by procedure and package.......3
- 8
Overall
program structure
showing all primary modules....3-12
Specification
of major options using the IUNIT array.....3-2
6
Sample input data showing role of the IUNIT array........3-2
7
Example of the boundary array (IBOUND) for a single
4- 3
layer ..................................................
Flow of head distributions
during a simulation...........4
- 4
Division
of simulation
time into stress periods and
4- 6
time steps .............................................
Sample overall
volumetric
water budget...................4
- 7
Prism of porous material
illustrating
Darcy's law........5
- 3
Calculation
of conductance through several
prisms
5- 5
in series ..............................................
Calculation
of conductance between nodes using
transmissivities
and dimensions of cells...............5
- 7
Diagram for calculation
of vertical
leakance,
Vcont,
between two nodes which fall
within
a single
5-14
geohydrologic
unit .....................................
Diagram for calculation
of vertical
leakance,
Vcont, between two nodes located
at the midpoints
of vertically
5-15
adjacent
geohydrologic
units ...........................
Diagram for calculation
of vertical
leakance,
Vcont,
between two nodes located at the midpoints
of aquifers
which are separated by a semiconfining
unit............5-17
Situation
in which a correction
is required
to limit
the
downward flow into cell i,j,k+l
as a result
of
partial
desaturation
of the cell.......................5-2
0
A model cell which uses two storage factors
during
5-29
one iteration
..........................................
xi
Page
Figure
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
Relationship
among the modules in the Block-Centered
Flow Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-43
Discretization
of a stream into reaches.................62
(a) Cross section
of an aquifer
containing
a stream,
and (b) conceptual
representation
of stream-aquifer
interconnection
in simulation
. . . . . . . . . . . . . . . . . . . . . . ...63
Idealization
of streambed conductance
in an individual
cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6- 4
Cross sections
showing the relation
between head at
the base of the streambed layer and head in the
ccl 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6- 7
Flow between stream and node i,j,k
as a function
of
head in the aquifer,
hi j,k . . . . . . . . . . . . . . . . . . . . . . . . . . . 6- 9
Limiting
seepage from a stream at unit hydraulic
gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-11
Hypothetical
problem showing which cells
receive
recharge under the three options
available
in the
7- 3
Recharge Package ..*...................................
Cross section
through cell i,j,k
illustrating
head
loss in convergent
flow into drain....................g2
Factors affecting
head loss immediately
around a
drain:
(a) buried drain pipe in backfilled
ditch;
(b) open drain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9- 4
Plot of flow into drain,
QD, vs. head in cell
i,j,k
using equations
(69-a) and (69-b).....................g6
Volumetric
evapotranspiration
from cell i,j,k
as a
eqUatiOnS
(75)-(77)...103
function
of head hi ’ k, Using
Hypothetical
problem <i 6wing cells
from which ET will
be abstracted
under the two options
available
in the
ET Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lo- 6
Schematic diagram illustrating
principle
of General.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. . . . . . . . . . . . . . ll- 2
head boundary package
Graph of flow from source into cell i,j,k
vs. head
in the cell,
as computed by the General-head
boundary package using equation
(78).................113
Correspondence
between the finite-difference
equations
and the matrix equation
for a grid of three rows,
four columns, and two layers.........................lZ3
Structure
of coefficient
matrix showing nonzero
diagonals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12- 4
Symmetric coefficient
matrix for a grid containing
two rows, three columns, and two layers..............lZ6
Decomposition
of a coefficient
matrix
into lower and
upper triangular
matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12- 7
Structure
of matrix
[A+B] showing nonzero diagonals....lZ-10
Structure,
showing nonzero diagonals,
of (a) the
lower triangular
factor
[L] of [A+B], and (b)
the upper triangular
factor
[U] of [A+B].............lZ-11
Estimation
of a function
at one corner of a rectangle
in terms of the values of the function
at the other
three corners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-14
xii
Page
Figure
53.
54.
55.
56.
Cell numbering schemes for a grid using three indices
and using one index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-18
Division
of the three-dimensional
model array into
vertical
slices
for processing
in the SSOR package....l32
Coefficient
matrix for slice
equations
and
corresponding
computer storage array..................l39
Illustration
of wrap and strip
forms of printed
output for a layer containing
7 rows and 17 columns...l42
TABLES
Table
of packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10
1.
List
2.
Print-format
codes for utility
modules
ULAPRS and ULAPRW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14- 3
...
Xl11
A MODULARTHREE-DIMENSIONAL FINITE-DIFFERENCE
By Michael
G. McDonald and Arlen
GROUND-WATERFLOW MODEL
W. Harbaugh
ABSTRACT
This report presents a finite-difference
model and its associated
modular computer program.
The model simulates
flow in three dimensions.
The report includes
detailed
explanations
of physical
and mathematical
concepts on which the model is based and an explanation
of how those concepts
are incorporated
in the modular structure
of the computer program.
The
modular structure
consists
of a Main Program and a series of highly
independent
subroutines
called
"modules."
The modules are grouped into
"packages."
Each package deals with a specific
feature
of the hydrologic
system which is to be simulated,
such as flow from rivers
or flow into
drains,
or with a specific
method of solving
linear
equations
which describe
the flow system, such as the Strongly
Implicit
Procedure or Slice-Successive
Overrelaxation.
The division
of the program into modules permits the user to examine
specific
hydrologic
features
of the model independently.
This also facilitates
development of additional
capabilities
because new packages can be added to
the program without
modifying
the existing
packages.
The input and output
systems of the computer program are also designed to permit maximum flexibility.
Ground-water
flow within
the aquifer
is simulated
using a block-centered
finite-difference
approach.
Layers can be simulated
as confined,
unconfined,
or a combination
of confined
and unconfined.
Flow associated
with external
stresses,
such as wells,
area1 recharge,
evapotranspiration,
drains,
and
streams, can also be simulated.
The finite-difference
equations
can be
solved using either
the Strongly
Implicit
.Procedure or Slice-Successive
Overrelaxation.
The program is written
in FORTRAN 77 and will
run without
modification
on most computers that have a FORTRAN 77 compiler.
For each program module,
this report includes
a narrative
description,
a flow chart,
a list
of variables,
and a module listing.
l-l
CHAPTER 1
INTRODUCTION
Puroose
Since
their
inception,
models described
Pinder,
basic
and others
concepts
presented
flow
by Trescott
and Larson
Survey
(1976)
for
with
minimal
changes,
a program
could
similar
tational
option
options
used for
thereby
of other
two-
user may select
with
The
in the model
was
of computers
respect
to computer
of changing
to options
that
of the
program.
size
that
is available
various
and specific
structure,
existing
of model input
Variable
without
has also
model output
1-2
compu-
Input
to suit
used can
procedures
data may be stored
allows
input
to the program.
been generalized
options
subroutines.
The model may be
formatting
modification
each
new
are not being
applications.
files.
structure
in such a manner that
the necessity
each type
external
together,
Because of this
the
so that
uses a modular
options.
to be read in any format
of output
report
or three-dimensional
and read from separate
The type
flow.
modified,
on a variety
are constructed
pertaining
reducing
have been generalized
arrays
Geological
a new ground-water
be readily
efficient
are grouped
options
subroutines
either
could
in this
functions
can be added without
be deleted,
of ground-water
be executed
documented
program
independent
In addition,
U.S.
have been incorporated
that
and Trescott,
time.
and hydrologic
is
(1976),
by the
in designing
and was relatively
The model program
wherein
models
finite-difference
and Larson
simulation
objectives
to use and maintain,
memory and execution
the
in those
The primary
here.
Trescott
have been used extensively
the computer
embodied
and three-dimensional
(1975),
model were to produce
simple
data
the two-
so that
a particular
need.
The program was originally
Harbaugh,
This
1984).
report
has subsequently
documents
portable;
it
computers,
about
It
will
minor
the
run,
The major
options
the effects
and "general-head
iteration
is contained
the
Overrelaxation
used in this
use the
series
turn,
program.
of highly
deals
with
report
The program
independent
into
a single
the effect
effect
and the
the
Strongly
which
the
Implicit
of This
drains,
procedures
to
evapotranspiration,
available
(SIP)
include
and the
two
Slice-
subroutines
the mathematical
and the
into
called
"packages."
modules.
A package
of wells,
the River
SIP Package solves
chapter
Package simulates
l-3
to use.
and a
The modules,
For example,
a system
report.
needed to
in
is a group of modules
Many of the packages
of this
input
concepts
a main program
of the simulation.
Procedure.
in a separate
Report
of the'program,
user may or may not have occasion
is described
include
Procedure
has been divided
aspect
Package simulates
of rivers,
A discussion
A.
algorithms
is to describe
the design
have been grouped
that
On some
method (SSOR).
of this
program,
0
Implicit
Organization
The purpose
rivers,
The solution
Strongly
or desirable.
available
recharge,
boundaries".
techniques,
Successive
are presently
of wells,
is highly
on most computers.
in Appendix
and
to use FORTRAN 77.
The program
may be necessary
that
FORTRAN66 (McDonald
been modified
modification,
modification
portability
using
FORTRAN77 version.
without
program
simulate
written
of equations
represent
Each of the
Two preliminary
the
Well
the
using
options
packages
chapters
describe
topics
relating
finite-difference
the overall
that
to the
equation
design
topics
4 through
of each package
(2)
of
input
tion
of the
individual
tion
and Implemementation
the
Package,
riverbed,
and a discussion
cribe
the
into
instructions
"items."
An item
similar
described
records,
section
or it
herein,
two-dimensional
arrays,
package described
consist
For items
which
the
line
first
records,
while
FORTRANnotation.
for
in the
the
of a single
gives
For an input
in the
approximates
record
12 and 13 des-
record
or a collection
input
in this
followed
fields
of those
consists
the model
list
by a note
of an array,
with
are numbered,
or comment).
records,
comprising
fields,
of
The input
associated
or a group of similar
shows the format
item which
items
of
of
read as a collection
each model layer.)
names of the
in terms
of arrays.(In
are always
a
can be
13 are presented
(sometimes
through
equation
4 through
of the
1-4
describing
flow
Chapters
the entries
the
chapter
in the model.
with
chapter;
and mathematical
or a collection
a list
The Conceptualiza-
available
arrays
one associated
second line
which
and
and (3) documenta-
physical
equation.
may be an array
entry
the
may be a single
presents
A-E
The description
package,
to show how that
Chapters
of input
Appendices
"Conceptualization
For example,
currently
of two lines
consist
the
describes
is derived
in
3 describes.
modules
tasks.
in the package.
is provided
in that
the
utility
packages.
entitled
contained
three-dimensional
in each chapter
and generally
a section
package.
procedures
special
individual
the finite-difference
solution
2 derives
of the model.
instructions
an equation
The input
input
(1)
section
the River
incorporated
operation
modules
used to build
Chapter
14 describes
to perform
13 describe
consists
Implementation,"
concepts
Chapter
packages
to the
program;
is used in the model and Chapter
of the program.
relating
Chapters
the
that
are used by various
cover
overall
the
in standard
the
first
line
the
of the entry
name of the
concerning
gives
utility
utility
modules
the
other
those
all
falls
items
example,
sented
items
for
pumping rate,
which
in a simulation).
read the
or,
Input
which
appear
to describe
that
in the model itself
Basic
Package,
input
which
with
is always
the optional
items
in
Chapters
the
separately;
input
thus
items
for
section
This
an independent
with
which
in capital
I-5
describes
Basic
letters
input
items
describes
associated
Package.
the
list
is followed
control
the
describes
input
following
of fields
to
and do not appear
under consideration.
explanation
read
used in the
4, which
explanation
the output
are further
one of these
of the
is presented
the package
associated
items;
repre-
subroutine
are terms
Chapter
(for
period
list
a utility
entirely
the other
13.
input
or procedures,
of input
fields
the
(subroutines)
call
case print
while
4 through
into
"FOR EACH SIMULATION"
in the model program;
fields
control"
of input
cases by a sample input
again,
input
required,
is subdivided
during
of the
are printed
two lists
"output
An explanation
put
which
as FORTRANvariables.
includes
time
the modules
or arrays
the
14.
is needed in each simulation;
sections
in mixed upper and lower
instructions
details
may be needed in each simulation
indicate
are used as FORTRANvariables
gives
"FOR EACH STRESS PERIOD", and includes
may change with
items
line
Further
items
one entry
in the case of an array,
array.
Chapter
second
under the heading
entries
which
the
array.
of input
These major
by headings
item,
list
only
heading
several
in
falls
which
which
subdivided
the
One of these
under the
for
the
while
reads the
are provided
packages,
sections.
and includes
name of the array,
module which
For most of the
two major
the
of inin most
In Chapter
option
4,
are treated
and sample input
are
provided
for
output
control.
In each simulation,
the program
input
for
array,
with
the
each option
is given
Chapter
is not
through
required
at the
4.
Following
provides
input
descriptions
of a module
generally
of the module,
module,
(2)
simple
of the
in which
narrative.
they
contains
a flow
four
chart
are performed.
The flow
used in the
user must
if
the
file
option
discussion
of
13, each chapter
up the associated
in the
package.
package,
followed
The detailed
description
(1) a narrative
description
(3)
is omitted.
performed
of terms
"output
a FORTRANlisting
of the
names which are used in the module.
chart
so that
Chapters
number of the
Further
of the modules
documents:
in the
the
4 through
making
of the functions
The blocks
for
is to be read;
of the module,
flow
in
in
3 and 4.
of the variable
the
A location
sections
unit
location.
Chapters
of a list
numbers used in the narrative
An explanation
Chapters
in
the
option
in this
section
input
of each of the modules.
modules,
is a numbered list
the
of the modules
and (4) a list
For very
in
consists
by detailed
for
is entered
a documentation
documentation
order
input
a one-dimensional
discussion
location,
the
numbers associated
is to be utilized,
IUNIT array
which
input
of
from which
system.
of the
of the
file
is done through
operating
beginning
of the options
the
are the unit
the option
is provided
the
array
beginning
If
a zero
IUNIT array
This
by the computer
in the designated
or channel
This
in this
13, and at the
in
enter,
entries
which
and must indicate
is to be read.
files
IUNIT array
control"
the
the
required
5 through
user must designate
are to be utilized,
IUNIT;
the
the
flow
The narrative
by the module showing
chart
chart
is a graphic
l-6
chart
the
can be cross
is contained
the
equivalent
are numbered with
the two documents
flow
description
on the
same
referenced.
sheet
with
the
flow
chart.
The program
corresponding
to those
fourth
of the listing
that
record
and definition
is used only
in other
given
its
modules
of the
as "Package";
range is
given
the
under
6 through
11 provide
and their
representation
operation
of particular
generated
provided
ated
input
in
narratives.
but not outside
name,
If the
as "Module";
is used in the modules
and day
shows the
used in the module.
package,
The
the time
of variables
range is given
organization
of this
and Implementation"
to the overall
if
it
variable
is used
the package,
its
of more than
one package,
design
"Conceptualization
and
discussions
Chapter
solvers
instructions,
section
of
range is
and functioning
flow
Implementation"
Input
instructions
for
and discussions
is
5; Chapters
or sinks
12 and 13 discuss
of finite
The appendices
Chapter
sources
the systems
a discussion
program;
the aquifer
in
external
4, provide
of the
within
and Chapters
2 and 3, and
Chapter
for
chapter;
14.
Chapters
of particular
in the model;
relevant
report,
representing
in the model.
in the
is provided
variable
of coefficients
discussed
tions
The list
numbers
as "Global."
relevant
formulation
and the
its
it
"Conceptualization
discussions
the
if
charts
comments with
a comment showing
modified.
module,
contains
flow
contains
of every
in that
To summarize
the
used in the
the module was last
range,
listing
provide
difference
each package
of input
the
for
utility
equaare
modules
a sample problem,
of certain
abbrevi-
computer-related
topics.
Acknowledgement
The authors
addition
to providing
he provided
of the
wish to extend
report
thanks
the administrative
encouragement
greatly
special
and guidance
improved
its
to Gordon Bennett.
support
along
clarity.
1-7
for
the way.
In
the model development,
His critical
review
CHAPTER2
DERIVATION OF THE FINITE-DIFFERENCE
Mathematical
The three-dimensional
porous
earth
material
Model
movement of ground water
may be described
EQUATION
by the
of constant
density
partial-differential
through
equation
%;(K,,a-h-,
+ii (Kyyii)
t a,(Kzzii)
- w=ss;;
ax
a2
(1)
where
KXX, Kyy and Kzz are values
and z coordinate
major
h
axes,
axes of hydraulic
W is a volumetric
sinks
of water
is time
conductivity
etc.)
equation
Equation
(l),
boundaries
system.
expression
the x, y,
to the
(Lt.-l);
volume and represents
sources
and/or
(t-l);
storage
of the porous
(1)
see for
material
example
and W may be a function
(1) describes
in a heterogeneous
axes of hydraulic
conditions,
per unit
of equation
Kxx = KXX(x,y,z),
conditions
are assumed to be parallel
(L-l);
Rushton
SS, KxX, Kyy, and KZz may be functions
W(x,y,z,t));
along
and
(t).
For a derivation
In general,
conductivity
head (L);
flux
S, is the specific
at the
which
is the potentiometric
t
of hydraulic
giving
are aligned
with
of an aquifer
constitutes
A solution
and anisotropic
conductivity
together
ground-water
specification
system
a mathematical
of equation
h(x,y,z,t)
(l),
of space (S, = Ss(x,y,z),
of space and time
flow
medium,
with
of flow
2-I
provided
and/or
and specification
in an analytical
(W =
under nonequilibrium
the
the coordinate
representation
such that,
and Redshaw (1979).
principal
directions.
head conditions
of initial-head
of a ground-water
sense,
when the derivatives
is
flow
an algebraic
of h with
respect
its
to space and time
initial
and boundary
distribution
of this
both the energy
to calculate
approximate
set
nature
of flow
for
very
possible,
wherein
conditions
simple
the continuous
points
points.
The process
leads
equations;
their
points
and times.
head distribution
that
partial-differential
rules
an alternative
physical
by equation
calculus;
of blocks
rows,
1 shows a spatial
called
columns,
cells,
and layers.
the
by a finite
derivatives
linear
are
at these
algebraic
of head at specific
to the time-varying
solution
of the
(1) may be derived
in the discussion
procedure
by applying
presented
aim of simplifying
the computational
regarding
to obtain
replaced
an approximation
however,
(1) are
method,
in head values
by an analytical
the
is
partial
values
of equation
used with
(1)
of simultaneous
here,
the mathematical
in terms of familiar
the flow system.
Discretization
Figure
and the
constitute
analog
is
measures
of equation
is the f inite-difference
yields
of flow.
approach
concepts
solution
equation
and explaining
treatment
to systems
be given
of difference
so lutions
from the differences
would
The finite-difference
the
described
These values
it
and can be used
methods must be employed
numerical
calculated
in storage,
and
head
in that
system,
flow
analytical
in space and time,
by terms
the equation
of movement.
systems,
system
replaced
difference
the
(l),
A time-varying
are satisfied.
One such approach
solutions.
equation
volume of water
and rates
so various
of discrete
into
characterizes
and the
directions
Except
rarely
are substituted
Convention
discretization
locations
An i,j,k
of an aquifer
of which
indexing
2-2
system with
are described
system
is used.
in terms
a mesh
of
For a system
Columns
(J)
123456789
Layers
(K)
Explanation
---
-
Aqurfer
0
Active
0
Inactive
Boundary
Cell
Cell
ArJ
Drmension
of Cell Along
the Row Direction
AC1
Drmension
of Cell Along
the Column
A”K
Dimension
of the Cell Along
Figure 1. -A
Subscript
Directron.
the Vertical
discretized
(J) Indicates
Subscrrpt
Direction.
2-3
(I) Indicates
Subscript
hypothetical
the Number
of the Column
the Number
(K) Indicates
of the Row
the Number
aquifer system.
of the Layer
consisting
of "nrow"
index,
i = 1,2,.
is the
layer
rows,
. . nrow;
index,
system with
"ncol"
columns,
j is the
k = 1,2,.
nrow = 5, ncol
column index,
. . nlay.
an assumption
was made that
to horizontal
geohydrologic
units
the
convention
followed
increment
k index
in the
in this
k index
rows would
be considered
row index,
i,
considered
parallel
j,
would
would
correspond
in constructing
that
the
parallel
to decreases
so that
in x.
1; however,
fall
and does not
the
to the x axis,
increases
figure
along
along
vertical,
applications
require
equations
correspond
of
Cartesian
z; because the
in elevation.
Similarly
increments
and columns
increments
and k
from the top down, an
in the
These conventions
consistent
the
generally
so that
in y;
in the
would
be
column
index,
were followed
of the model requires
orthogonal
the designation
row
1 shows a
Thus in terms
to a decrease
to the y axis,
rows and columns
layers,
corresponds
. . ncol;
figure
would
model is to number layers
correspond
to
layers
changes
i is the
In formulating
= 5.
or intervals.
denotes
layers,
j = 1,2,.
For example,
= 9, and nlay
of the model,
coordinates,
and "nlay"
directions
of x, y,
only
within
or z coordinate
axes.
Following
row direction,
in the
the
conventions
at a given
column direction
ness of cells
coordinates
in a given
(i,j,k)
used in figure
column,
j,
at a given
layer,
= (4,8,3)
k,
1, the width
is designated
row,
i,
Arj;
is designated
is designated
Avk.
has a volume of ArgC4AV3.
2-4
of cells
the width
ACi;
in the
of cells
and the thick-
Thus a cell
with
Within
each cell
Figure
to be calculated.
for
defining
the
nodes--the
configuration
start
sets
of the
cells.
In the
around the
nodes with
of nodes should
are,
in fact,
lines
aquifer
respect
with
sets
faces
two sets
the
halfway
be chosen so that
location
lines,
the hydraulic
ence equation
developed
in the following
however,
the block-centered
of parallel
lines
the blocks
and cells
formed
are drawn
In either
properties
over the extent
holds
spacing
The finite-differ-
for
is presently
case,
of the system
of a cell.
section
formulation
formulation.
the nodes are at the
between nodes.
uniform
of
nodes are at the center
formulation,
of parallel
head is
two conventions
to the
formulation,
are the cells;
point-centered
of the
at which
and the point-centered
generally
only
with
In the block-centered
of parallel
points
the
a "node"
in two dimensions,
of cells
by dividing
intersection
called
formulation
are orthogonal.
by the
is a point
2 illustrates,
block-centered
Both systems
which
there
either
formulation;
used in the
model.
In equation
that,
time
in the
(l),
the head,
finite-difference
domain is also
h, is a function
formulation,
discretization
follows
into
from the
of the
constant,
the cell.
ground-water
application
and out of the cell
within
as well
as space so
of the
continuous
required.
Finite-Difference
Development
of time
flow
of the
must be equal
equation
equation
continuity
Under the assumption
the continuity
Equation
equation:
to the
that
expressing
in finite-difference
rate
sum of all
flows
of change in storage
the density
the
the
form
balance
of ground
of flow
water
for
is
a cell
(2)
2-5
is
Block-Centered
Grid System
A ‘J
Point-Centered
Grid System
Explanation
0
Nodes
Grid Lines
-
-
-
Cell Boundaries for Point
Centered Formulation
Cells Associated
Selected Nodes
Figure 2.-Grids
With
showing the difference between block-centered
and point-centered
grids.
2-6
where
Qi is a flow
rate
into
the
SS has been introduced
finite-difference
that
cell
(L3tW1);
as the
notation
formulation;
can be injected
its
per unit
specific
definition
(I)--i.e.,
of S, in equation
for
it
storage
in the
is equivalent
to
is the volume of water
volume of aquifer
material
which
per unit
change
in head (L-l);
AV is the volume of the cell
Ah is the
into
Equation
storage
(2)
right
over
is stated
are represented
and
change in head o er a time
The term on the
taken
(L3);
hand side
a time
by defining
to the
At given
of inflow
outflow
of length
is equival'ent
nterval
in terms
interval
volume of water
a change in head of Ah.
and storage
as negative
At.
gain.
inflow
Outflow
and loss
and loss
as negative
gain.
Figure
i+l,j,k;
3 depicts
i,j-1,k;
development,
and the
all
i,j+l,k;
flows
negative
terms.
direction
i,j,k
sign
from cell
usually
these
i,j-l,k
and six
i,j,k-1;
are considered
Following
qi,j-l/Z,k
a cell
adjacent
and i,j,k+l.
positive
incorporated
conventions,
(figure
if
they
is given
the
are entering
into
i-l,j,k;
cells
To simplify
in Darcy's
flow
4),
aquifer
following
cell
i,j,k;
law has been dropped
cell
i,j,k
by Darcy's
in the
row
law as
(hi ,j-1,k
- hi,j,k)
= KRi ,j -1/2,kA CiA Vk-------------------
(3)
Arj-1/2
where
hi,j,k
qi,j-1/2,k
is the
head at node i,j,k,
is the volumetric
cells
i,j,k
and hi,j-l,k
fluid
and i,j-l,k
discharge
(L3tW1);
2-7
that
through
at node i,j-1,k;
the face
between
from
Figure 3.-Cell
i,j,k and indices for the six adjacent cells.
2-8
0
0
0
/-
Cell i,j-l,k
/
/
Cell i,j, k
0
.
.
..
.
0
0
0
0
:0
I
Avk
I
-
I;
l
f
I
I
I
\
-
Figure 4.-Flow
into cell i,j,k from cell i,j-l,k.
2-9
KRi,j-1/2,k
is the hydraulic
and i,j-1,k
i,j,k
is the distance
Arj-1/2
Although
with
it
the discussion
can be misleading
a specific
equation
point
described
by, for
gives
the exact
block
of aquifer
cross
sectional
Similar
through
the
face
for
and flow
into
9i-1/2,j,k
row direction;
of flow
in terms
calculated
into
Rather,
the term
conductivity
for
as a harmonic
(1961).
If this
from node i,j-1,k
the
central
of equation
the entire
is done,
of
region
sense
equation
case,
to node i,j,k
(3)
KRi,j-1/2,k
mean in the
steady-state
and
(L).
j-1/2
the subscript
hydraulic
(3)
through
a
and having
a
,
can be written
five
faces,
i,j,k
approximating
for
i.e.,
flow
the flow
in the
into
the
row direction
cell
through
and i,j+l,k,
= KRi ,j+l/e,kACi
- hi,j,k)
(hi, j+l,k
AVk--------------""
(4)
Mj+1/2
the column direction,
qi+1/2,j,k
nodes
ACiAvk.
between cells
qi,j+1/2,k
while
remaining
to the
is phrased
a one-dimensional
extending
row between
and i,j-1,k
Collins
for
flow,
expressions
the
normal
between the nodes.
example,
area
faces
to associate
normally
the
between nodes i,j,k
(3) is the effective
between the nodes,
along
(Lt'l);
is the area of the cell
ACiAVk
cell,
conductivity
flow
into
the
(hi+l,j,k
= KCi+1/2,j,k~jAVk------,f;;;;------
the
block
through
= KCi -1/2,j
the
rear
block
- hi,j,k)
face
(hi-l,j,k
the
forward
(5)
is
- hi,j,k)
,kllrj AVk----------““-----.
Ei -l/2
2-10
through
(6)
face
is
For the
vertical
inflow
direction,
qi,j,k+l/Z
the
bottom
face
is
(hi,j,k+l
- hi,j,k)
A rjA Ci -0---0-0-0-----o-o-
KVi ,j ,k+1/2
=
through
(7)
A”k+l/Z
while
inflow
through
the upper face
by
(hi,j,k-1
= KVi , j ,k-l/g
qi ,j &-l/2
is given
- hi,j,k)
rjACi-------------------
(8)
l
A Vk-1/2
Each of equations
of heads,
grid
be simplified
a single
expresses
and hydraulic
dimensions,
by combining
constant,
the
inflow
grid
through
conductivity.
dimensions
"hydraulic
a face
or,
i,j,k
The notation
and hydraulic
conductance"
of cell
in terms
can
conductivity
more simply,
the
into
"conduct-
For example,
ance."
D
(3)-(8)
mi,j-1/2,k
= KRi ,j-1/2,kACiAVk/Arj-1/2
mi,j.,1/2,k
is the conductance
(9)
where
i,j-1,k
Conductance
is thus
area of flow
divided
distance
between the
and i,j,k
the product
by the
in row i and layer
k between
nodes
(L2t-l).
of hydraulic
length
of the flow
nodes.)
l
2-11
conductivity
path
(in
and cross-sectional
this
case,
the
Substituting
conductance
= CRi,j-1/2,k(hi,j-1,k
qi,j-l/Z,k
Similarly,
equations
(4)-(8)
(9) into
equation
(3) yields
(10)
- hi,j,k)*
can be rewritten
to yield
qi,j+l/2,k
= CRi,j+l/2,k(hi,j+l,k
- hi,j,k)
(11)
qi-1/2,j,k
= CCi-1/2,j,k(hi-l,j,k
- hi,j,k)
(12)
qi+1/2,j,k
= CCi+l/E,j,k(hi+l,j,k
- hi,j,k)
(13)
qi,j,k-l/2
= cvi,j,k-1/2(hi,j,k-1
- hi,j,k)
(14)
qi,j,k+l/il
= Cvi,j,ktl/2(hi,j,ktl
- hi,j,k)
(15)
where the conductances
Equations
adjacent
cesses
account
To account
cells.
external
for
or wells,
for
flows
on the head in the
cell.
to CRi,j-1/2,k
the flow
into
additional
or they
heads in the aquifer,
receiving
analogously
into
terms
cell
may be entirely
the aquifer
in equation
i,j,k
drains,
(9).
from the six
from features
are required.
receiving
Flow from outside
cell
the cell
such as streams,
to the aquifer,
may be dependent
other
are defined
(lo)-(15)
evapotranspiration
the
from equation
area1
or prorecharge,
These flows
but independent
independent
of all
of head in
may be represented
by
the expression
ai,j,k,n
= Pi,j,k,nhi,j,k
(16)
t qi,j,k,n
where
di j k n represents
, ,
(LW1):
and pi,j,k,n
flow
from the rlth external
are constants
and qi,j,k,n
source
((L*t-1)
into
cell
i,j,k
and (Lst'l),
respectively).
For example,
from a well
suppose
a cell
and seepage through
is
receiving
a riverbed.
2-12
flow
from two sources,
For the first
source
recharge
(n=l),
since
B
iS
the
zero
flow
from the well
aquifer
rate
(n=2),
the
can be treated
seepage is proportional
to the
head in cell
vertical
streambed
In this
pi,j,k,l
case,
from the
16, while
as it
Similarly,
all
other
expression
of the
or stresses
external
into
conductivity
the cell,
(18)
stream-
so that
between the
river
stage
we have
(18)
cell
is a conductance
i,j,k.
For example,
5, CRIV would
of the
divided
can be rewritten
be given
riverbed
in
as the
material
and the
by the thickness
of the
as
(19)
+ aIVi,j,k,2Ri,j,k*
corresponds
-mIvi,j,k,z
CRIVi,j,k,2Ri,j,k
sources
form of equation
affecting
the
conductance,
(L) and aIVi,j,k,2
river
crosses
term,
the term
thus
in figure
hydraulic
conductance
as a simple
river
= - mIVi,j,k,2hi,j,k
The negative
is made that
- hi,j,k)
Equation
material.
ai,j,k,2
sources
flow
assumption
5);
shown schematically
of the
streambed
(figure
head in the
controlling
area of the
equation
i,j,k
is the
situation
product
the well.
head difference
= aIVi,j,k,2(Ri,j,k
where Ri,j,k
(L2tW1)
for
of head,
(17)
second source
ai,j,k,2
D
recharge
interconnection
and the
the
assumed to be independent
= qi,j,k,l*
For the
the
is the
and qi,j,k,l
ai,j,k,l
is
a single
corresponds
or stresses
In general,
16.
to pi,j,k,2
cell,
t0
qi,j,k,2.
can be represented
if
there
the combined
Of
by an
are N external
flow
is expressed
by
QSi,j,k
Defining
Pi,j,k
N
= "ai ,j ,k,n
n=l
e and Qi,j,k
=
N
cPi,j,k,n
hi,j,k
n=l
by the
eXpreSSiOnS
2-13
N
+ cqi,j,k,n*
n=l
(20)
Head in Stream, Ri,j,k
/
Conductance used to
Represent Stream-Aquifer
Interconnection, CRIvi,j,k
Head in Cell
h i,j,k
Figure S-Conceptual
representation of leakage
through a riverbed into a cell.
2-14
r4
pi ,j,k
= Epi,j,k,n
n=l
Qi,j,k
N
= cqi,j,k,ns
n=l
the general
external
Q%,j,k
Applying
flows
and
flow
term for
= pi,j,khi,j,k
the continuity
from the
six
cell
i,j,k
is
(21)
+ Qi,j,k*
equation
adjacent
(2) to cell
cells,
as well
i,j,k,
taking
into
account
as the external
flow
rate,
the
QS,
yields
qi,j-1/2,k
+ qi,j+1/2,k
+ qi,j,k-l/2
B
+ qi-1/2,j,k
+ 9i ,j,k+1/2
+ qi+l/Z,j,k
Ahi,j,k
= SSi,j,k--;;--4rjAciAvk
+ QSi,j,k
(22)
where
Ahi,j,k
-------
is a finite-difference
approximation
for
the
derivative
of head
At
with
ssi , j
,
k represents
At’jACiAVk
Equations
give
the
respect
(10)
is the
through
the specific
volume of cell
(15)
finite-difference
(Lt-I);
storage
i,j,k
of cell
i,j,k
- hi,j,k)
(L-l);
and
(L3).
and (21) may be substituted
approximation
mi,j-1/2,k(hi,j-1,k
D
to time
for
cell
i,j,k
+ ai,j+l/2,k(hi,j+l,k
into
equation
as
- hi,j,k)
t CCi-1/2,j,k(hi-l,j,k
- hi,j,k)
+ CCi+l/P,j,k(hi+l,j,k
- hi,j,k)
+ cvi,j,k-1/2(hi,j,k-1
- hi,j,k)
+ ~i,j,k+l/2(hi,j,k+l
- hi,j,k)
+ pi,j,khi,j,k
+ Qi,j,k
= SSi,j,k(ArjACiAVk)Ahi,j,k/At*
2-15
(22)
(23)
to
The finite-difference
Ahi,j,k
-------
must next
At
approximation
be expressed
6 shows a hydrograph
of equation
in terms
of head values
shown on the horizontal
axis:
of head at time
by the time
with
interval
tm-tm,1;
hydrograph
slope,
)m
the time
at which
approach,
in that
backward
in time
There are other
we could
flow
is centered
is,
the
successive
it
of flow
or propagation
flow
tm.
are designated
is
interval
This
terms
The head
by superscript
to the time
derivative
m-l
- hi,j,k
h;,j,k
at which
could
approximated
which
is termed
over
a time
the
which
time;
evaluation,
terms
or over
both
of error
during
2-16
are calculated.
a time
may cause numerical
in a simulation.
extends
example,
at the time
however,
the
and ends with,
which
for
begins
extending
the
a backward-difference
interval
flow
using
precedes,
be approximated;
interval
to some later
These alternatives,
times
bh/At
over a time
and extends
precedes
head difference
derivative,
a time
from tm, the time
at the time
growth
'
approximated
ways in which
the
are
m
m-l
hi,j,k
- hi,j,k
--------------tm
- tm-1
is evaluated.
Ah/ At is
approximate
evaluation
from it.
flow
the
Figure
is,
or time
change in head at the node over
which
times
of head,
of time
at which
An approximation
that
At
Thus the
a time
by dividing
bi,j,k
( -------
Two values
is the time
these
respectively.
tm is obtained
derivative
heads and times.
at node i,j,k.
and tm-1,
associated
the time
of specific
tm, which
(23) are evaluated;
values at node i,j,k
m
m-l
and hi,j,k,
as hi,j,k
for
calculation
interval
forward
of
which
and backward
instability--that
of heads at
Head
---------------I
I
----------*$yk
11
---- t -T
../ I
I
I
I
II
I
I
/j
I
i
-At,
-I
t m-l
i
I
I
tm
t m+l
Time
Explanation
tm
h;k3I
time at end of time step m
head at node i,j,k at time t,
-------.*a Backward difference approximation
slope of hydrograph at time t,
Figure 6.-Hydrograph
2-17
for cell i,j,k.
to
In an unstable
situation,
at a particular
progresses,
the
until
will
introduced
For this
they
to large
each time
Equation
approach
diminish
systems
of equations
terms
time
derivative
which
flow,
equation
calculation
By contrast,
stable--that
is,
at succeeding
times.
is preferred
must be solved
interval,
interval
even though
simultaneously
for
to tm; that
the
is:
m
- hi,j,k)
+ CRi,j+I/2,k(hY,j+I,k
- hy,j,k)
+ Qvi,j,k+I/2(hy,j,k+I
m
m-l
- hi,j,k)
(hi,j,k
= SSi ,j ,k ( Arj ACi Avk)-----------------tm - tm-1
of the partial
Like
the term
equation
differential
the
Qi,j,k,
which
(24)
can be used as the
equation
of ground water
coefficients
of the
various
in equation
(24) are all known, as is the head at the beginning
m-l
The seven heads at time tm, the end of the time
of the time step, hi,j,k.
head terms
step,
are unknown;
represents
this
type
is only
equations
that
is,
Thus equation
predicted.
a single
they
(24)
equation
can be written
for
one unknown head for
in
it
form by specifying
and approximating
tm,I
is a backward-difference
a simulation
(1).
as the
- hF,j,k)
+ %,j,k
+ pi,j,khT,j,k
for
any reason
result.
in backward-difference
- hy,j,k)
+ cvi,j,k-I/2(h!i,j,k-I
basis
numerically
approach
can be rewritten
cBi,j-1/2,k(h!l,j-1,k
(24)
the
for
heads are to be computed.
of head over the
Equation
time
progressively
at tm, the end of the time
flow
dominate
is always
backward-difference
(23)
the calculation
at each succeeding
the
at which
enter
completely
at any time
reason,
which
increase
finally
backward-difference
errors
leads
time
errors
"n" unknowns.
are part
cannot
of the head distribution
be solved
in seven unknowns.
each active
each cell,
cell
independently,
However,
Such a system
2-18
with
can be solved
since
an equation
in the mesh; and,
we are left
to be
since
a system
it
of
there
of "n"
simultaneously.
The objective
distributions
boundary
of transient
at successive
conditions,
The initial-head
is,
finite-difference
Values
the
time
is taken
time
2
Of hi,j,k
as 2, while
is taken
is,
k - hi' j,k)
Y
¶
and the external
of hf,j,k
(25),
axis
in the solution
t2,
therefore,
which
the superscripts
and should
stresses.
beginning
of the
is divided
process
which
in
in the
is to
marks the end of
the head superscript
appears
in only
m
one head
becomes
+ CRi,j+l/p,k(hf
j+I k - hi' j k)
,
, ,
Y
- hi' j k) + Cvi,j,k+l/E(hf
Y Y
+ Qi,j,k
the
at each point
of head at the
heads at time
therefore
= 55i,j,k
taken
step
head
head distribution,
which the time
The equation
j k-I
, ,
+ pi,j,khf,j,k
are
into
The first
--that
initial
to predict
j k - hf j k) +CCi+l/Z,j,k(ht+I
Y Y
Y Y
+ cvi,j,k-1/2(ht
where again
values
m-l,
j-I
Y
+CCi-1/2,j,k(hf-I
steps
generally
a value
the superscript
as 1.
CRi,j-I/2,k(hf
the
In equation
step.
the
parameters
provides
provides
process.
Calculate
term,
it
is
given
the hydraulic
of the discrete
first
times,
distribution
the mesh ---that
first
simulation
j k - hi j k)
Y ,
Y Y
j k+I
, ,
- hi j k)
, ,
1
(Arj ACi AVk)(h:,j,k
- hi,j,k)
-----L---------------~~~~~~~
t2 - t1
1 and 2 refer
not be interpreted
(25)
to the time
as exponents.
2-19
at which
the heads
An equation
which
of this
head is free
of equations
to vary with
is solved
have been obtained,
2 as time
the process
step.
subscript
t3;
set of equations
at time
as necessary
to cover
It
is
reformulated
step
the
for
to note that
step;
is
the end of the
and the
heads at time
to obtain
equation
t2.
(25)
subscript
is
m.
is continued
Again,
the
now
a system
heads at time
the
head
as many time
steps
the set of finite-difference
that
is,
at each step
which
equations
there
is
is a new system
The heads at the end of the time
this
system
must be solved;
are among the known terms
repeated
t3,
reapplied,
to obtain
for
system
When these
heads at time
simultaneously
to be solved.
of the step
process
cells),
range of interest.
make up the unknowns for
solution
process
the time
equations
beginning
repeated
is solved
This
at each time
of simultaneous
the
in the mesh in
where the unknowns are now the
t3.
important
cell
(variable-head
for
is
every
m-l and 3 as time
is formulated,
distribution
for
To do this,
of equations
and this
time
simultaneously
end of the second time
using
form is written
at each time
in the
step yielding
the
heads at
equations.
a new array
The
of heads
step.
Iteration
The model described
the
solution
In these
step
to the
methods,
is started
in this
system
the
report
initiated
calculation
by arbitrarily
head values
which
which
these
step.
the end of a given
time
value,
values,
with
then take
of calculation
2-20
for
each time
A procedure
estimated
head values
and the procedure
a trial
step.
agreement
methods to obtain
equations
of head values
assigning
are in closer
These new, or interim,
assumed heads,
alters
iterative
of finite-difference
head at each node at the end of that
then
utilizes
for
or estimate,
of calculation
producing
the system
the place
is
for
a new set
of equations.
of the
repeated,
initially
producing
the
is
of
a third
set
stage
producing
system
"iteration."
during
for
for
which
the
number,
of the
end of step m; Tim,* would
array
also
of final
head values
shows the array
the array
for
of final
step Tim-1~~ (where again
closure).
represent
for
The head values
they
it
in this
(24)-- in the calculation
heads for
which
the time
iteration
computed
were initially
appear
7, a total
array
is designated
for
appear
the preceding
of heads for
time
step,
2-21
step
Thus
for
the
in the
assumed for
in the
of n iterations
step
fim~n.
7
time
for
in the storage term of
m-l
hi,j,k
on the right side
for
which
m.
the
Figure
were required
t ime step
is
m; thus
the end of the preceding
n iterations
symbol,
second indicates
of iteration,
step
are
by an array
of values
are used in the term
equation
represent
the time
is assumed that
(24)--i.e.,
arrays
the heads at the end of time
head values
equation
head
the head array.
computed in the first
closure
one interim
the
of values
The head values
paragraph.
head
indicates
produced
In the example of figure
l?',o.
to achieve
which
in
of interim
7, these
while
m, to begi n the process
step
designated
are calculated,
iteration
and so on.
the end of time
arrays
superscript
would
is utilized
each identified
lattices,
an
by succeeding
containing
In figure
the
which
in a subsequent
step,
each array
satisfies
values
behaviour
a time
The first
the array
second iteration;
This
at each
is termed
heads approach
node in the mesh.
the heads in the array
Tim,* represents
required
for
in succession,
or level,
more nearly
as discussed
iteration,
two superscripts.
successively,
the changes produced
of equations,
as three-dimensional
bearing
array
interim
the calculations
each active
repeated
of the calculation
become very small.
are generated
represented
li,
the set
when to stop
Thus,
values
as the
is
heads which
Each repetition
of calculation
determining
procedure
of interim
Ultimately,
satisfy
stages
value
a new set
of equations.
exactly
This
of head values.
of
Recause they
computations
have
c
hm+l,o
qp
----------
Initial Trial
Head Values
for Time Step.
m+l (Set
-m+l.o= firn)
h
Start Time Step m+l
-Be
End Time Step m
The Criteria for Terminating
Iteration for Time Step, m is
1 iv”
- iP”-’
1 5
gitit~lyd
fp,n
c,os”re
Final Head
Values for
Time Step, m.
After n Iterations
Criterion
hm,n-I
Interim Head Values
After One Iteration
fp.0
Interim Head Values for
Time Step, m, after
(n-l) Iterations
Step, m
Initial Trial Head Values for Time Step, m
(set pw = p-1 )
Start Time Step m
End Time Step m-l
h-ml=
-ml.n
h
Final Head Values for Time Step, m-l
Figure 7.4terative
calculation
2-22
of a head distribution.
already
for
been completed,
time
time
step
step.
they
m; thus
they
Similarly,
constants
Ideally,
retain
the
in the storage
one would
like
the
solution
iterating
specify
level
After
absolute
it
is
less
value
exceeds
and the
'criterion
comparable
a value
level
of accuracy
values
m+l.
stop when the
However,
method of specifying
termed
is specified
when to
is to
the
"closure
by the user.
The largest
the closure
criterion,
criterion,
iteration
is terminated
is said
for
that
iteration
calculated
is an order
of thumb,
of magnitude
if
to have "closed"
step.
is adequate.
head,
If
continues;
time
to a level
As a rule
criterion.
of these
criterion.
iteration
to change in computed
that
because
from one iteration
quantity,
the closure
criterion
Normally,
Note that
and that
values
of
of accuracy
it
is wise to use
smaller
than
the
in the head results.
herein
per time
maximum number of iterations,
step
solution.
nodes in the mesh.
necessarily
desired
m are used as
of computed head change in that
when to stop
The program described
number of iterations
which
process
to the closure
of closure
criterion,"
refers
head are not themselves
step
time
iteration
is compared with
method of determining
the closure
a certain
all
than the closure
or "converged,"
this
for
head change values
largest
than
absolute
are examined
for
to the exact
an indirect
time
equation
of the
The method most commonly employed
must be less
each iteration,
calculations
that
in the
in each iteration
in computed heads occuring
or "convergence
iteration
this
is unknown,
the changes
to the next
criterion"
close
constants
of head for
to specify
must be used.
that
values
term during
heads are suitably
stop
the same value
final
calculated
actual
appear as predetermined
step.
the
also
incorporates
If
closure
iterative
2-23
is
process
a maximum permissible
not achieved
will
within
be terminated
this
and a
corresponding
message printed
designated
per time
in the
output.
HCLOSE in the model input,
while
step
is designated
The initial
of figure
would
eventually
initial
than
heads computed
values
the
for
array
Tim-l~n
iterations,
for
are complete,
user
for
succeeding
final
time
estimates
step.
of head,
of head are transferred
initial
estimates,
Head values
for
beginning
of the
or trial
to be equal
and to provide
of convergence.
Chapters
basis
first
in this
the
report,
initial
to the
trial
Thus in figure
obtained
the
time
after
for
7,
n
step m-l
array
wso,
heads at the end
step
in the
heads specified
of various
including
and Molz (1971).
discussions,
an introduction
of iteration
for
to the
for
of
by the
simulation.
references,
one of these
choice
calculations
values,
the end of the
of the mathematical
in many standard
When the
process
be much greater
are used as the
same values
review
reading
would
these
reader
rate
step
iterative
of the
In the model described
the
and Remson, Hornberger
role
the work required
the end of the
(1977)
the
regardless
Tihs"
be chosen according
the
step m-l.
Discussions
be found
same result
are assumed initially
the
Theoretically,
end of each time
contains
step m, in array
could
end of time
step m.
simulation
or they
the
and used as the
of time
to the
others.
the
of head for
arbitrarily,
although
for
is
the maximum number of iterations
the end of time
conventions.
converge
head values,
some choices
of head for
be assigned
to a number of different
criterion
MXITER.
estimates
7, could
The closure
both
to such topics
parameters,
In particular,
12 and 13 of this
and the
2-24
methods may
Peaceman (1977),
It
is suggested
Crichlow
that
to? clarify
general
as the
use of matrix
influence
such a review
report.
iterative
of various
is
the
concepts
notation,
factors
recommended prior
on
to
c
An iterative
D
the system
of this
of finite-difference
which
solutions
each step,
these
discrepancy
for
be given
this
point
are increased.
solution
be only
with
regard
storage
The model described
options
for
iterative
and is organized
disruption
it
solution
so that
of the program
is convenient
D
and all
the current
step
time
terms
for
and time-step
even if
it
time
would
that
are on the
accuracy,
are generally
2-25
normally
and
present.
all
are grouped
side.
nt
@i
two diffe
equations,
may be added without
scheme of solution
are independent
right-hand
a formal
hydraulic
incorporates
(24) so that
step
In
Solution
presently
Whatever
equation
heads at the end of the current
of the equation,
error.
in that
schemes of solution
structure.
of
equation
of the set of finite-difference
alternative
to rearrange
that
be obtained,
boundaries
report
The
to the system
the truncation
are seldom known with
in this
at
and the head h(Xi,yj,Zk,tm)
in the field,
of Equations
even if
(1)).
as the mesh spacing
could
to hydrologic
Formulation
(equation
must be recognized
equation
closure
an approximation
of the differential
to become greater
of
were obtained
by the solution
is termed
to conditions
and specific
uncertainties
solution
the
to note that
be only
of flow
solution
the accuracy
including
important
node and time,
it
step;
equations
given
and time,
of the differential
conductivity
hy,j,k,
Finally,
an approximation
is
equation
a given
tends
factors,
it
to the
each time
would themselves
by the formal
error
for
of finite-difference
solutions
corresponding
general,
However,
of the differential
equations
which would
length
exact
an approximation
upon several
between the head,
difference
the
set
only
equations
is employed.
to the
to the solution
for
yields
approximation.depends
criterion
exact
procedure
terms
on the
is employed,
containing
left-hand
side
of head at the end of
The resulting
equation
is
m
m
+ CRi,j-1/2,khi,j-1,k
j ,k-1 t CCi-1/2,j,khy-l,j,k
Cvi , j ,k-1/2hi,
+ (-CVi,j,k-l/2
- CCi-1/2,j,k
- CCi+l/2,j,k
- Cvi , j ,k+1/2
- CRi,j-1/2,k
- CRi,j+l/2,k
+ HCOFi,j,k)hY,j,k
t CRi,j+l/2,kh!l,j+l
,k
m
+ CVi,j,k+l/2hi,j,k+l
+ CCi+l/2,j,kh~+l.,j,k
(26)
= RHSi,j,k
where
HCOF.
~,j,k
- SCli
= 'i,j,k
= - %,j,k
SCli,j,k
= SSi,j,kArjACiAVk.
equation
for
system
(LVl)
- tm,1);
- SC1,i ,j ,khy;:
RHSi,j,k
The entire
,j ,k/(tm
,k/(tm
- tm,1)
; and
(LWl)
(L2)
of equations
each variable-head
of the
cell
form of
(26),
wh ich
includes
in the mesh, may be wr itten
one
in matrix
form as
CA1{h) = (9)
where [A]
equation
at the
is a matrix
(26),
end of time
the constant
this
for
report
a series
(27)
of the
all
active
step
terms,
RHS, for
assembles
the
of subroutines,
comprising
[A]
the matrix
equations
m for
coefficients
of head,
nodes in the mesh; {h)
all
all
vector
nodes of the mesh.
{q)
for
transferred
the
vector
to modules
Ih)
.
2-26
of
of head values
of
The model described
in
{q)
which
side
is a vector
and the terms that
The vector
left
is a vector
nodes in the mesh; and {q)
or "modules".
are then
from the
comprise
[A] through
and the terms
actually
solve
Types of Model Cell
In practice,
the form of
cells
it
(24)
is generally
for
is specified
and Simulation
every
cell
in advance
unnecessary
in order
to simulate
In the model described
are grouped
into
two categories--
cells.
Constant-head
specified
steps
flow
of the
into
tion.
this
in advance,
The remaining
report,
vary with
cell
to represent
figure
along
cells
is always
been used to delete
The figure
also
may be used,
major
surface
constant
through
water
inflow
for
features.
head is
through
are those
step
all
for
system
time
which
of the
cells
Other
in
and free
varies
terms
terms.
2-27
to
for
of equations
each
must
in the simulation.
boundaries.
superimposed
no-flow
array
along
boundary
no
simula-
cells
on an array
shape,
cells
beyond the
one section
is
with
or through
head,
of
whereas
have there-
aquifer
of the
in direct
conditions,
herein
For example,
is of irregular
of the
or areas where inflow
source
type
(or
(24) must be formulated
where the aquifer
source
the
are unspecified
in outline;
the portion
the use of external
and external
The aquifer
rectangular
example,
which
“variable-head"
hydrologic
boundary
shows constant-head
these
of this
are used in the model described
various
the model.
step
conditions
and "inactive"
in any time
form of
each time
and no flow
for
the model array
cells
of the
of
of certain
cells
value
cells
by heads which
for
conditions
generated
specified
or no-flow
8 shows the map of an aquifer
cells
fore
at this
in the mesh, and the resulting
simultaneously
Constant-head
for
are those
of the mesh, termed
An equation
variable-head
report,
cells
is permitted,
are characterized
time.
be solved
cells
in this
cells
Inactive
or out of the cell
an equation
the boundary
"constant-head"
and is held
simulation.
to formulate
in a model mesh, as the status
of the problem.
"no-flow")
of Boundaries
boundary.
boundary;
contact
such as areas
with
of
can be simulated
a combination
of no-flow
Explanation
-
Aquifer
--
-
Boundary
Model Impermeable
tal
........
Boundary
Inactive Cell
cl
........
:i:i:;:f:;:i:;:i
Constant-Head
........
.......
Variable-Head
Cell
Cell
Figure 8.-Discretized aquifer showing boundaries and cell
designations.
2-28
Conceptual
Aspects
The model described
in the horizontal
columns
cells
contain
direction
to be used,
or embody the
to explicit
reading
ways of viewing
vertical
the flow
vertical
aquifers
or permeable
shows a typical
to both
there
no attempt
this
leads,
into
segments
desired
along
in the
--in
is followed
arbitrary
which
in preference
two different
first
leads
between geohydrologic
is made to make the mesh conform
the
model layer
varying
to a deformed
thickness
mesh.
B
2-29
Figure
9-a
according
viewpoint,
to rigid
extreme,
individual
of the model.
mesh on the geohydrologic
correspondence
in part
At the opposite
to represent
as an
of
governed
has been discretized
to the
viewpoint
simply
process
vertical,
results.
sequence which
The first
the
layers
9-b according
to simulate
in effect,
of
the
parameters
to accomodate
as an effort
Under the second viewpoint,
variable,
approach
more or less
three-dimensional
irregulaties.
of the
Discretization
can be visualized
zones by individual
to the second.
model layers,
the width
hydraulic
in order
can be viewed
may be a general
sidered
This
discretization
geohydrologic
of an orthogonal
is,
number of
in the model by specifying
and by specifying
thickness
vertical
interpretations
according
(that
of space
the
row or column).
is handled
thickness.
resolution
discretization
discretization
discretization.
system
vertical
handles
the number of rows,
to the
of area1 discretization--a
dividing
by the
layer
of layer
At one extreme,
extension
by reading
transverse
vertical
number of layers
document
Discretization
of each row and column
in the direction
space in the
in this
direction
and the width
of Vertical
and in 9-c
superposition
system;
layers
while
and
to stratigraphic
thickness'
is con-
of geohydrologic
units;
...........
........
.......
.:..........
.......
...
........
_:
.:.
’
.......
..
: .*......r\.*:.:
-‘-:**,.Coarse.‘.’
....
(a) Aquifer Cross Section
Grid Layer 1
Cell Contains Material
Grid Layer 2
from Three Stratigraphic
Units. All Faces Are
Rectangles
Grid Layer 3
(b) Aquifer Cross Section With
Rectilinear Grid Superimposed
-la
Grid Layer 1
Grid Layer 2
Cell Contains Material
from Only One Stratigraphic
Unit. Faces Are Not Rectangles
Grid Layer 3
(c) Aquifer Cross Section With
Deformed Grid Superimposed
Figure 9.-Schemes
of vertical discretization.
2-30
Each of these
B
has advantages,
based on the
dual
cells,
methods
and each presents
hydraulic
or at least
that
meaningful
for
greater
within
likely
conform
accuracy
which
under the
configuration
model equations
aligned
l
with
departures
model layers
for
the model axis.
is also
On the
hand,
the deformed
of the
necessary
viewpoints
boundaries
to use more than
simply
more
the
may no longer
conductivity
is always
to achieve
discretization
have
may not be
introduced
illustrated
in figures
conform
to geohydrologic
one layer
the
schemes turn
by these
resolution
are of uniform
thickness,
and each could
deformation
nor fully
vertical
within
each unit.
of the mesh.
each unit
Similarly,
is
figure
sands is sustained
from storage
in the
of storage
required,
clay.
release
several
separated
flow
if
in any of the layers;
in the
be represented
However,
information
If
by vertical
the objective
in the
Figure
results.
by a clay;
the
by a single
fully
flow
layer
horizontal
in which
of water
of
represent
pumpage
released
is to determine
model layers
10
units
on the direction
system
of analysis
clay,
several
2-31
may be
must be used to
11 shows a sand-clay
partially
it
geohydrologic
is neither
layers
For example,
contacts,
a single
required
of two sand units
out to be a com-
9-b and 9-c.
to simulate
consisting
pattern
upon which
cells
axes of hydraulic
shows a system
from the
other
individual
Some error
many vertical
even where layer
flow
to inter-
from assumed conditions.
bination
without
More-
and this
example,
and the major
9-c.
correspond
to many of the assumptions
are based;
In practice
unit,
as in figure
to be met
is negligible,
of 9-c.
to conform
faces,
if
indivi-
parameters
are more likely
units
are
within
or integrated
conditions
can be expected
head loss
are uniform
average
these
process
The model equations
properties
to geohydrologic
vertical
mesh of 9-c fails
rectangular
each cell;
discretization
difficulties.
that
when model layers
vals
the vertical
assumption
can be specified
over,
of viewing
would
be
the
Sand
Clay
Sand
Figure lO.-Possible
pattern of flow in a cross section consisting
of two high conductivity units separated by a low
conductivity unit.
2-32
Layer
Sand
Clay
Sand
Figure Il.-A
cross section in which a low conductivity
represented by six model layers.
2-33
unit is
required
hand,
only
to represent
figure
flow
used to represent
each sand,
conductance
tization.has
sometimes
The approaches
step.
the various
been termed
the
this
as noted
above,
the user.
(24))
in confined
product
of hydraulic
conductivity
storage
coefficient,
the product
is also
used.
hydraulic
as head minus bottom
calculated
as hydraulic
layer
thickness
and head.
contains
can vary
Chapter
a discussion
corresponding
layer,
for
to vertical
elevation,
times
from cell
to cell
5, which describes
of the formulation
2-34
rather,
specified
which
by
is the
is specified;
and layer
bottom
is
is then
thickness.
depending
on bottom
of conductance
and
thickness
saturated
Centered
and
thickness,
elevation
Saturated
ways of conceptualizing
is
(hvk of
and transmissivity
the Block
and
by the program;
storage
each cell.
results,
discretization
layers
thickness,
at
in general,
document
coefficients
aquifer
conductivity
to the various
in this
lead to
in the way
of the
transmissivity,
of specific
are input
calculated
layers
and layer
For an unconfined
conductivity
hydraulic
discre-
simutaneously
and,
resolution
read explicitly
is embedded in various
For example,
the
by
approach.
arise
are formulated
of individual
is never
simply
above all
approaches
in
may be
to vertical
described
approaches
the thickness
model layer
three-dimensional"
The model described
l
any of these
1 and equation
thickness
terms
occurs
and flow
which must be solved
to be solved,
results.
of implementing
figure
"quasi
among these
and storage
release
horizontal,
approach
discretization
The differences
of the
storage
may be represented
This
of the form of (26),
On the other
case a single
the clay
layers.
in the number of equations
in that,
while
between
conductances
the accuracy
in which
In this
to vertical
a set of equations
system
vertical.
the vertical
capable
as shown in the figure.
in the sand is essentially
is essentially
each time
unit,
12 shows a sand-clay
in the sands,
the clay
that
Thus,
elevation
Flow Package,
and storage
the vertical
terms
discretization.
Heads in This Layer Are Not Calculated.
Resistance
in the Conductance
Terms Between Layers 1 & 2.
Figure 12.-A
to Flow in This Layer Is Included
cross section in which a low conductivity unit is
represented by the conductance between model
layers.
2-35
Clay
CHAPTER 3
PROGRAMDESIGN
Overall
This
chapter
describes
program consists
dependent
the overall
subroutines
called
design
of the model program.
(MAIN) and a large
of a main program
of MAIN and explain
tions
Structure
modules.
This
chapter
The
number of highly
will
explain
how the modules can be grouped
into
the
infunc-
"packages"
and "procedures".
The functions
shown in figure
"stress
l
which
Each stress
within
period,
which
in turn,
time
stress
into
into
parameters
a series
a series
of
are constant.
of time
of the form of equation
steps.
(27)
The
is
Iterative
solution
methods are used to solve
Thus within
step.
loop,
within
an iteration
prior
to entering
which
pertain
a simulation,
which
there
there
for
are three
is a time-step
the heads for
nested
loop,
which
loops:
a
in turn
loop.
in figure
the
stress
to the simulation
13 is termed
loop,
as a whole.
is defined:
simulation
(transient
or steady-state),
hydrologic
options,
and the solution
Procedure,
In the Read and Prepare
a "procedure".
the program executes
to be simulated
the Allocate
is divided
are
the head at each node at the end of each
Each rectangle
problem
equations
simulation
to yield
stress-period
contains
specified
a typical
and solved
step.
each time
for
of simulation
is divided
system of f inite-difference
formulated
D
The period
13.
per iods"
must be performed
the size
three
procedures
In the Define
Procedure,
of the model,
the type
the number of stress
periods,
the
of
the
In
scheme to be used are specified.
memory space required
Procedure,
For example,
by the
a 11 data that
3-l
program
is allocated.
are not functions
of time
DEFINE - Read data specifying number of rows,
columns, layers, stress periods, and major program
options.
ALLOCATE
store data.
-
Allocate
space in the computer
to
READ AND PREPARE- Read data which isconstant
throughout
the simulation.
Prepare the data by
performing whatever calculations
can be made at
this stage.
L
I
I
Read & Prepare
STRESS - Determine the length of a stress period
and calculate terms to divide stress periods into trme
steps.
I
READ AND PREPARE - Read data whrch changes
from one stress period to the next. Prepare the data
by performrng whatever calculations can be made at
thts stage
Formulate
I
ADVANCE - Calculate length of trme step and set
heads at beginning of a new time step equal to heads
calculated for the end of the previous time step.
1
,
3
.!
:
FORMULATE - Calculate the coefficients
finrte difference equatrons for each cell.
:
f
APROXIMATE - Make one cut at approximating
a
solution to the system of finite difference equations.
of the
C
i
OUTPUT
should
CONTROL
be written
-
or saved
Determine
whether
results
on disk for this time step.
Send signals to the BUDGET and OUTPUT procedures to rndrcateexactly
what information should
be put out.
BUDGET - Calculate terms for the overall volumetric budget and calculate and save cell-by-cell
flow terms for each component of flow.
OUTPUT - Print and save heads, drawdown
overall volumetric
budgets
in accordance
signals from OUTPUT CONTROL procedure.
Figure 13.~Overall
program structure.
3-2
and
with
These data may include
are read.
conditions,
initial
conductivity,
tops
heads (starting
specific
and bottoms,
Certain
further
Within
stress
period
are also
made in this
period,
length
of the time
Procedure
proceeds
the Output
heads,
budget
budget
entries
recorded,
heads,
of layer
solution
scheme.
procedure
to prepare
is termed
the
the number of time
to calculate
which
until
terms,
drawdown,
is calculated
and cell-by-cell
volumetric
section.
terms
contains
Procedure
for
a specified
head.
maximum
iteration
of the computed
Procedure,
are printed
In the Output
budget are printed
3-3
loop
In the Budget
flow
in the
and coefficients
the disposition
terms.
are
and the heads
At the end of the
determines
in a subsequent
13);
equations
or until
that
recharge,
and the Approximate
reached.
flow
data
(figure
the conductances
is achieved
is
all
of each time
The iteration
(27),
and cell-by-cell
and the
step
(NSTP) in the
length
and area1
to the system of linear
Procedure
are calculated
as explained
determines
by equation
iterations
Control
the
Procedure,
are initialized.
closure
steps
loop is then entered
of the time
step
a solution
number of allowable
loop,
procedure
such as pumping rates
The time-step
the
approximates
Iteration
procedure
information
each node as required
which
loop the first
In a second Read and Prepare
Advance Procedure,
for
period
In this
to a stress
the Formulate
elevations
calculations
and certain
are read.
the start
coefficients,
hydraulic
by the specified
read and processed.
for
storage
transmissivity,
required
the stress
Procedure.
pertain
heads),
boundary
processing.
Stress
step
yield,
or some of the following:
and parameters
preliminary
data for
all
or
Procedure,
or recorded.
As shown in the preceding
for
the overa 11 program
of the
indication
also
within
itself
most of which
required.
for
do that
termed
"secondary"
according
to
1, modules
various
the
procedure
can also
modules
required
algorithm
into
package
which
the
Well
it
The work
of figure
13--is
of call
determine
performed
The
modules
a module is
do the work of
in the
directly
statements,
whether
does not itself
proper
sequence
by the main program
are called
the
these
they
by other
modules
to
are
are termed
example,
(Modules
packages
are required
hydrologic
process
in all
or solution
The procedure
is
perform.
SIP Package)
hydrologic
modules
indicates
required
simulations,
3-4
(for
includes
example,
or solution
on the other
be active
only
and while
package
of
The
will
most are needed only
in the
.
the operation
modules
simulation;
Chapter
those
process
by the main program
in the
in
are both useful.
which
method embodied
classification,
As noted
of understanding
are called
be grouped
where a package
a particular
of grouping
for
to
or the
two methods
13 are implemented
can accordingly
by "packages",
In terms
of a package which
in figure
help
simulation.
simulation.
user.)
indicated
Package,
to incorporate
are part
by the
that
and an
are implemented;
sequence
and the modules
be grouped
classification,
in a given
various
procedures,
by the main program.
which
are called
procedures
modules;
Package,
the model,
the
those
modules;
individual
River
tests
chart
modules.
Thus the
through
called
a flow
of the model.
rectangles
the main program
Modules which
"primary"
the
various
procedures
an organized
to "IF"
calls
13 provides
the main program
is simply
merely
work.
those
or modules,
are coupled
it
of the
within
Accordingly,
simulation;
the
chart
subroutines,
main program
a list
in which
the procedures--i.e.,
by individual
figure
structure,
sequence
a flow
provides
discussion,
if
they
some
when the
is
hand,
specified
defines
the
specific
function
modules
of the
allocate
package.
allocates
the
few options
in the
relatively
small
increase,
to complete
Allocate
the
indicates
that
package.
Entries
utilize
secondary
modules
the
for
procedure
submodules
the
which
to accomplish
are available
of primary
which
used in a single
few packages
package.
are
is handled
specified
modules
(i.e.,
by a
by the user
are called
is not
a subscript
only
"U" indicate
utility
to many packages.
‘3-5
required
modules
in the
primary
function;
modules
called
in
indicated
modules
submodules
package.
which
are
Entries
utilize
are secondary
by
to procedures,
absence of an "X"
in a single
primary
modules
and
An "X" is entered
"S" indicate
their
by procedure
14 correspond
to packages.
in question
tasks;
of modules
a module exists;
are utilized
their
is to
each of these
and more modules
rows in figure
in accomplishing
subscript
Procedure;
As the options
correspond
marked with
modules
marked with
of a matrix
of the matrix
whose function
Procedure
the classification
columns
of other
task.
The horizontal
vertical
modules
relatively
the simulation,
space allocation
in terms
each block
which
enter
functions
the arrays
Allocate
number of modules.
the main program).
while
and the
14 illustrates
by package
for
are specified,
simulation,
the
Figure
which
under the
space required
more packages
to the
several
or features
involved
in relation
For example,
space are grouped
modules
If
of the module
utility
modules
Flow Component
Packages
Solver
Pat kages
Stress Pat kages
6
A
S
Procedures
B
C
F
WRRDEGSS
E
C
I
R
V
H
I
L
H
V
N
T
B
P
0
R
x
x
x
x
x
x
x
x
x
x
Xs
Xs
Define (DF)
X
Allocate
(AL)
x
x
Read & Prepare (RP)
xU
Xus
X
Stress (ST)
X
Read & Prepare (RP)
xu
x
x
xu
x
i
Advance
X
(AD)
Formulate
X
(FM)
Approximate
XS
x
x
x
x
x
x
(AP)
Output Control
Budget
(BD)
Output
(OT)
(OC)
X
Xus
Figure 14.-Organization
packages.
of modules by procedures
3-6
and
The primary
cates
both the
three
characters
number,
modules
package
last
14, a module is
indicated
module is designated
that
the module is part
that
it
for
allocate
the
the
a package
ments,
version
a different
modified
Figure
matrix
modules
that
primary
was used in figure
submodules
14.
are utilized
is to
data.
The number
module designation
place
to effect
to distinguish
modified
modules
the
versions.
arranged
As in figure
improve-
in the
same
14, a subscript
"S"
and "U" indicates
that
utility
are utilized.
Submodules
character
are designated
is always
designating
number,
or from other
that
well
is modified
from the original
Thus
function
of the six-character
be used in this
AL,
of specified
particular
would
WEL, indicate
package.
simulation
memory used to store
If the package
Procedure.
two letters,
in that
the
and its
15 shows the names of the
format
indicates
number.
with
version
in figure
letters,
the last
indi-
The first
For example,
Procedure
wells,
place
belong.
is a package
three
Package;
deals
which
Package and Allocate
Allocate
that
fourth
integer
package
the fourth
Well
Well
as through
in the
they
the procedure.
the
space in computer
one appearing
to which
package,
of the
performs
or input,
to a convention
as WELlAL; the first
module is one of those
withdrawal
is
the
two indicate
This
this
and the procedure
designate
and the
indicate
are named according
the
the
package
letter
"S".
in version
for
one of the
indicating
example,
the
Block-Centered
3-7
name in which
is followed
mnemonic to distinguish
of the same package;
is a submodule
This
name, a numeral
and a one-character
submodules
by a six-character
by three
the
the
first
characters
package version
the module from other
secondary
module "SBCFlC"
Flow Package.
Utility
Packages
I
I
BAS
P
R
0
C
E
D
U
R
E
S
I
BCF
Define (DF)
BASl DF
Allocate (AL)
BASlAL
BCFlAL
Read 8. Prepare (RP)
BASl RP,
BCFl RP,,
Stress (ST)
BASlST
Read 8. Prepare (RP)
Advance (AD)
BASlAD
Formulate
BASlFM
(FM)
Approximate
BCFlFM,
I
WEL
WELlAL
I
I
RCH
RI’/
DRN
EVT
GHB
SIP
SOR
RCH~AL
RlVlAL
DRNlAL
EVTlAL
GHBlAL
SlPlAL
SORlAL
SlPlRP
SORlRP
WELlRP
RCHlRP,
RlVlRP
DRNlRP
EVTlRP”
GHBlRP
WELlFM
RCHlFM
RlVlFM
DRNlFM
EVTlFM
GHBlFM
(AP)
Output Control
(OC)
Budget (ED)
Output (OT)
BASl OT,
I
Figure 1S-Primary modules organized by proceduie and
pat kage.
3-8
I
I
modules
are designated
mnemonic.
which
For example,
the
1 lists
the
real
various
the three-character
and provides
a brief
"U" followed
secondary
reads two-dimensional
Table
gives
by the letter
module "UPDREL" is a utility
packages
description
solver
packages;
those
which
each cell.
This
formulates
the
category
internal
packages
or boundary
describing
flow
are those
which
difference
category,
and the
which
between
implement
This
one incorporating
utilizing
a variety
However,
approach,
Centered
for
describes
categories
formulation
of the entire
packages,
certainly
of internal
for
example,
be developed
Flow Package.
3-9
utilizing
Each of the
external
packages
systems
of finitein this
of solution,
The only
Basic
package
Package,
which
simulation.
option
flow
which
the coefficients
Procedure
is the
described
terms
in this
in the equations.
a point
and used in place
for
and flow
two packages
Overrelaxation.
in support
equation
The solver
of the
Implicit
are
a particular
stream.
Flow Package is the only
the
alternative
could
Strongly
any of these
of tasks
The Block-Centered
documentation
documentation
the
packages
packages.
solution
a stress
between cells
describing
cate-
and the
packages,
Package calculates
for
Slice-Successive
into
flow
and a surface
algorithms
packages
Flow Package,
of stress
the River
scheme,
Two major
finite-difference
(describing
the coefficients
a cell
publication,
component
Block-Centered
subcategory
example,
equations.
other
The flow
the
terms
and the
for
does not fit
addresses
flow
component
component
of the
includes
formulates
flow;
of flow
the coefficients
to or from storage);
stress
the category
flow
may be recognized.
calculate
in this
of the package operation.
of package may be recognized--the
subcategory
documented
used in the module designation
gories
package
module
arrays.
abbreviation
within
by a five-character
centered
of the
Block-
Table
1 .--List
of packages.
Package Name Abbreviation
Package Description
Basic
BAS
Handles those tasks that are
part of the model as a whole.
Among those tasks are specification
of boundaries,
determination
of time-step
length,
establishment
of
initial
conditions,
and
printing
of results.
BlockCentered
Flow
BCF
Calculates
terms of finitedifference
equations
which represent
flow within porous medium; specifically,
flow from cell to
cell and flow into storage.
Well
WEL
Adds terms representing
to wells to the finitedifference
equations.
Recharge
RCH
Adds terms representing
areally
distributed
recharge to the
finite-difference
equations.
flow
River
RIV
Adds terms representing
flow to
rivers
to the finite-difference
equations.
Drain
DRN
Adds terms representing
flow
to drains to the finitedifference
equations.
Evapotranspiration
EVT
Adds terms representing
the finite-difference
tions.
General-Head
Boundaries
GHB
Adds terms representing
generalhead boundaries
to the finitedifference
equations.
Strongly
Implicit
Procedure
SIP
-
Flow
_ Component
Packages
_ Stress
Packages
ET to
equa-
-
Iteratively
solves the system
of finite-difference
equations
using the Strongly
Implicit
Procedure.
-
SliceSuccessive
Overrelaxation
SOR
Iteratively
solves the system
of finite-difference
equations using Slice-Successive
Overrelaxation.
3-10
Solver
Packages
Similarly,
additional
algorithms,
could
simulation
(or
solver
be added,
must include
a suitable
depend on the
are totally
Basic
other
packages.
loped
for
addition
If
an entirely
modules
influencing
in proper
problem.
of the three
of an individual
sequence)
of the
in such a way that
involved
Every
packages.
Flow Package
Beyond this,
the
new package
solution
Block-Centered
package.
the exception
or removal
stress
the
have been designed
with
different
are at the option
processes
each of the procedures
those
Package,
in a simulation
independent;
above,
additional
and a solver
hydrologic
noted
call
the
in the program
incorporating
as could
replacement)
ages to be included
modules
packages,
the
user,
packand will
The individual
the
packages
required
packages
package has no effect
is desired,
modules
on
can be deve-
(and the main program modified
without
affecting
other
packages
to
of
the program.
Figure
all
16 shows a detailed
of the
primary
modules
or not each module
tion
all
with
beginning
tion
tions,
design
flow
of the
during
determine
an appreciation
of the model is such that
simulation,
whether
in conjuncof the over-
conductances
takes
place
depend upon saturated
Flow Package,
be developed.
formulation
although
The lateral
3-11
the conductance
(26))
and are reformulated
Reformulation
Block-Centered
indicating
of the model.
only
readily
which
16 may be studied
1, for
At present,
age could
the tests
Figure
change at each iteration.
by the
of the main program,
(CC, CR, and CV of equation
solution.
where the
with
13 and 15, and table
and operation
The overall
cell-to-cell
together
chart
is to be called.
figures
structure
flow
terms
are formulated
if
necessary
only
conductance
situa-
which may
of conductances
again,
at the
at each itera-
in unconfined
thickness,
is done
a replacement
terms
for
pack-
(CC and CR
Figure 16.-Overall
program structure showing all primary
modules.
3-12
in equation
nodes,
tical
(26))
using
are computed
parameters
conductance
is specified
solver
specified
terms
package,
for
the
are stored
HCOFi,j.k
formulation
is done progressively,
process
of each iteration,
throughout
the
the mesh.
interval
which
equations
for
active
with
that
of HCOFi,j,k
The Block-Centered
- tm,1)
tO
at each node.
RHSi,j,k
given
by an expression
(constant)
stream
and adds the
until
each package
transferred
arrays
time
to the
step,
value
nodes in the mesh.
calculates
package.
that
nodes.
The solver
are affected
and adds terms
At the beginning
adds the term
and adds the term
by flow
(hs-hi,j,k),
This
with
sums the
3-13
process
continues
contribution
the three
heads at the
identifies
of HCOF at each node to create
to HCOFi,j,k,
-Psi,j,k
to HCOF
The HCOF and RHS arrays
together
which
from a stream,
where h, is the
h, to RHSi,j,k.
package
This
are set to zero
package adds the term
containing
IBOUND array,
are
i ,j ,k
package,
and the
(26)
hm-1
node of the mesh.
solver
are solved.
of equation
by the user has added its
(CC,CR and CV), an array
and active
the
-Psi,j,k
specified
and RHS at each indicated
then
the River
term
(27))
at each node,
of the form Psi,j,k
head,
constant
For cells
passed to the
Flow Package then
-ssi , j ,kArjACiAVk
----m-----------tm - tm-1
which
The various
nodes.
and RHSi,j,k
to HCOFi,j,k
the ver-
information
are ultimately
as each package
associated
values
-SSi,j,kArjACiAVk/(tm
between
between
cells;
using
(equation
all
intervals
individual
and the term RHSi,j,k
anew at each iteration,
the particular
the
is calculated
in arrays
formulated
for
(26))
vertical
where the matrix
The coefficient
means for
by the user for
(CV in equation
directly
conductance
as harmonic
six
a single
conductance
beginning
constand
head,
conductance
coefficient
are
of the
no flow
terms
of hi,j,k
and
(corresponding
to the term in brackets
one iteration
solution
array,
of the solution
procedure
the
the program
stored
in Chapter
in terms
packages.
discussion
of each module included
describes
of a particular
and listing
Array
As noted
dimensional
out
used in the
one-dimensional
assemblage
The size
water
document
Each of these
including
chapters
and
of this
calculations,
in the model,
contains
a listing
The remainder
budget
discuss
space
and provides
a brief
of the main program.
Boundaries
and Aquifer
Boundaries
2, the model may be visualized
of cells,
each cell
associated
of the model array
in terms
with
s specified
of a three-
a node of the
by the user
in terms
number of rows (NROW), number of co umns (NCOL) and number of layers
(NLAY);
these
a rectangular
terms
define
box.
In formulating
conductance
surface
cell-to-cell
of this
terms
a three-dimensional
rectangular
conductance
array.
term
a conductance
term
for
of cells
interval
for
to the
is developed
(NCOL), but not for
Similar
are established
the
for
3-14
the
equations,
flow
the
interval
form of
cell-to-
on the outer
along
interval
opposite
interval
in the other
in the
of cells
Thus considering
(NCOL-1) and column
conventions
the exterior
is developed
the
array
the finite-difference
are omitted
1 and column 2, but not for
similarly,
arrays
of a single
in the package.
are handled
in Chapter
model array.
cell
and carries
13 of this
package,
the way boundaries,
and input-output
description
4 through
of individual
description
of the
as segments
1, Chapters
a detailed
allocation
The various
procedure.
are actually
(26)),
"X" array.
As noted
chapter
in equation
a row,
a
between column
side
of column
1;
between column
beyond column
two directions,
(NCOL).
so that
in
effect
B
the array
cell
flow
is
occurs.
bounded externally
If
these
embedded in the program,
they
can be relied
boundaries
boundaries
impermeable
character.
by specifying
head,
by using
cells
and external
further
cell
will
external
stress
representing
is formulated;
to a constant-head
constant-head
cell.
from the
inactive
between an inactive
As pointed
thus
cell
B
with
this
portions
of the array
for
no-flow
box.
which
shape,
fall
while
interval
layer
stress
example,
terms
seepage.
(26)
is formulated
cells,
each variable-head
cells,
flow
for
no equation
cell
adjacent
to and from the
no equation
is simulated
is formulated,
cell
for
flow
to or
across
the
interval
cell.
as initially
Where the
inactive
3-15
no cell-to-
above the uppermost
terms--for
of any adjacent
outside
2, and is
from above is frequently
a term describing
no flow
rectangular
be noted that
the
of no-flow
in Chapter
For constant-head
the model array
has the form of a rectangular
however,
not be of a simple
a combination
of the form of
and any adjacent
out above,
coincide
for
this
in the equation
cell;
also
external
For inactive
and no term appears
or will
or by using
or stream
contains
In general,
aquifer
or constant-
the equation
cell
those
as no-flow
in the mesh.
however,
in form,
along
the array
equation
cell
by the user.
in the aquifer,
within
into
evapotranspiration
each variable-head
condition
are actually
must be simu-
are formulated
A finite-difference
boundaries
This was discussed
in the model through
which
boundary
should
flow
no cell-to-
the aquifer
terms.
of the model array,
represented
the no-flow
terms,
It
which
cases,
cells
stress
terms
impermeable
be irregular
below.
conductance
with
In these
across
of the model array,
intervention
certain
discussed
layer
coincide
further
the aquifer
lated
boundaries
upon to simulate
without
by planes
the
limits
cells
aquifer
generated
of an aquifer
always
do not
may be used to delete
boundaries;
this
was
discussed
through
constant-head
bodies
an example
cells
which
aquifer
Well
level
which
are characterized
may be simulated
Package,
nodes just
varies
the
in proportion
boundary.
specifying
artificial
streambed
cell
the
boundary,
a way as to duplicate
Constant-head
guished
array
cells,
one element
for
a given
by a constant
rate
of flow
a no-flow
boundary
for
cell
where these
again
conductance
values
inactive
cells
the
with
rates
General
are applied
the
to
which
Head Boundary
to nodes just
Package would
involve
values
at each
chosen in such
relationships.
and variable-head
in the model through
the
in the mesh.
the type
or out of the
are deliberately
head-flow
Bound-
by inflow
and stream-head
required
indicates
into
characterized
using
water
the aquifer.
or recharge
Use of the River
each cell
as surface
in conjunction
withdrawal
Boundaries
where these
the
from one another
contains
with
boundary.
to a no-flow
along
contact
appropriate
Package,
in the same example,
such features
to head can be simulated
Package or the River
interior
As noted
are in full
using
by assigning
inside
2.
may be used to represent
of constant
aries
in Chapter
of cell
cells
IROUND array,
The entry
are distinwhich
in the
according
IBOUND
to the following
convention:
IBOUND (I,J,K)
IBOUND (I,J,K)
IBOUND (I,J,K)
< 0 . . . .Cell
= 0 . . . .Cell
> 0 . . . .Cell
The IBOUND codes are initially
the
codes are adjusted
by the user
specified
equal
and with
as active
so that
specified
they
intermediate
but are given
a water
budget.
In this
report,
are consistent
cells
head
head
user.
with
For example,
transmissivity
Volumetric
inflows
is constant
is inactive
is variable
by the
results.
to zero are changed to inactive
A summary of all
I,J,K
I,J,K
I,J,K
If
other
necessary,
data specified
cells
which
are
and vertical-leakance
values
by the program.
Budget
and outflows
the water
3-16
to a region
budget
is generally
is termed
called
a volumetric
budget
B
thus
because
strictly
it
deals
speaking
been used in reference
model program
the
on the
attained.
should
also
Each flow
flows
and flow
flow
storage
process,
are all
as printed
is also
effectively
effectively
in itself,
involves
acceptability
equal
budget
and in this
is,
the
is calculated
sense may
solution.
into
flow
its
own contribution
part
does not include
to or from constant
budget
regime.
3-17
of water
budget
from the
to the flow--even
the transfer
internal
into
head cells,
terms.
of the overall
removes water
adds water
to the
or out of the model as a whole.
in the overall
considered
is
Continuity
should
the water
in the output
flows
solution
by the model actually
outflow
process,
of a valid
to the
may stop
and out of the model--that
and total
solution
included
solvers
each model cell.
In the model program,
budget
in storage
release
ground water
into
to or from rivers,
to wells
accumulation
for
do not always
of the overall
solved
component package calculates
and out of storage
B
flows
between model cells--only
For example,
iterative
an indication
inflow
evidence
The total
The
summarized
equations
approximation
statement
of the equation
independent
budget.
provides
the total
change in storage.
provide
term has
model as a check on
to provide
simultaneous
close
between total
independently
for
in particular,
continuity
for
this
rates;
model reports.
the overall
and in order
The system of equations
exist
the difference
total
budget
of a flow
in other
budget for
techniques
a sufficiently
A water
budgets
although
flow
system.
answer;
of the solution.
consists
a water
solution
before
and volumetric
is not a mass balance,
to volumetric
flow
in a correct
iterating
volumes of water
of the solution,
Numerical
result
it
calculates
acceptability
information
with
Flow into
inasmuch
flow
system,
though
neither
or out of the
as
and
For every
time
step,
rate
of flow
calculates
the
simulated
by the
flow
are stored
the
volumes
volumes,
stored
in the
of flow,
entering
from the
in array
beginning
volumes
in the
step
printed
ouflows;
inflow.
from the
of flow.
the convention
as an outflow
In addition,
while
total
step
step
length.
calculated
inflows,
outflows
with
to flow,
the time
are then
budget
beginning
Inflows
water
inflow
above,
Cumulative
and
for
the
last
are
from
entering
storage
is treated
are printed,
and outflow.
the
requested
separately
water
outflow
using
and cumula-
of simulation
form storage
and total
error , calculated
rates
are printed
released
inflow
at the times
the flow
indicated
between total
as a percent
the
is printed,
volumes
each component
as the difference
printed
and time
simulation,
to print
When a budget
following
is treated
of the
In addition
the model during
rate
only
Plow Package deals
to storage.
BAS Package uses the
and cumulative
for
of flow
VBVL array
by the model user.
time
Most packages deal with
VBVL.
Module SBASlV in the
tive
and flow
due to the process
for each component of
Block-Centered
and leaving
as the product
system
and outflows
VBVL array.
but the
head cells
of water
are calculated
and out of the
The inflows
separately
to constant
module of each flow component package
budget
into
package.
one such component
two--flow
the
as an
as well
The difference
is then
formula:
lOO(IN-OUT)
D = iiN;O--Tj72-
where
IN is the total
is the percent
the
percent
error
an indication
while
error
cumulative
inflow
term.
should
of solution
volumes
to the
If
OUT is the total
the model equations
be small.
validity
system,
In general,
for
the time
are an indication
3-18
outflow
are correctly
flow
rates
step
to which
of validity
for
and D
solved,
may be taken
they
apply,
the entire
as
simulation
up to the time
end of each stress
period
There are situations
various
subregions
of the printout.
The budget
whether
or not.
requested
in which
of the model.
has been made to save flow
terms
it
is useful
individual
cells
external
cell
flows
to here as "cell-by-cell"
four
general
individual
types:
cell
(1)
such as evapotranspiration
terms,
which
net flow
cell;
the
flows,
is,
between
(3)
which
cell-by-cell
adjacent
model cells.
in subsequent
two flags
sect ion of the
Basic
set
each time
for
In addition,
each flow
the cell-by-cell
the
types
ICBCFL flag
in the
flow
flows--are
under the
Basic
will
computed
control
storage
cell
faces--that
term are
to the Output
which
is set
Package input
each time
is
step
set,
for
constant-head
in the
Block-Centered
Flow Package,
3-19
cell-bywhich
Three of the four
above --storage,
flag,
if
Thus if
listed
of a single
must be
are to be saved.
a flag
set.
cell-by-cell
ICBCFL, which
terms
the
cell-by-
of cell-by-cell
a f lag,
is also
give
internal
package are to be saved.
be saved for
in an
which
The input
includes
Package input
terms
terms,
individual
which any cell-by-cell
terms
in the
To save any of these
Package includes
package
or from an
of storage
and (4)
kinds
in the Evapotranspiration
of cell-by-cell
fall
across
must be set.
computed by that
evapotranspiration
and internal
thus
flag
cells;
paragraphs.
component
terms
the appropriate
cell
step
flow
These four
in the model input
Control
for
the flows
into
cell-by-cell
or depletion
constant-head
can
and are of
represented
(2)
constant-head
for
provision
so they
terms,
or flows
stresses
of accummulation
are actually
discussed
terms,
rate
flow
or recharge;
to or from individual
cell
further
give
terms
These individual
flows,
due to one of the external
model,
individual
stress
flow
on disk
to the model itself.
cell-by-cell
at the
such calculations,
be used in computations
are referred
to calculate
To facilitate
for
is printed
IBCFCB, in the
input
cell
and
to that
Thus in general
package.
set,
and ICBCFL is also
in the cell-by-cell
volumes
Cell-by-cell
a particular
the
cell,
cell-by-cell
water
flows
are flow
evapotranspiration
is out of the
cell.
model cell,
for
requested.
That
for
flow
Package,
cells
for
that
is,
flow
is
flow
terms
even when that
for
i,j,k
cell
into
would
data.
The
cell,
value
is
is zero,
saved,for
the cell-by-cell
For example,
budget
and terms
if
it
every
flow
stress
is
components,
when using
values
value
stress
is saved on disk
is
the River
only
amount of disk
a flow
at
the flow
and negative
For many of the
Thus the
give
Cell-by-cell
of the model grid
can be large;
value
where
For example,
i,j,k.
the
which
cell-by-cell
by rivers.
time,
or out of the model,
stress.
for
at most model cells.
are traversed
water
UBUDSV module for
external
flow
of flow.
be nonzero
at those
space required
stored
for
each
may be saved at many
steps.
The cell-by-cell
in a variable:head
the mesh is
storage
cell.
term
An array
saved in transient
is
are saved
nor cumulative
the
into
stress
the size
component
flag
form to make the most
from cell
component
an array
will
cell-by-cell
model cell
time
each stress
be zero
there
if
values
model input
for
rates
term
A cell-by-cell
each requested
will
positive
this
to disk.
due to one particular
are considered
all
in unformatted
are written
if
are volume per unit
used for
out of the model by evapotranspiration
flows
volumes
see the narrative
space;
stress
Only flow
step.
dimensions
are stored
on how the data
are saved on disk
the time
neither
files;
values
use of disk
information
for
types
are in the same units
flow
efficient
three
The flow
are included.
cell-by-cell
set
disk
volume and time
all
gives
the
of these
simulations
3-20
net flow
terms,
if
to or from storage
one for
the appropriate
each cell
flags
in
are
set.
Withdrawal
accumulation
from storage
in storage
The cell-by-cell
the constant-head
cells
which contribute
all
provides
representing
the net flow
portion
into
The internal
value
cells.
value
flow
Flow Package for
and i+l,j,k),
and flow
these
flow
across
values
(Although
flow
across
flow
for
they
opposite
across
the right
face
flow
has six
three
(between
layer
flows
indicates
that
is
sides
cell
cell
only
is accounted
sides.)
of increasing
number,
These internal
cell
for
i,j,k
cell
flow
terms
Each of
cell.
are required;
in the calculations
Flows are considered
row number,
cell-by-cell
i,j,k
and i,j+l,k),
and i,j,k+l).
and are considered
3-21
are set.
(between
and a neighboring
three
the
and constant-head
flags
face
i,j,k
across
are saved by the
cell
(between
cell
neighbors,
to those
are in the direction
directions.
face
between a given
adjacent
number or increasing
and
the net flow
cell-by-cell
the front
the other
cells
cell
the variable-head
that
each variable-head
across
each cell
(into
represent
are flow
the lower
represents
value
Three such terms
of a model cell.
terms
The cell-by-
between that
cell
in the mesh, whenever the appropriate
These three
may be
each constant-head
A positive
indicates
cell
cells.
for
associated
cell.
cell-by-cell
faces
Block-Centered
if
variable-head
flow
or
the surrounding
A constant-head
sum of the flows
a negative
whereas
into
is always
than with
is away from the constant-head
the constant-head
cell
a single
variable-head
of the mesh);
individual
adjacent
the flow
This term
the flow.
the algebraic
of the adjacent
term gives
rather
or receive
positive,
negative.
cell.
itself,
by as many as six
calculation
cell,
cell
is considered
flow
constant-head
with
cell
is considered
constant-head
out of an individual
surrounded
in the cell
flow
positive
increasing
negative
values
of
column
if
in the
are useful
in calculations
model,
of the ground-water
or in constructing
In theory
budget
one could
by using
in practice
flow
flow
calculate
a budget
the cell-by-cell
flow
The cell-by-cell
component
is the net flow
that
of the same type,
Only the net flow
for the cell
other
hand,
a negative
budget
positive
flow
and outflow
inflow
summing individual
ponding
terms
However,
either
at a cell
flows
cell
at the same cell
terms
cell-by-cell
as calculated
the difference
of the
to the overall
is not always
a given
stress
which could
include
and some positive.
disk
in the model,
are assembled
file.
on the
separately,
so that
would be added to the outflow
the entire
values,
inflow
inflow
term
term.
model are calculated
they may differ
by the model program
between
or flow
possibly
would be added to the
for
true
may be summed
for
as performed
at an individual
Thus if
subregions
is saved in the cell-by-cell
and negative
flow
the budgets
some negative
calculations
and a positive
This
component,
two or more flows
In the overall
identical
terms.
value
for
various
vectors.
because in some situations
differently.
into
from the corres-
in the overall
and outflow
should
by
budget.
be the same for
calculation.
Space Allocation
Space in the central
lists
is allocated
"X" array.
at execution
The'Allocate
the model which
memory of the computer
allocates
Procedure
in a simulation
number of cells
referring
contains
a module for
package.
depends on the type
and generally
in the grid.
to the length
in a one-dimensional
space needed by that
of words needed in the X array
required
time
used by data
will
array
called
the
each package of
The total
number
range from 10 to 20 times
the
two statements
both of which appear
3-22
and
and number of packages
The main program contains
of the X array,
arrays
in the first
part
of the program
ation
these
listing.
statements
are
30000 in the statements
must be increased
if
In the
COMMONX(30000)
refers
the
listing
reproduced
this
and LENX = 30000.
to the length
storage
with
of the X array;
requirements
of the
document-
The number
this
problem
number
exceed
30000
elements.
Three-Dimensional
The conceptualization
designate
cell
Subscripts
for
and implementation
locations
by row, column,
Model Arrays
sections
and layer
indices
(usually
designated
as i,j,k),
as is customary
however,
this
of indices
is not the most efficient
subscripts
three
in the model program.
dimensional
The order
stored
array
in computer
subscripts
program.
should
Typically
row,
is important
when comparing
sections
memory.
of the
in the
of the
program,
this
array
are declared
difference
3-23
order
order
to be
in the
how data
such that
for
subscripts.
are
the model
the most
has been used throughout
the column subscript,
is J,I,K
the model program to the conceptualization
report.
is
J is used for
but the order
to bear in mind this
for
determines
program
row, and layer
on most computers;
layer,
literature;
order
FORTRANlanguage
be in column,
and K for
order
have row, column and layer
The design
in the
report
in that
in scientific
Many model parameters
and accordingly
subscripts
memory access
is used for
It
arrays
of array
efficient
the
order
of this
rather
subscript
than
I,J,K.
ordering
and implementation
I
Input
The input
gathered,
element
the
structure
as it
of the
file
file
externally
the
Output
an optional
output,
segments
considered
input
for
here as an option,
This
Block-Centered
even though
Flow in the
number,
number;
of the
a major
for
generally
in terms
Basic
option.
since
is presently
the addition
done
of "major
are utilized
individual
only
packages;
Package are considered
package
but
flexibility
The balance
it
is to
statements.
Package providing
Block-Centered
it
is
is not an individual
Basic
identifies
the output
to the
the
to be
is based on an
which
program which
except
input
name of each input
this
system
generally
an option
be read.
has been done to allow
It
between the
operating
which
Control,
Package is not considered
must always
unit
packages
Basic
it
unit
a link
They correspond
segment of the
is also
files.
program may be discussed
of the existing
options.
the
to permit
is to be read (or to which
through
are major
request.
all
program
called
corresponding
purposes,
at the user's
rather
input
to the program,
these
in fact,
the
is designed
from many different
FORTRANlanguage
and the
For input
options";
program
The user must provide
be written).
major
is needed,
from which
or output
of the
Structure
is always
in
a
of the
utilized
and
Flow has been treated
required
in all
of replacement
simulations.
packages
for
future.
c
3-24
One of the first
the major
options
(figure
17) which
option
is invoked
steps
are to be used.
is
by inserting
of the
IUNIT array;
element
is set to zero.
whether
an option
data
required
to the unit
B
if
it
number of the file
In the main program,
the
program
If
procedures.
procedure
is not called.
is called
and input
is zero,
data
is
of
array
Package.
the value
to specify
An
if
the
the Drain
number
the Drain
IUNIT array
of the
element
input
of the
data
for
(figure
array
zero,
associated
is set
of the
module associated
read from the file
18)
the package.
in several
than
of the
to indicate
the unit
For example,
IUNIT (3) is greater
If
Basic
as a flag
IUNIT (3) is tested
of
which
"IUNIT"
by the
serves
the third
containing
value
it
serves
element
is to be used,
the
is not desired,
by the option.
the third
is to specify
number in the appropriate
IUNIT array
and also
data
is done using
unit
an option
Thus the
Package is not to be used,
is set to zero;
if
input
Procedure
an input
is active,
input
This
read in the Define
element
containing
in organizing
with
the
with
the
subroutine
the
unit
number.
As noted
trol
option,
above,
the
Basic
(BAS) Package,
is used for
every
simulation;
Package are always
unit
number 1 as specified
number for
Basic
required.
BAS input
exclusive
and input
Package data
in the main program.
can be changed to meet the
of the Output
data
(figure
If
for
the
Con-
Basic
18) are read from
necessary,
requirements
the unit
of a particular
computer.
The first
which
data
present,
for
the
because
cell-to-cell
always
element
flow
of the
IUNIT array
Block-Centered
BCF is the only
terms,
must contain
the
unit
number from
Flow (BCF) Package are to be read.
package available
a non-zero
entry
required.
3-25
for
in the first
the formulation
element
of
At
of
IUNIT is
Assignment
of Major Options to Elements
in the IUNIT Array
IUNIT
Element
Number
Sample IUNIT Input Record
IUNIT
Element
Number
.
13
41
0
0
81
0
0
0
26
0
0
17
,
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
7
8
9
11
12
BCF
WEL
DRN
RIV
EVT
GHB
RCH
SIP
SOR
Output Control
Figure 1 ‘I.-Specification
Input Is on
Input Is on
Is Inactive
Is Inactive
Input Is on
Is Inactive
Is Inactive
Input Is on
Is Inactive
Input Is on
Unit 13
Unit 41
Unit 81
Unit 26
Unit 17
of major options using the IUNIT array.
3-26
----_-----------------------7
This Is BAS Input Read from Unit 1
Options Are Specified in
UNIT. The Locations
n IUNIT Are Assigned
---L --------------------------- ._--------------------This Is the First Record on Which User Puts Heading for the Problem
This Is the Second Card of the Heading
IS Follows:
I
J
1 BCF package
2 WEL package
3
4
5
7
8
9
11
12
DRN package
RIV package
EVT package
GHB package
RCH package
SIP package
SOR package
Output control
lunit24.
I
1.
l.
r-----------w-------------,
I
These are IBOUND Array Values for Layer Two Read on Unit 24
I
J
L ------------------------
I
1111110
1111111
1 1 1 1 1 l-l
---
--------------e---
r----
1
This Is BCF Input Read from Unit 17.
i,,----
----1
0
17
1
-,,,-,-,----A
10
1.
4.
(2OF4.0)
17
.3048
(12F7.2)
50.
70.
90.
110.
125.
0
30.48
. 0001
t
0
. 0oo~oOi
17
l.
5
5
(8i8.3)
7
5
5
6
6
4
i
5
2
135.
140.
6
7
6
5
8
7
6
6
9
7
7
This Is for WEL Input Read on Unit 23
i---,,----------
--------J
1
0
:
3
1
.003
#------------------------1
I
I
r
I
This Is RCH Input Read on Unit 57
I
L _--_--__--
-------------:,
:
0 .00000005
This Is SIP Input Read on Unit 77
L
50
1.
Figure 18.-Sample
I-I
----c-----------------
5
.Ol
input data showing
3-27
1
2
role of the IUNIT array.
Most of the data
and two-dimensional
record"
major
control
option
is
calls
for
have the same value,
is
not necessary
array
the
on the
array
specified
in the control
from which
the control
is a great
deal
record
If
values
according
The unit
is
read,
elements.
for
the
of an array
record
the elements
and it
of the
are read from the unit
to a format
which
is also
number may be the same as that
or it
regarding
the elements
control
may be different.
the organization
Thus there
of the
input
data
a simulation.
a certain
to avoid
length
in units
any mixing
of ftz/day
results
and time
amount of freedom
of units.
the use of inconsistent
the
record
record.
of flexibility
Any consistent
gives
control
the array
on the control
array.
the array
as an "array
number specified
all
is specified
containing
specified
for
If
the array.
of one-dimensional
containing
read from the unit
value
consist
are submitted
of records
to read the associated
records
vary,
a series
record
which
by the user will
Those arrays
arrays.
optionally,
plus,
The array
submitted
will
units
to the user,
There is
units.
frequency
and pumpage as ms/s,
of the overall
if
model data.
This
must be exercised
the program
transmissivity
the program will
to detect
is entered
run,
but
be meaningless.
structure
of information
the printing
but care
no way for
For example,
Outout
The output
may be used for
Structure
is designed
to be printed
to control
or written
of head and drawdown by layer
volumetric
budget.
It
the
also
3-28
amount,
on disk.
and time
step,
controls
disk
type,
It
controls
and the
output
and
printing
of head,
drawdown,
and cell-by-cell
the model,
or in user-supplied
Output
Package,
Control,
receives
frequency
unit
option
twelfth
element
read,
output
file
is specified
convention
and budget
terms
is
option
invoked.
printed
for
some printer
output.
specified
in the main program.
of a particular
within
unit
the
(IUNIT
12);
input
default
the
printer
This
for
unit
Basic
of the
output
output
the
the
Output
as the
information
by this
is
unit
IUNIT array,
consists
the end of each stress
All
data
input
identified
element
to
amount and
number must be entered
from the file
This
the
the
the user must specify
from which
This
external
programs.
contained
option,
as the twelfth
generates
requirements
and plotting
this
IUNIT array
step,
use in calculations
from the user to control
or channel
are to be read.
of the
for
is a major
To utilize
at each time
a zero
terms
printing
instructions
of output.
Control
If
which
number of the
then
flow
number.
a default
of head values
period.
Every
goes to unit
simulation
number 6 as
number can be changed to meet the
computer.
The Main Program
The main program-serves
in which
system
for
the primary
information.
modules
which
purposes:
are executed,
It does so with
name, a module to be executed
arguments)
two major
are accessible
and lists
and (2)
(1)
it
it
controls
serves
CALL statements
the names of data
by both the main program
3-29
the
order
as a switching
which
fields
specify,
by
(subroutine
and the module.
The arrangement
procedures
the
shown in the system
calls
to specific
procedure
precede
of CALL statements
modules
all
other
correspond
to the
3.
chart
Set the
length
dimension
of the
the
output
to unit
Define
the problem
stress
periods,
If
the
with
Note:
input
for
a procedure,
X array
6.
Read and prepare
7.
For each stress
if
all
a
CALL must
modules
numbers in the following
LENX should
list
listing).
data
be set equal
arrays
to the
to compilation.
the Basic
Package to unit
1; assign
printed
6.
in terms
and major
space in the
X and redefine
of number of rows,
options
X array
for
columns,
layers,
to be used.
individual
is not big enough for
the
data
problem,
arrays
and lists.
STOP.
(Redimension
LENX.)
information
which
is constant
throughout
the simulation.
period:
(a)
Read stress-period
timing
information.
(b)
Read and prepare
information
that
(c)
that
(LENX) in which
prior
of
one exception:
Package,
(the
"X" array
X array
Assign
5.
in order
of the
are stored.
Allocate
Within
numbers of the comments in the main program
and lists
4.
13).
the order
The main program calls
procedure.
tasks,
reflects
(figure
can be in any order
CALLS in that
the following
2.
flow
has a CALL to a module in the Basic
to perform
1.
in the program
For each time
step:
3-30
changes
each stress
period.
(1)
Calculate
the current
time-step
heads from the preceding
"old"
(2)
time
heads of the current
Iteratively
formulate
length
step
time
and solve
a.
Formulate
the finite-difference
b.
Calculate
an approximate
and move "new"
to the array
containing
step.
the system
of equations:
equations.
solution
to the system
of
equations.
If
c.
(3)
Determine
time
(4)
(5)
8.
the type
Calculate
overall
and print
or record
Print
If
criterion
has been met,
and amount of output
stop
iterating.
needed for
this
step.
overall
(6)
convergence
and/or
budget
record
volumetric
iteration
fails
terms
and,
if
cell-by-cell
flow
heads and/or
drawdown.
budget
and timing
to meet convergence
END PROGRAM.
3-31
specified,
calculate
terms.
Print
the
summary.
criterion,
STOP.
*~**W*t****W**X*t******~*********~**~~******~*~~~~~~**~~*~*~*~*~~*
9/1/87
MAIN CODE FOR MODULAR MODEL -BY MICHAEL G. MCDONALD AND ARLEN W. HARBAUGH
C
C
C
C-----VERSION 1638 24JUL1987MAIN1
************************************************************~*****
:
SPECIFICATIONS:
C
-----------------------------------------------------------------C
COMMONX(30000)
CObt4ON /FLWCOM/LAYCON(80)
CHARACTER*4 HEADNGsVBNM
DIMENSION HEADNG(32)rVBNM(4,20)rVBVL(4r20)rIUNIT(24)
DOUBLE PRECISIONDUMMY
EQUIVALENCE
(DUMMY,X(l))
E
Cl----
SET SIZE OF X ARRAY. REMEMBER TO REDIMENSION
X.
LENX=30000
C
c2---
ASSIGNBASIC INPUT UNIT AND PRINTER UNIT.
INBAS=l
IOUT=
C
Q------
DEFINE PROBLEM-ROWS, COLUMNS,LAYERS, STRESS PERIODS, PACKAGES
CALL BASlDF(ISUM,HEADNG,NPER,ITMUNI,TOTIM,NCOLrNRCW,NLAY,
NODES~INBAS~IOUTIIUNIT)
1
C
c4------ALLOCATE
CALL BASlAL
1
2
IN “X” ARRAY.
(ISUM,LENX, LCHNEW,LCHOLD, LCIBOU,LCCR, LCCC, LCCV,
SPACE
LCHCOF, LCRHS, LCDELR, LCDELC, LCSTRT, LCBUFF, LCIOFL,
INBAS,ISTRT,NCOL,
NROWnNLAY,IOUT)
IF(IUNIT(l).GT.O) CALL BCFlAL(ISUM,LENX,LCSClrLCHY,
1
LCBOT,LCTOP,LCSC~,LCTRPYIIUNIT(~)~ISSI
2
NCOLrNRChVW,NLAY,IOUT,IBCFCB)
IF(IUNIT(P).GT.O) CALL WELIAL(ISUMILENXILCWELL,MXWELLINWELLS,
1
IUNIT(2),IOUT,IWELCB)
IF(IUNIT(3).GT.O)
CALL DRNlAL~ISUM,lENX,LCDRAI.NDRAIN.MXDRN.
1
IUNIT(3).IOUT,IDRNCB)
IF(IUNIT(B).GT.O) CALL RCHlAL(ISUM,LENX,LCIRCHrLCRECHrNRCHOP,
1
NCOLrNROWrIUNIT(8)rIOUT,IRCHCB)
IF(IUNIT(S).GT.O) CALL EVTlAL(ISUM,LENXtLCIEVT,LCEVTFbLCEXDP,
LCSURF, NCOL, NRW, NEVTOP, IUNIT(
IOUT,IEVTCB)
1
IF(IUNIT(4).GT.O) CALL RIVlAL(ISUM,LENX,LCRIVR,MXRIVR,NRIVER,
1
IUNIT(4)rIOUT,IRIVCB)
IF(IUNIT(‘I).GT.O) CALL GHB~AL(ISUM,LENX,LCBNDS,NBOUNDIMXBNDI
1
IUNIT(7)rIOUT,IGHBCB)
IF(IUNIT(9).GT.O) CALL SIP~AL(ISUM,LENXILCEL~LCFL~LCGLILCVI
LCHDCGrLCLRCH, LCW,MXITER,NPAJ?MINCOLINROW,NLAYI
:
IUNIT(9),IOUT)
IF(IUNIT(ll).GT.O)
CALL SOR~AL(ISUM,LENXILCAILCRES,LCHDCGILCLRCH~
1
LCIEQP,MXITER,NCOL,NLAY,NSLICE,MBWIIUNIT~~~~~IOUT~
C
c5------IF
ME “X” ARRAY IS NOT BIG ENOUGH THEN STOP.
IFtISUM-l.GT.LENX) STOP
C
C6----
READ AND PREPARE INFORMATION FOR ENTIRE SIMULATION.
CALL BASlRP(X(LCIBOU)rX(LCHNEW)rX(LCSTRT)rX(LCHOLD)r
1
ISTRT,INBAS,HEADNG,NCCL, NROW,NLAY, NODES, VBVL,X(LCIOFL)
2
,
IUNIT(~~),IHEDFM,IDDNFM,IHEDUNIIDDNUNIIOUT)
IF(IUNIT(l).GT.O) CALL BCFlRP(X(LCIBOLJ)rX(LCHNEW)rX(LCSCl)r
1
X(lCHY),X(LCCR)rX(LCCC)rX(LCCV)rX(LCDELR)r
2
X(LCDELC)rX(LCBOT)rX(LCTOP)rX(LCSCZ)rX(LCTRPY)r
3
IUNIT(~)~ISS,NCOL,NRCWINLAY,NODESIIOUT)
3-32
IF(IUNIT(9)
.GT.O) CALL SIPlRP(NPARM,MXITER,ACCL,HCLOSE,X(LCW),
IUNIT(9) rIPCAL& IPRSIP, IOUT)
IF(IUNIT(ll).GT.O)
CALL SOR~RP(MXITER,ACCL~HCLOSEIIUNIT(~~)~
1
IF’RSOR, IOUT)
1
C
C7------
SIMULATE EACH STRESS PERIOD.
DO 300 KPER=lrNPER
KKPER=KPER
C
C7A.ms-m- READ STRESS PERIOD TIMING INFORMATION.
CALL BASlST( NSTP, DELT, TSMULT, PERTIM, KKPER, INBAS, IOUT)
C
C7&---READ AND PREPARE INFORMATION FOR STRESS PERIOD.
IF(IUNIT(2).GT.O)
CALL WELlRP(X(LCWELL)rNWELLS,MXWELL,IUNIT(P)r
1
IOUT)
IF(IUNIT(3).GT.O)
CALL DRNlRP(X(LCDRAI)rNDRAIN,MXDRN,IUNIT(3),
1
IOUT)
IF(IUNIT(8).GT.O)
CALL RCHlRP(NRCHOP,X(LCIRCH)rX(LCRECH)r
X(LCDELR),X(LCDELC)~NRCW,NCQLIIUNIT(~)~IDUT)
1
IF(IUNIT(5).GT.O)
CALL EVTlRP(NEVTOP,X(LCIEVT)rX(LCEVTR)r
1
X(LCEXDP),X(LCSURF)rX(LCDELR)rX(LCDELC)rNCDLrNRC%‘r
1
IUNIT(5) rIDUT)
IF(IUNIT(4).GT.O)
CALL RIV~RP(X(LCRIVR)~NRIVER,MXRIVRIIUNIT(~)~
1
IOUT)
IF(IUNIT(71.GT.O)
CALL GHB~RP(X(LCBNDS)~NBOUND,MXBNDIIUNIT(~)~
1
IDUT)
C
C7C----- SIMULATE EACH TIME STEP.
00 200 KSTP=lrNSTP
KKSTP=KSTP
C
C7Cl---- CALCULATE TIME STEP LENGTH. SET HOLD-HNEW..
CALL BAS~AD(DELT,TSMULTITOTIM,PERTIM,X(LCHN~)~X(LCHOLD)~KKSTPI
1
NCQL, NRCW, NLAY 1
C
C7C2---- ITERATIVELY FORMULATE AND SOLVE THE EQUATIONS.
DO 100 KITER=lrMXITER
KKITER=KITER
C
C7CPA---FORMULATE THE FINITE DIFFERENCE EQUATIONS.
CALL BASlFM(X(LCHCOF)rX(LCRHS),NODES)
IF(IUNIT(l).GT.O)
CALL BCFlFM(X(LCHCOF)rX(LCRHS)rX(LCHOLD)r
X(LCSCl)rX(LCHNEW)rX(LCIBOU)rX(LCCR),X(LCCC)rX(LCCV)r
1
2
X(LCHY)rX(LCTRPY)rX(LCBOT)rX(LCTOP)rX(LCSC2),
X(LCDELR)rX(LCDELC),DELT,ISS,KKITER,KKSTP,KKPER,NCOL,
3
4
NROW,NLAY, IOUT)
IF(IUNIT(2).GT.O)
CALL WELlFM(NWELLS,MXWELL,X(LCRHS)rX(LCWELL)r
1
X(LCIBoU) rNCOLrNROW,NLAY)
IF(IUNIT(3).GT.O)
CALL DRNlFM(NDRAIN,MXDRN,X(LCDRAI)rX(LCHNEW)r
1
X(LCHCDF),X(LCRHS),X(LCIBOU),NCCLINROW,NLAY)
IF(IUNIT(81.GT.O)
CALL RCHlFM(NRCHOP,X(LCIRCH),X(LCRECH)r
1
X(LCRHS)rX(LCIBDU)rNCOL,NROW,NLAY)
IF(IUNIT(S).GT.O)
CALL EVTlFM(NEVTOP,X(LCIEVT)rX(LCEVTR)r
1
X(LCEXDP)rX(LCSURF)rX(LCRHS)rX(LCHCOF)rX(LCIBOU),
1
X(LCHNEW)rNCDLrNROWtNLAY)
IF(IUNIT(4)
.GT.O) CALL RIVlFM(NRIVER,MXRIVR,X(LCRIVR)rX(LCHNEW)r
1
X(LCHCDF)rX(LCRHS)rX(LCIBDU)rNCDLrNRCW,NLAY)
IF(IUNIT(7).GT.O) CALL GHBlFM(NBCUND,MXBND,X(LCBNDS)rX(LCHCQF)r
1
X(LCRHS)rX(LCIBDU),NCCLrNROWrNLAY)
C
3-33
ONE CUT AT AN APPROXIMATE SOLUTION.
IF(IUNIT(9).GT.O) CALL SIPlAP(X(LCHNRJ)rX(LCIBOU)rX(LCCR);X(LCCC)r
X(LCCV),X(LCHCOF),X(LCRHS),X(LCEL),X(LCFL)rX(LCGL)rX(LCV)r
1
X(LCW),X(LCHDCG),X(LCLRCH)~NPARM,KKITER,HCLOSE,ACCLIICNVGI
2
KKSTP,KKPER, IPCALC, IPRSIP,MXITER,NSTP, NCCL, NRwklr NLAY, NODES,
3
4
IOUT)
IF(IUNIT(ll).GT.O) CALL SORlAP(X(LCHNEW)rX(LCIBOU)rX(LCCR)r
X(LCCC),X(LCCV),X(LCHCOF)rX(LCRHS)rX(LCA)rX(LCRES)rX(LCIEQP)r
1
C7CZB---MAKE
X(LCHDCG),X(LCLRCH),KKITER,HCLOSE,ACCL~ICNVG,KKSTP,KKPERI
IPRSOR,MXITER,NSTP,NCOL~NRC~!W~NLAY,NSLICE~MBWIIOUT)
C
C7C2C---IF CONVERGENCECRITERIONHAS BEEN luET STOP ITERATING.
IF(ICNVG.EQ.l) GOTO 110
100 CONTINUE
KITER=MXITER
110 CONTINUE
C
WHICHOUTPUT IS NEEDED.
c7c3---- DETERMINE
CALL BASlOC(NSTP,KKSTP,ICNVG,X(LCIOFL)rNLAY,
1 IBUDFL,ICBCFL,IHDDFL,IUNIT(12)rIOUT)
C
c7C4---- CALCULATE BUDGET TERMS. SAVE CELL-BY-CELL FLOW TERMS.
9
MSUMl
IF(IUNIT(l).GT.O) CALL BCFlBD(VBNM,VBVL,MSUM,X(LCHNEW)r
X(LCIBOU),X(LCHOLD),X(LCSC1),X(LCCR)rX(LCCC)rX(LCCV)r
1
X(LCTOP),X(LCSC~),DELT,ISS,NCOL,NROW,NLAY,KKSTP,KKPERI
2
IBCFCB,ICBCFLrX(LCBUFF)rIOUT)
3
IF(IUNIT(2).GT.O) CALL WELlBD(NWELLS,MXWELL,VBNM,VBVLrMSUM,
X~LCWELL~,X~LCIBOU~,DELT,NCOL,NROW,NLAY,KKSTP,KKPERIIWELCBI
1
ICBCFLrX(LCBUFF)rIOUT)
1
IF(IUNIT(31 .GT.O) CALL DRNlBD(NDRAIN,MXDRN,VBNM,VBVL,MSUM,
X(LCDRAI),DELT,X(LCHNEW),NCOL,NROW,NLAYIX(LCIBOU),KKSTPI
KKPER,IDRNCB,ICBCFL,X(LCBUFF)rIOUT)
IF(IUNIT(81.GT.O) CALL RCHlBD(NRCHOP,X(LCIRCH)rX(LCRECH)r
XtLCIBOU),NR(XJ, NCOL,NLAY,DELT, VBVLrVBNM,MSUM,KKSTP,KKPER,
1
IRCHCF3.ICBCFLrX(LCEtlFF),IOUT)
2
IF(IUNIT(S).GT.O) CALL EVTlBD(NEVTOP,X(LCIEVT),X(LCEVTR)r
1
X(LCEXDP)rX(LCSURF)rX(LCIBOU)rX(LCHNEW)rNCOLrNRCklrNLAY,
2
DELT,VBVL,VBNM,MSUM,KKSTP,KKPER,IEVTCB,ICBCFL,X(LCBUFF)rIOUT)
IF(IUNIT(4) .GT.O) CALL RIV~BD(NRIVER,MXRIVRIX(LCRIVR)~X(LCIBOU)~
X(LCHNEW),NCOL,NROW,NLAY,DELT,VBVL,VBNM,MSUMI
1
1
2
2
KKSTPIKKPER,IRIVCB,ICBCFL~X(LCBUFF)~IOUT)
IF(IUNIT(71.GT.O) CALL GHB~BD(NBOUND,MXBND,VBNMIVBVLIMSUMI
X(LCBNDS)rDELT,X(LCHNEW)rNCOL,NROWrNLAY,X(LCIBOU)rKKSTP,
KKPER,IGHBCB,ICBCFLrX(LCBUFF)rIOUT)
:
C
c7c5--- PRINT AND OR SAVE HEADS AND DRAWDOWNS.PRINT OVERALLBUDGET.
CALL BASlOT~X~LCHNEW~,X~LCSTRT~,ISTRT,X~LCBUFF~,X~LCIOFL~r
MSUM,X(LCIBOU),VBNM,VBVL,KKSTP,KKPER,DELT,
PERTIMsTOTIM, ITMUNI,NCOL, NRW, NLAY, ICNVG,
1
2
3
IHDDFL,IBUDFL,IHEDFM,IHEDUN,IDDNFM,IDDNUN,IOUT~
C
C7C6---- IF ITERATIONFAILED TO CONVERGE
THENSTOP.
IF(ICNVG.EQ.0) STOP
200 CONTINUE
300 CONTINUE
C
PROGRAM
ca------END
STOP
C
END
3-34
CHAPTER 4
BASIC PACKAGE
Conceptualization
The Basic
periods,
it
Package handles
a number of administrative
It reads data on the number of rows,
model.
for
and Implementation
on the major
those
options
It allocates
options.
reads data specifying
implements
starting
budget;
to be used,
data establishing
head arrays
and it
for
controls
columns,
layers,
and on the
location
space in computer
initial
and boundary
step;
model output
it
calculates
according
to user
Selection
of Major
Options
and Designation
The selection
of major
options
and the designation
numbers were discussed
in the preceding
Basic
operations
Chapter
option
Package in these
3, the entries
array
is to be used and (b) the unit
is to be read.
element
in this
is to read the
menever
corresponding
a new major
to that
option
determine
option
it
up the
an overall
water
specification.
Files
of their
IUNIT array;
(a) whether
input
role
unit
of the
as noted
in
or not a major
data
for
the option
is added to the program,
must be added to the
4-1
model arrays;
sets
of Input
number from which
data
reads and
The primary
chapter.
the
of input
it
of time;
for
and stress
memory for
conditions;
the discretization
each time
tasks
IUNIT array.
an
The IBOUND Array
Recall
that
the finite-difference
CRi,j-1/2,k(hY,j-l,k-hY,j,k)
+ CVi,j,k-1/2(hy,j,k-l-hy,j,k)
+ Cvi,j,k+l/2(hF,j,k+l-h!i,j,k)
= scli,j,k
of this
Package,
contains
head varies
(constant-head
with
(h~,j,k-IJ~T~,k)/btm-
form is written
which
The IBOUND array,
for
cell),
(variable-head
cell).
the state
of a cell
IBOUND code entries
for
a typical
at the
of each time
after
the first,
equal
to the head distribution
the
first
specified
time
step;
time
initial
however,
"starting
step
time
is
step
required
(figure
at the
(1)
head is constant
the
cell
(no-flow
packages
the distribution
start
form,
if
of
heads"
may also
are specified
head calculation
be saved,
4-2
a head distribu-
to calculate
20).
the
For each time
of one time
at the end of the previous
heads are used for
they
whether
Conditions
the head distribution
step,
and read by the
by other
is in backward-difference
(28)
at the end of that
in the
model layer.
Because equation
distribution
within
19 illustrates
Initial
beginning
(2) the
place
cell
indicates
can be modified
Figure
changes.
which
cell),
takes
The IBOUND array
or inactive
by the user
each cell
or (3) no flow
(28)
each variable-head
is specified
a code for
time
has the form
- h;,j,k)
m
- hi,j,k)
+ CCi+l/2,j,k(hT+l,j,k
grid.
tion
a cell
+ CCi-1/2,j,k(h?-l,j,k-h!i,j,k)
One equation
the
for
+ CRi,j+l/E,k(hy,j+l,k
+ Pi,j,khT,j,k%,j,k
Basic
equation
time
by the user.
only
in the array
step
step.
head
step
is set
For
These
in the first
STRT, and used to
Area Where
Heads Vary
Aquifer
Boundary
Constant
Head
IBOUND Codes
< 0 Constant Head
= 0 No Flow
> 0 Variable Head
Figure 19.-Example
of the boundary
layer.
array (IBOUND)
4-3
for a single
52
Start
Starting heads (STRT) are the heads at
the beginning
of the simulation.
Set New
Heads (HNEW)
Equal to
STRT
New Heads (HNEW) are the latest
estimate of the heads at the end of the
current time step. Each iteration
produces a new estimate.
Old Heads
beginning
They are,
at the end
I
I
Set Old
Heads (HOLD)
Equal to
HNEW
Use HOLD and
HNEW to
Formulate
Equations
I
(HOLD) are the heads at the
of the current time step.
therefore, equal to the heads
of the previous time step.
v
Solve Equations
for New
Estimate of
HNEW
(-xi--)
Figure 20.-Flow
of head distributions
4-4
during a simulation.
I
1
calculate
drawdown,
and some later
the difference
between the starting
head distribution.
Discretization
Simulation
which
all
time
steps
time
external
steps
is divided
stresses
period,
the time
21.
step multiplier,
time
of each time
stress
Within
or ratio
step.
step
periods--time
steps
in turn,
each stress
period,
into
specifies
which
of the length
Using these
in the stress
intervals
are,
The user
progression.
the number of time
of the preceding
length
into
of Time
are constant--which
as shown in figure
form a geometric
stress
head distribution
terms,
it
during
divided
into
the time
the
length
of the
is to be divided,
of each time
the program
step
and
to that
calculates
the
period.
output
The primary
control
the
Output
If
the frequency
"Output
Other
output
Control
Output
items
Control
of each stress
option,
include
option
head distribution
were saved.
at which
Control"
output
also
the end of a stress
heads are printed
a major
option
or saved on disk
contained
drawdowns and volumetric
provides
for
storage
The user may
budget
or printing
terms;
output
option
and the overall
volumetric
budget
are printed
printed
22 shows an example of a volumetric
period.
4-5
if
Package.
the
of these
a default
and drawdowns are also
through
in the Basic
is not utilized,
period,
Figure
of the program is head distribution.
terms.
is invoked--the
starting
budget
at the end
heads
printout
for
Well 1
Well 2
c
5 .o
;ii
$7
ZE
iii
100 GPM
0 GPM
Well 1
Well 2
Stress
Period 1
100 GPM
400 GPM
Well 1
Well 2
Stress
Period 2
)
0 GPM
400 GPM
Stress
Period 3
6
5 c
1
Time
Step 1
4)
Time
Step 2
Delt (1) = PERLEN
Time
Step 1
* (l-TSMULT)
1 - TSMULT*
Delt (m + 1) = TSMULT*
Time
Step 1
Time
Step 2
Specified
Time
Step 4
by User
PERLEN..
. . . . . . . . Length of Stress Period
TSMULT
. . . . . . . . . .Time Step Multiplier
NSTP . . . . . . . . . . . . . Number of Time Steps
in Stress Period
* NSTP
Delt (m)
Calculated
Delt(m).
Figure 21.- Division
Time
Step 3
by Program
. . . . . . . . . . Length
of Time Step m
of simulation time into stress periods and
time steps.
4-6
o--m
5:
zl
..
5
0
Y
I
s;
I
zi:
gi
w
ocl
-
8
d
I
i
I
ii
I-
a
4-7
Budget Calculations
The calculation
the
calculation
of budget
explained
in Chapter
of flow,
are calculated
one-dimenisonal
which
of the
array
sums and prints
volumetric
entries
, which
in the flow
the
budget
The array
budget
correspond
component
Package
is carried
and the summation
3 the entries
VBVL.
in the Basic
out in two parts,
of those
to individual
packages
and stored
VBVL is passed to the
entries.
4-8
entries.
Basic
As
components
in the
Package
Basic
Input for the Basic
from unit 1 as specified
number for BAS input can
computer.
Input for the
specified
in IUNIT( 12).
Information
for
Packaae Inout
(BAS) Package except for output control
is read
in the main program.
If necessary,
the unit
be changed to meet the requirements
of a particular
output control
option is read from the unit number
the Basic
Package must be submitted
in the following
order:
FOR EACH SIMULATION
BASlDF
1. Data:
Format:
HEADNG(32)
20A4
2. Data:
Format:
HEADNG (continued)
12A4
3. Data:
Format:
NLAY
110
NROW
110
NCOL
110
NPER
110
ITMUNI
110
4. Data:
IUNIT( 24)
Format: 2413
(BCF wEL DRN RIV EVT xxx GHB RCH SIP xxx SIR oc)
BASlAL
5. Data:
Format:
IAPART
110
ISTRT
110
BASlRP
6. Data:
Module:
NOTE:
IBOUND(NCOL,NROW)
U2DINT
(One array for each layer
7. Data:
Format:
HNOFLO
FlQ.0
8. Data:
Module:
Shead(NCOL,NROW)
U3DREL
(One array for each layer
in the
grid)
in the
grid)
IBOUND and Shead are treated
as three-dimensional
arrays in the
program.
However, the input to each of these arrays is handled
a series of two-dimensional
arrays,
one for each layer in the
grid.
4-9
as
FOR EACH STRESS PERIOD
BASlST
9. Data:
Format:
PERLEN
F10.0
NSTP TSMULT
110
F10.0
Explanation
Input
of Fields
Used in
Instructions
HEADNG--is the simulation
title
that is printed
on the printout.
It may
be up to 132 characters
long; 80 in the first
record and 52 in
the second.
Both records must be included
even if they are blank.
NLAY--is
the
number of model layers.
NROW--is the
number of model rows.
NCOL--is
the
number of model columns.
NPER--is
the
number of stress
periods
in the
simulation.
(It is used only for printout
ITMUNI--indicates
the time unit of model data.
It does not affect model calculations.)
of elapsed simulation
time.
o-
3- hours
4 - days
undefined
1 - seconds
2 - minutes
5 - years
The unit of time must be consistent
for all data values that involve
For example, if years is the chosen time unit,
stress-period
length,
must all be expressed using years
step length,
transmissivity,
etc.,
Likewise,
the length unit must also be consistent.
their
time units.
4-10
time.
timefor
IUNIT--is
a 24-element
table of input units for use by all major options.
Only 10 elements (l-5,
7-9, 11, and 12) are being used.
Element 6
has been reserved for a transient
leakage package, while element 10
has been reserved for an additional
solver,
both on the assumption
that such packages will
be added to the model in the future.
Elements 13-24 are reserved for future major options.
MAJOR
IUNIT
OPTION
LOCATION
Block-Centered
Flow Package
Well Package
Drain Package
River Package
Evapotranspiration
Package
Reserved for Transient
Leakage Package
General-Head Boundary Package
Recharge Package
SIP Package
Reserved for additional
solver
SSOR Package
Output Control Option
1
2
3
4
6”
7
8
1;
11
12
If
IUNIT
-< 0, the corresponding
If
IUNIT
> 0, the corresponding
major option is being used and
data for that option will
be read from the unit
number contained
in IUNIT(
The unit numbers in
IUNIT should be integers
from 1 to 99.
Although
the same number may be used for all or some of the
it is recommended that a different
major options,
Printer
number be used for each major option.
output is assigned to unit 6 (unless it is changed
to meet computer requirements).
That unit number
should not be used for any other input or output.
The user is also permitted
to assign unit numbers
Those numbers should be different
for output.
from those assigned to input.
The Basic Package
reads from unit 1 (unless it is changed to meet
It is permissible
but
computer requirements).
unwise to use that unit for other major options.
IAPART--indicates
whether
array
major
BUFF is separate
option
is
from array
not being
used.
RHS.
If
IAPART = 0, the arrays BUFF and RHS occupy the same space.
This
This option should be used
option conserves space.
unless some other package explicitly
says otherwise.
If
IAPART f 0, the arrays BUFF and RHS occupy different
space.
This
option is not needed in the program as documented in
It may be needed for packages yet
this publication.
to be written.
4-11
ISTRT--indicates
whether starting
heads are to be saved.
If they are saved,
they will
be stored in array STRT. They must be saved if drawdown
is calculated.
If
ISTRT = 0, starting
heads are not saved.
If
ISTRT f 0, starting
heads are saved.
IBOUND--is
the
boundary
array.
If
IBOUND(I,J,K)
< 0, cell
I,J,K
has a constant
If
IBOUND(I,J,K)
= 0, cell
I,J,K
is inactive
If
IBOUND(I,J,K)
> 0, cell
I,J,K
is variable-head.
head.
(no-flow).
HNOFLO--is the value of head to be assigned to all inactive
cells
(IBOUND = 0) throughout
the simulation.
Since heads at inactive
cells
are unused, this does not affect
model results
but serves
to identify
inactive
cells when head is printed.
This value is
also used as drawdown at inactive
cells
if the drawdown option is
Even if the user does not anticipate
having inactive
cells,
used.
a value for HNOFLO must be submitted.
Regardless of whether starting
of the simulation.
values must be input to initialize
the solution.
Shead--is
head at the start
head is saved, these
PERLEN--is the
period.
NSTP--is
the
length
of a stress
number of time
TSMULT--is the multiplier
of the first
time
by the relation
steps
period.
It is specified
in a stress
for
each stress
period.
for the length of successive
time steps.
The length
step DELT(l) is related
to PERLEN, NSTP and TSMULT
DELT( 1) = PERLEN(l-TSMULT)/(l-TSMULT**NSTP).
4-12
s-l
r-l
m
r(rlrld
N
N
4-13
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Outout
Control
1nm.A
Output Control is a major option separate from the rest of the Basic
Package.
Input to Output Control is read from the unit specified
in IUNIT(12).
If IUNIT(12) is zero, no output control
data are read, and default
output
control
is used.
Under the default,
head and total
budget are printed
at
the end of every stress period.
Additionally,
if starting
heads are saved
(ISTRT is not 0), drawdown is printed
at the end of every stress period.
The default
printout
format for head and drawdown is 10611.4.
All printer
If
necessary,
the
output goes to unit 6 as specified
in the main program.
unit number for printer
output can be changed to meet the requirements
of a
particular
computer.
FOR EACH SIMULATION
BASlRP
1.
Data:
Format:
IHEDFM
110
IDDNFM
110
IHEDUN
110
IDDNUN
110
FOR EACH TIME STEP
BASlOC
2.
Data:
Format:
INCODE IHDDFL
110
110
IBUDFL
110
ICBCFL
110
3.
Data:
Format:
Hdpr
110
Hdsv
110
Ddsv
110
Ddpr
110
(Record 3 is read 0, 1, or NLAY times,
depending on the value of INCODE.)
Explanation
Input
IHEDFM--is
a code for
the
format
of Fields Used in
Instruct ions
in which
heads will
be printed.
IDDNFM--is a code for the format in which drawdowns will
be printed.
Format
A positive
codes have the same meaning for both head and drawdown.
format code indicates
that each row of data is printed
completely
This means that when there are more
before starting
the next row.
columns in a row than will
fit
on one line,
additional
lines are used
This format is called the wrap format.
as required
to complete'the
row.
A negative
format code indicates
that the printout
is broken into strips
where only that number of columns that will
fit
across one line are
As many strips
are used as are required
to print
printed
in a strip.
This
format
is
called
the
strip
format.
The
the entire
model width.
absolute
value of the format code specifies
the printout
format as
follows.
4-14
0
1
2
3
4
5
6
IHEDUN--is the unit
on disk.
7 - (2OF5.0)
8 - (20F5.1)
9 - (20F5.2)
- (10611.4)
- (11610.3)
- (9613.6)
-
10 - (20F5.3)
11 - (20F5.4)
(15F7.1)
(15F7.2)
(15F7.3)
(15F7.4)
12 - (10611.4)
number to which
heads will
IDDNUN--is the unit number to which
saved on disk.
INCODE--is the head/drawdown ouput
records in input item 3.
be written
drawdowns will
be written
It determines
code.
if
INCODE < 0, layer-by-layer
specifications
from the
are used.
Input item 3 is not read.
If
INCODE = 0, all
will
If
INCODE > 0, input
IHDDFL--is
If
item
3 will
a head and drawdown output
IHDDFL = 0, neither
consist
if
are saved
they
are
the number of
If
layers are treated
the
consist
of one record.
they
same way.
last
time
steps
Input
item
3
of one record
for
each layer.
flag.
heads nor drawdowns will
be printed
or saved
on disk.
If
IBUDFL--is
IHDDFL # 0, heads and drawdowns will
be printed
or saved according
to the flags for each layer specified
in in$ut item 3.
a budget
print
flag.
If
IBUDFL = 0, overall
volumetric
budget
will
not be printed.
If
IBUDFL # 0, overall
volumetric
budget
will
be printed.
(Note that the overall
volumetric
budget will
always be printed
at
the end of a stress period,
even if the value of IBUDFL is zero.)
ICBCFL--is
a cell-by-cell
flow-term
flag.
If
ICBCFL 7 0, cell-by-cell
If
ICBCFL # 0, cell-by-cell
flow terms are printed
or recorded
depending on flags set in the component of flow
IWELCB, IRCHCB, etc.
i.e.,
flow
4-15
terms
are not saved or printed.
on disk
packages,
Hdpr--is
the output
flag
for
head printout.
If
Hdpr = 0, head is not printed
for
If
Hdpr # 0, head is printed
the corresponding
Ddpr--is
the output
flag
for
for
Ddpr = 0, drawdown is
If
Ddpr # 0, drawdown is printed
the output
flag
for
not printed
for
Hdsv = 0, head is not saved for
If
Hdsv f 0, head is saved for
the output
flag
for
for
the corresponding
the
corresponding
layer.
layer.
head save.
If
Ddsv--is
layer.
drawdown printout.
If
Hdsv--is
layer.
the corresponding
the corresponding
the corresponding
layer.
layer.
drawdown save.
If
Odsv = 0, drawdown is
not saved for
If
Ddsv f 0, drawdown is saved for
4-16
the
the corresponding
corresponding
layer.
layer.
Module Documentation
The Basic
submodules.
Package (BASl)
The modules
for
consists
the
Basic
of eight
Packaae
primary
modules
and five
are:
Primary
Modules
BASlDF
Defines
and sets
key model parameters.
BASl AL
Allocates
space for
Package.
BASlRP
Reads and prepares
BASIST
Reads timing
information
and initializes
needed to calculate
the length of time
BASl AD
Calculates
the length of time
elapsed time, and intializes
of each time step.
BASl FM
Clears
BASlOC
Sets flags which indicate
or recorded on disk.
when data
BASlOT
Prints
and records heads,
volumetric
budget.
drawdowns,
data
arrays
data
accumulators
for
used by the
the
Basic
Basic
Package.
variables
steps.
steps, accumulates
heads at the beginning
RHS and HCOF.
should
be printed
and overall
Submodules
SBASlD
Calculates,
SBASlH
Writes
SBASlI
Initializes
SBASlT
Prints
SBASlV
Calculates
writes,
and records
and records
the
a time
drawdown distribution.
head distribution.
Output
Control
System.
summary.
and prints
4-18
the
overall
volumetric
budget.
Narrative
The BASlDF module defines
the
following
Print
3-.
Read and print
3.
Read the
the
number of layers,
4.
Print
5.
Select
major
option.
option
will
counter
input
table.
If
indicates
does so in
that
into
columns,
and stress
IUNIT entry
option
is
major
the codes).
the total
4-19
periods.
all
major
options.
to a particular
option
is to be used
corresponding
not going
of
input
to that
to the major
to be used,
the
to zero.
time
RETURN.
units
units.
number from which
is set equal
(ISUM) and calculate
the time
and units
is used when printing
for
a certain
the
the total-elapsed
but
has been assigned
is the unit
a major
periods,
the time
numbers IUNIT for
Each entry
integer
stress
instructions
rows,
unit
specifies
IUNIT element
Initialize
input
a message showing
The integer
be read.
(see the
the
The user
corresponding
8.
and print
a positive
columns,
model calculations
number of layers,
a 24-element
by putting
array
time
Read and print
option.
7.
the
rows,
ITMUNI is a code which
the amount of elapsed
major
It
a heading.
It does not affect
model data.
IUNIT is
key model parameters.
name of the program.
code ITMUNI.
' 6.
and sets
order:
1.
of time
Module BASlDF
for
counter
(TDTIM) and the storage-
number of cells.
Flow Chart
for
Module BASlDF
ITMUNI is a code which
indicates
units
of time used in the input data.
This code is only used to print
a
table showing elapsed time in seconds,
It
minutes,
hours, days, and years.
is not used in forrmlating
or solving
the finite-difference
equation.
IUNIT is a table that indicates
which
major options
are to be used and the
unit numbers from which input is to
be read.
TOTIM is an accumulator
in which
It
simulation
time is stored.
incremented
at each time step.
total
READ AND PRINT
A HEADING
is
ISUM is a location
counter for the
first
unallocated
space in the X
It
is
incremented
by each
array.
module in the Allocate
Procedure.
READ # OF LAYERS,
ROWS, COLUMNS,
STRESS PERIODS,
AND ITMUNI
PRINT # OF LAYERS,
ROWS, COLUMNS,
AND STRESS PERIODS
SELECT AND PRINT
MESSAGE SHOWING
TIME UNITS
READ IUNIT TABLE
4-20
B
1
c
C-----VERSION
1513 12MAY1987 BASlDF
******************************************************************
C
C
DEFINE KEY MODEL PARAMETERS
******************************************************************
C
C
C
SPECIFICATIONS:
C
B
SUBROUTINE BAS~DF(ISUMIHEADNG~NPERIITMUNI~TOTIM,NCOL~NRCW~
NLAY,NODES,INBASIIOUT,IUNIT)
CHARACTER*4 HEADffi
DIKNSION HEADNG(32)rIUNIT(24)
------------------L-___________________L----------------
&------PRINT
THE NA~~E0F x-iE pRcGFaw.
WRITE(IOUT,l)
1 FOFIMAT(lH1,20X,‘U. S. GEOLOGICAL SURVEYMODULAR’,
1
’ FINITE-DIFFERENCE GROUND-WATERMODEL’)
c
c2--READ AND PRINT A HEADING.
READ(INBAS,Z) HEADNG
2 FOF&‘AT(2OA4)
WRITE(IOUTs3) HEADNG
3 FORMAT(lH0’32A4)
C
C3------READ
NUMBEROF LAYERStROWS,COLUMNS,STRESSPERIODS AND
B------UNITS
OF TIE CODE.
READ(INBAS,4) NLAY,NRCW,NCOL,NPERtITMUNI
4 FOf@lAT(8110)
c
C4------PRINT
# OF LAYERS, ROWS, COLUMNSAND STRESS PERIODS.
WRITE(IOUT,5) NLAY,NROllrNCDL
5 FORMAT(lX,I4,’
LAYERS’rIlO,’
RQVS’rIlO,’
COLUMNS’)
WRITE(IOUT,6) NPER
6 FORMAT(lX,I3,’
STRESS PERIOD(S) IN SIMULATION’)
C
C5------SELECT
AND PRINT A MESSAGESHOWINGTIME UNITS.
IF(ITMUNI.LT.0
.OR. ITMUNI.GT.5) ITMUNI=O
GO TO (10,20r30.40,50)
rITMUN1
WRITE(IOUT,9)
9 FORMAT(lX,‘MDDEL TIME UNITS ARE UNDEFINED’)
GO TO 100
10 WRITE(IOUT,ll)
11 FORMAT(lX,‘MODEL TIME UNIT IS SECONDS’)
GO TO 100
20 WRITE(IOUT’21)
21 FORMAT(lX,‘MODEL TIME UNIT IS MINUTES’)
GO TO 100
30 WRITE(IOUT,31)
31 FORMAT(lX,‘MODEL TIRE UNIT IS HOURS’1
GO TO 100
40 WRITE(IOUT,41)
41 FORMAT(lX,‘MODEL TIRE UNIT IS DAYS’)
GO TO 100
50 WRITE(IOUT,Sl)
51 FORMAT(lX,‘MODEL TIME UNIT IS YEARS’ 1
c
C&--m READ 6 PRINT INPUT UNIT NUMBERS(IUNIT) FOR MAJOR OPTIONS.
100 READ(INBAS,lOl)
IUNIT
101 FORJdAT(2413)
WRITE(IOUT,lOZ)
(1,1=1,24),IUNIT
102 FORMAT(lHO,‘I/O UNITS:‘/lXt’ELEMENT
OF IUNIT:‘r2413,
1
/1x, ’
I/O UNIT:‘,24131
C
C7---INITIALIZE
TOAL ELAPSED TIME COUNTERSTORAGEARRAY COUNTER
C7---AND CALCULATE NUMBEROF CELLS.
TOTIM=D.
ISUHl
NODES=NCOL*NROW*NLAY
c
C&-----RETURN
RETURN
END
4-21
List
Variable
of Variables
for
Module BASlDF
Definition
Range
I
Module
Index.
I NBAS
Package
Primary unit number from which input to the
Package will
be read.
INBAS = 1.
IOUT
Global
Primary
ISUM
Global
Index number of the lowest element in the X array which
has not yet been allocated.
When space is allocated
for an array,
the size of the array is added to ISUM.
ITMUNI
Package
Code for
unit
number for
time
units
all
for
printed
this
output.
BASl
IOUT = 6.
problem:
o-
undefined
seconds
2 - minutes
3- hours
4 - days
5 - years
l-
IUNIT
Module
DIMENSION (24), Primary
major options.
input
HEADNG
Package
DIMENSION (32),
the problem.
printed
NCOL
Global
Number of columns
NLAY
Global
Number of layers
NODES
Global
Number of cells
NPER
Global
Number of stress
NROW
Global
Number of rows in the
TOTIM
Package
Elapsed time
Heading
in the
in the
(nodes)
4-22
for
on output
each of the
to identify
grid.
grid.
in the
periods.
in the
units
grid.
simulation.
finite-difference
grid.
Narrative
for
Module BASlAL
Module BASlAL allocates
space for data arrays used by the BAS Package.
Space is al located
for HNEW, HOLD, IBOUND, CR, CC, CV, HCOF, RHS, DELR, DELC,
and IOFLG. Space is allocated
for the STRT array if the user intends to
calculate
d rawdown.
Space is also allocated
for an array called BUFFER,
which is used to accumulate various data arrays such as drawdown and cellby-cell
flow terms when they are being calculated
prior to output.
To
conserve space, the user may specify
that arrays BUFFER and RHS should
occupy the same space.
The number of spaces allocated
for each of the arrays--HOLD,
IBOUND, CR,
CC, CV, HCOF, RHS, STRT, and BUFFER is equal to the number of cells
in the
grid.
Twice that number of spaces is reserved for HNEW because it is double
precision.
DELR and DELC are allocated
a number of spaces equal to the
number of rows and columns, respectively.
IOFLG (an array of flags used by
Output Control)
is allocated
a number of spaces equal to four times the
number of layers.
Module BASlAL performs
1.
Print
its
functions
a message identifying
in the
following
order:
the package.
2. Read and print
flags IAPART and ISTRT which indicate
whether the
BUFFER and RHS arrays should occupy the same space and whether the start
array (STRT) should be saved.
3.
Store
in
Calculate
space.
4. Allocate
DELC, and IOFLG.
location
number of cells
ISOLD the
the
space for
in the X array
in the grid.
of the
first
unallocated
HNEW, HOLD, IBOUND, CR, CC, CV, HCOF, RHS, DELR,
If the user specified
that BUFFER and RHS should share space
(IAPAk
equal to zero)
set the address of the BUFFER (LCBUFF) equal to
allocate
separate space for BUFFER.
the address of RHS(LCRk);
otherwise,
6.
allocate
If the user specified
space for STRT.
7.
Print
8.
RETURN.
that
the starting
array
must be saved,
the amount of space used by the BAS Package.
4-23
Flow Chart
for
Module BASlAL
IAPART is a flag specified
by
the user which, if equal to
zero, indicates
that the
arrays BUFFER and RHS should
overlay
each other.
BUFFER is an array in which
data is temporarily
stored
while it is being gathered
for printing.
I
PRINT A MESSAGE
IDENTIFYING
THIS PACKAGE
I
RHS is an array which contains
the right
hand side of each
finite-difference
equation.
READ AND PRINT
FLAGS IAPART
AND ISTRT
ISTRT is a flag specified
by
If it is not
the user.
equal to zero, starting
heads are to be saved.
STORE ISUM IN
ISOLD. CALCULATE
# OF CELLS IN GRID
ISOLD marks the location
of
ISUM before any space was
allocated
by this module.
After
all space is allocated,
ISOLD is subtracted
from
ISUM to calculate
the amount
of space allocated
by this
module.
ALLOCATE SPACE
FOR EACH ARRAY.
ISUM is a counter which contains
the location
of the first
unallocated
element in the
Each time space is
X array.
allocated
for an array;
the
value in ISUM is incremented
by the size of the array.
7
r-l
PRINT THE AMOUNT
OF SPACE USED
4-24
c
Cl---PRINT
A KSSAGEIDENTIFYINOTHEPACKAGE.
uRITE(IOur,1)INBAS
1 FOFMAT(lHO.'BASl- BASICMDDEL PACKABE, VERSION1, 9/l/87',
2’ INPUTREAD FRCU UNIT’,131
C
C2----READ
C2------FLAG
6 PRINT FLAB IAPART (RHS 6 BUFFER SHARE SPACE?) AND
ISTRT (SHCULD STARTINGHEADS BE SAVED FOR MAWDCUN?)
READ(INBAS,2)IAPART,ISTRT
2 FORMAT(2110)
IF(IAPART.EQ.0) WRITE(IOUT,3)
3 FOFMAT(lX,‘ARRAYS
FOiS AND BUFF WILL SHARE EMORY.‘)
1FtISTRT.NE.D) WRITE(IDUT,4)
4 FOIMAT(lX,‘START
HEAD WILL BE SAVED’)
IF(ISTRT.EQ.0) URITE(IOUT,S)
5 FORMAT(lX.‘START HEAD WILL NOT BE SAVED’,
1
’ -- DRAWDCMNCANNOT BE CALCULATED’ )
C
Q----STORE,IN
ISaD,
ISOLD=ISUM
LOCATION OF FIRST UNALLOCATED SPACEIN
NRCL=NRCW*NCOL”NLAY
c
C4------ALLOCATE
SPACE FOR ARRAYS.
LCHNEW=ISUM
ISlJM=ISUM+2*NRCL
LCHOLD=ISUM
1sUN=1suMwRCL
LCIBOU=ISUN
'ISUM=ISUFHNRCL
LCCR=ISUM
ISUM=ISuMcNRCL
LCCC=ISUM
ISUM=ISUM+NRcL
LCCv=IsUM
ISUM=ISUM+NR~*NCOL*(NLAY-1)
LCliCOF=ISUM
IsUM=IslJMtNRCL
LCRHS=ISlM
ISUM=ISUM+NRCL
LCDELRISUM
ISUKISUM+NCOL
LCDELOISUM
ISUM=ISUM+NROW
LCIOFL=ISUM
ISUK;ISUM+NLAY*4
Es------IF
BUFFER AND RRS SHARE SPACE THEN LCBUFF*LCRHS.
LCBUFPLCRHS
IF(IAPART.EQ.0) GOTO 50
LCBUFF=ISUH
ISUKISUMeNfiCL
ii6------IF STRTWILL BE SAVEDMEN ALLaTE SPACE.
50 LCSTRT=ISUM
IF(ISlRT.NE.0) ISUKISUMtNRCL
ISP=ISU~ISOLD
C
C7-----PRINT AHOUNT OF SPACE USED.
WRITE(IOLJT,6)ISP
6 FOfMAT(lX,IS,' ELEMENTS IN X ARRAY ARE USED BY BA.3’)
1sUM1=1sUM-1
WRITE(IOUT,7)ISlJMl.LENX
7 FDMAT(lX,I8,' ELEKNTSOF X ARRAYUSEDOUTOF',181
IF(ISUHl.GT.LENX) WRITE(IOUT.8)
8 FOFIMAT(1X, '
*“*X ARRAY MUST BE DIMtENSIONED
LARBET(r**O
:
C8------RETURN
RETURN
C
4-25
X.
List
Variable
Ranqe
IAPART
Module
I NBAS
Package
IOUT
ISOLD
Global
Package
ISP
I STRT
Module
Package
ISUM
Global
I SUM1
Module
LCBUFF
LCCC
LCCR
LCCV
LCDELC
LCDELR
LCHCOF
LCHNEW
LCHOLD
LCIBOU
LCIOFL
LCRHS
LCSTRT
LENX
Package
Package
Package
Package
Package
Package
Package
Package
Package
Package
Package
Package
Package
Global
NCOL
NLAY
NRCL
NROW
Global
Global
Module
Global
of Variables
for
Module BASlAL
Definition
Flag set by user.
= 0, arrays RHS and BUFFER will
share space in
the X array.
f 0, arrays RHS and BUFFER will
not share space
in the X array.
Primary unit number from which input to the BASl
Package will
be read.
INBAS = 1.
Primary unit number for all printed
output.
IOUT = 6.
Before this module allocates
space, ISOLD is set equal
ISOLD is subtracted
to ISUM. After allocation,
from ISUM to get ISP, the amount of space in the X
array allocated
by this module.
Number of words in the X array allocated
by this module.
Flag.
f 0, starting
heads will
be saved so that drawdown
can be calculated.
= 0, starting
heads will
not be saved.
Index number of the lowest element in the X array which
has not yet been allocated.
When space is allocated
for an array,
the size of the array is added to ISUM.
Index number of the last element of the X array allocated
by this module.
Location
in the X array of the first
element of array BUFF.
Location
in the X array of the first
element of array CC.
Location
in the X array of the first
element of array CR.
Location
in the X array of the first
element of array CV.
Location
in the X array of the first
element of array DELC.
Location
in the X array of the first
element of array DELR.
Location
in the X array of the first
element of array HCOF.
Location
in the X array of the first
element of array HNEW.
Location
in the X array of the first
element of array HOLD.
Location
in the X array of the first
element of array IBOUND.
Location
in the X array of the first
element of array IOFLG.
Location
in the X array of the first
element of array RHS.
Location
in the X array of the first
element of array STRT.
Length of the X array in words.
This should always be
equal to the dimension of X specified
in the MAIN program.
Number of columns in the grid.
Number of layers in the grid.
Number of cells
in the grid.
Number of rows in the grid.
4-26
Narrative
for
Module BASlRP
This module reads and prepares data for the BAS Package.
It reads the
boundary array (IBOUND) and the starting-head
array (HNEW), sets the heads in
no-flow
cells to a user-supplied
value (for printout
convenience),
initializes
the starting-head
array (STRT) and the volumetric-budget
accumulators
(VBVL),
and sets up the Output Control System.
The IBOUND codes are as follows.
Code
,
Status
negative
zero
positive
*
constant
inactive
variable
head
(no-flow)
head
The user must specify
a head value HNOFLO that he wants printed
for no-flow
(inactive)
cells.
That value is only used during printing
and makes inactive
cells
stand out on the listing
(e.g.,
0.0 and 9999.99).
Recall that initial
heads are needed for each time step; however, they
must be read for only the first
time step, at which time they are called the
starting
heads.
For subsequent time steps, the ending heads of the preceding
time step will
be used as the initial
heads of the current
time step.
The
starting
heads are read in single
precision
into the array HOLD and converted
to double precision
as they are moved into HNEW.
Module BASlRP performs
its
functions
in the following
1.
Print
2.
Read the
3.
Read and print
4.
Read the
starting
heads into
5. Copy the
HOLD into HNEW.
starting
heads (and convert
the
simulation
title
and calculate
the
order:
number of cells
in a
layer.
6.
If
the
7.
Initialize
8.
Call
9. .
RETURN.
boundary
starting
array
the head value
to be printed
array
heads must be saved,
volumetric-budget
submodule
(IBOUND).
for
no-flow
cells
HOLD.
to double
precision)
from
copy them from HOLD to STRT.
accumulators.
SBASlI to initialize
4-27
(HNOFLO).
the Output
Control
System.
Flow Chart
for
Module BASlRP
HNOFLO is a value assigned to head in
It makes
inactive
(no-flow)
cells.
those cells
stand out in listings
of
heads.
HNEW is an array containing
the latest
estimates
of heads.
It starts
each
time step with heads calculated
for
the end of the previous
time step.
It is changed at each iteration
until
the last iteration
when it contains
the heads at the end of the time step.
HOLD is an array containing
heads at the
beginning
of the current
time step.
At the beginning
of a time step, HOLD
AND HNEW contain
identical
values.
HNEW changes from one iteration
to the
next; HOLD does not.
OUTPUT CONTROL is part of the Basic
Package which gives the user the
ability
to control
the kind and
amount of information
that is
printed
by the program.
UEDINT is a utility
two-dimensional
module which
integer
arrays.
CALL MODULE
UPDINT TO READ
BOUNDARY ARRAY
1
FOR EACH LAYER
reads
IF STARTING
HEADS ARE TO
BEc%-D*
HOLD TO START
INITIALIZE
THE ;;l--td;TRIC
ACCUMULATORS
CALL MODULE
SBASlI TO SET
UP OUTPUT CONTROL
4-28
.
SUBROUTINE BASlRP(IBOUND,HNEWtSTRTtHOLD,ISTRT,INBAS,
HEADNGINCOL~NROW,NLAY~NODES,VBVL~IOFLG,INOC,IHEDFN,
2
IDDNFM,IHEDUN,IDDNUN,IOUT)
1
C-----VERSION 1628 15MAY1987
BASlRF
****~*************************************************************
C
c
READ AND INITIALIZE BASICMODEL ARRAYS
Y***((t****lt**************~*********~*~~***********~**~********~~**
:
C
SPECIFICATIONS:
CHARACTER*4 HEADNG,ANAME
DOUBLE PRECISION
HNEW,HNOFLO
DIMENSION
HNEW(NODES),IBOUND(NODES)rSTRT(NODES),HOLD(NCDES),
1
ANAME(6r2)rVBVL(4,20)rIOFLG(NLAY,4),HEADNG(32)
C
DATA ANAME~lrl~,ANAME~2rl~rANAME~3rl~rANAME~4,1~,ANAME~Srl~,
‘,’
BD’r’UNDA’r’RY
A’r’RRAY’/
ANANE(6,l) /’
1,’
DATA ANAME(l,2)rANAME(2,2)rANAME(3r2),ANAME(4,2),ANAME(5,2)r
1 ANAME(6,2)/'
1,'
1,'
','INIT'r'IAL
‘,‘HEAD’/
1
cCl------PRINT
SIMULATION
TITLE. CALCULATE # OF CELLS IN A LAYER.
WRITE(IOUT,l) HEADNG
1 FORMAT(lH1,32A4)
NCR=NCOL*NROW
C
C2------READ
BOUNDARYARRAY(IBOUND) ONE LAYER AT A TIME.
DO 100 K=l,NLAY
KK=K
LOC=l+(K-l)*NCR
CALL U2DINT(IBCUND(LOC),ANAME(l,l)rNROW,NCCL,KK,INBAS,IOUT)
100 CONTINUE
------READ ANDPRINTHEADVALUETO BE PRINTED FOR NO-FLOW CELLS.
READ(INBAS,Z) TMP
2 FORMAT(FlO.0)
HNOFLO=TMP
WRITE(IOUT,3)TMP
3 FO~AT(lHOr’ADUIFER
HEAD WILL BE SET TO ‘rlPGll.5,
1
’ AT ALL NGFLON NODES (IBOUND=O).‘)
&------READ
STARTING HEADS.
DO 300 K=l,NLAY
KK=K
LOC=l+(K-l)*NCR
CALL U~DREL(HOLD(LCC)~ANAME(~~~)~NR~IV~NCOL,KKIINBAS,IOUT)
300 CONTINUE
C
c5------COPY INITIAL HEADS FROMHOLD TO HNEW.
DO400 I=l,NODES
HNEW(I)=HOLD(I)
IF(IBOUND(I).EQ.O) HNEW(I)=HNOFLO
400 CONTINUE
C
(X------IF STARTING HEADS ARE TO BE SAVED THEN COPY HOLD TO STRT.
IF(ISTRT.EQ.0) GOTO 590
DO500 I=l,NODES
STRT(I)=HOLD(I)
500 CONTINUE
C
C7------INITIALIZE
VOLUMETRIC BUDGET ACCUMULATORS
TO ZERO.
590 DO 600 I=1120
DO 600 J=lr4
VBVL(J,I)=O.
600 CONTINUE
&------SET
UP OUTPUT CCNTRDL
CALLSBASlI(NLAY,ISTRT,iOFLG,INOC,IOUT,IHEDFM,
1
IDDNFM,IHEDUN,IDDNUN)
&----~~RN
1000 RETURN
END
4-29
List
Variable
Module
Package
HNEW
Global
HNOFLO
Module
HOLD
Global
I
I BOUND
Module
Global
I DDNFM
IDDNUN
Package
Package
I HEDFM
I HEDUN
Package
Package
INBAS
Package
INOC
Package
I OFLG
Package
I OUT
I STRT
Global
Package
J
Module
Module
Module
LOC
NCOL
NCR
NLAY
NODES
NROW
STRT
TMP
VBVL
Module
Global
Module
Global
Global
Global
Package
Module
Global
for
Module BASlRP
Definition
Range
ANAME
HEADNG
K
KK
of Variables
Label for printout
of input array.
DIMENSION (32), Heading printed
on output to identify
problem.
DIMENSION(NCOL,NROW,NLAY), Most recent estimate of
HNEWchanges at each iteration.
head in each cell.
User specified
value for head in cells which are inactive
at the start
of simulation.
DIMENSION (NCOL,NROW,NLAY), Head at the start
of the
current
time step.
Index.
DIMENSION(NCOL,NROW,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
Code for format in which drawdown should be printed.
Unit number on which an unformatted
record containing
drawdown should be recorded.
Code for format in which head should be printed.
Unit number on which an unformatted
record containing
head should be recorded.
Primary unit number from which input to BASl Package
INBAS = 1.
will
be read.
Unit number from which input to output control
option
will
be read.
DIMENSION (NLAY,4),
Flags to control
printing
and
recording
of head and drawdown for each layer.
(NLAY ,l) f 0, heads will
be printed.
(NLAY,E) # 0, drawdown will
be printed.
(NLAY,3) f 0, heads will
be recorded.
(NLAY,l) f 0, drawdown will
be recorded.
Primary unit number for all printed
output.
IOUT = 6.
Flag.
f 0, starting
heads will
be saved so that drawdown
can be calculated.
= 0, starting
heads will
not be saved.
Index.
Index.
Temporary variable
set equal to K. KK‘is used as an
actual argument in subroutine
calls
to avoid using
the DO loop variable
K as an argument, which causes
problems with some compilers.
Pointer
to location
in an array for a specific
layer.
Number of columns in the grid.
Number of cells
in a layer.
Number of layers in the grid.
Number of cells
(nodes) in the finite-difference
grid.
Number of rows in the grid.
DIMENSION (NCOL,NROW,NLAY), Starting
head.
Single-precision
temporary
storage place for HNOFLO.
DIMENSION (4,20),
Entries
for the volumetric
budget.
For flow component N, the values in VBVL are:
(l,N)
Rate for current
time step into the flow field.
(2,N) Rate for current
time step out of the flow field.
(3,N) Volume into the flow field
during simulation.
(4,N) Volume out of the flow field
during simulation.
4-30
B
Narrative
for
Module BASlST
Module BASlST reads timing
information
for a stress period and
initializes
variables
used to calculate
the length of time steps and elapsed
time.
Each stress period is divided
into time steps which form a geometric
progression
(for a stress period,
there is a multiplier
TSMULT such that the
length of a time step is equal to TSMULT times the length of the previous
time
If the length of the stress period (PERLEN) and the number of time
step).
steps (NSTP) is known, the length of the first
time step DELT can be calculated
with the equation
DELT = (l-TSMULT)*PERLEN/(l-TSMULT**NSTP).
Note: When TSMULT is equal to one, all the time steps are the same length.
In
that case, the time-step
length is the length of the stress period (PERLEN)
divided
by the number of time steps (NSTP).
Module BASlST performs
steps'in
2.
l
its
functions
in the
following
order:
Read the length of the stress period (PERLEN) the number of time
the stress period (NSTP), and the time-step
miltiplier
(TSMULT).
Calculate
the
length
of the
first
(a)
Assume the time-step
calculate
(b)
the
If the time-step
multiplier
first
term of the geometric
3.
Print
time
multiplier
step.
is
equal
to one.
-
4.
within
5.
the timing
Initialize
the
a stress period.
(TSMULT) is not equal
progression.
to one,
information.
variable
PERTIM which
RETURN.
4-31
keeps track
of elapsed
time
Flow Chart
PERLEN is the length
of a stress
NSTP is the number of time
stress period.
steps
for
Module BASlST
period.
in a
TSMULT is a constant
which, when rmltiplied by the length of a time step,
gives the length of the next time
step.
DELT is the length of the first
time
Since
the
time
steps
form
a
step.
geometric
progression,
the formula
for calculating
DELT is:
READ PERLEN,
NSTP, AND TSMULT
DELT=(l-TSMULT)*PERLEN/(l-TSMULT**NSTP)
PERTIM is a field
in which elapsed time
during a stress period is accumulated.
During each time step, the length of
the time step is added to PERTIM.
CALCULATE THE
LENGTH OF THE
FIRST TIME STEP
PRINT PERLEN,
NSTP, TSMULT,
AND
4-32
DELT
SUBROUTINE BASlSTt NSTP, DELT, TSMULT,PERTIM, KPER, INBAS,IOUT)
C
C
C-----VERSION
C
C
C
1614 08SEP1982 BASlST
*+****************************************~***********************
SETUP TIME PARAMETERSFOR NEW TIME PERIOD
****i*************************************************************
E
SPECIFICATIONS:
-----------------------------------------------------------------C
-----------------------------------------------------------------C
C
Cl--READ LENGTH OF STRESS PERIOD, NUMBEROF TIME STEPS AND.
STEPMULTIPLIER.
Cl ------TIME
READ (INBAS,l) PERLEN,NSTP,TSMULT
1 FORMAT(F10.O,I10,F10.0)
C
c2 ------CALCULATE
THE LENGTH OF THE FIRST TIME STEP.
C
(-J2/+-ASSUME TIME STEP MULTIPLIERIS EQUAL TO ONE.
DELT=PERLEN/FLOAT(NSTP)
:2Eb ----IF
TIME STEP MULTIPLIERIS NOTONETHENCALCULATE
FIRST
c25 ----TERM OF GEOMETRIC
PROGRESSION.
IF(TSMULT.NE.1.)
DELT=PERLEN*(l.-TSMULT)/(l.-TSMULT**NSTP)
C
c3------PRINT
TIMING INFORMATION.
WRITE ( IOUT, 2 1 KPER, PERLEN, NSTP, TSMULT,DELT
2 FORMAT(lHlr51X,‘STRESS
PERIOD NO.‘rI4,‘,
LENGTH =‘rG15.7/52X
1,46(‘-‘)//52X,‘NUMBER
OF TIME STEPS =‘,I6
2//53X, ‘MULTIPLIER FOR DELT =‘rF10.3
3//50X,'INITIAL
TIME STEP SIZE =',G15.7)
C
c4------INITIALIZE
PERTIM=O.
C
PERTIM (ELAPSED
TIME WITHIN STRESS PERIOD).
c5 ------RETURN
RETURN
END
4-33
List
Variable
of Variables
Module BASlST
for
Definition
Range
DELT
Global
Length
of the current
INBAS
Package
Primary unit number from which input to the
Package will
be read.
INBAS = 1.
IOUT
Global
Primary
KPER
Global
Stress
NSTP
Global
Number of time
PERLEN
Module
Length
PERTIM
Package
Elapsed
TSMULT
Package
Multiplier
next.
unit
time
number for
period
printed
BASl
IOUT = 6.
output.
counter.
steps
of the stress
time
all
step.
during
in the current
period.
period.
the current
to get from one time
4-34
stress
stress
step
period.
length
to the
Narrative
Module BASlAD calculates
elapsed
time
for
the old
head values
Within
the
equal
a stress
progression--the
length
stress
of the
calculated
previous
step
period
to the
time
the
are copied
If
length
period
the
length
step.
of the time
step
steps
is a constant
The length
accumulates
period,
the
and sets
form a geometric
(TSMULT) times
of the first
this
for
the heads at the
time
step
the
is
the end of the
beginning
last
time
of the current
HOLD.
its
functions
is not the first
step
time
(DELT).
in the
step
following
in the
stress
Note:
The length
since
the
order:
period;-‘calculate
of the first
time
step
by BASlST.
Accumulate
the elapsed
time
Set the
heads at the
of the stress
beginning
heads at the end of the previous
4.
step,
simulation
the heads calculated
(TOTIM) and the beginning
3.
and the total
are also
into
of the time
is calculated
2.
of the time
new head values.
the
HNEW contains
Module BASlAD performs
1.
length
of each time
Those heads which
time
Module BASlAD
in module BASlST.
The array
step.
the
period,
length
for
-of this
time
RETURN.
4-35
step
beginning
period
time
of the simulation
(PERTIM).
step
(HNEW).
(HOLD) equal
to
Flow Chart
for
Module BASlAD
TOTIM is an accumulator
in which the
total
elapsed time since the
beginning
of the simulation
is
stored.
PERTIM is an accumulator
in which
total
elapsed time during the
current
stress period is stored.
the
HOLD is the head distribution
beginning
of a time step.
at the
HNEW is the head distribution
end of a time step.
at the
(K)
I
CALCULATE
LENGTH OF
TIME STEP
YES
2
I
ADD TIMESTEP LENGTH
TO TOTIM
AND PERTIM
EQUAL TO HNEW
c
RETURN
4-36
4
B
SUBROUTINE
BAS~AD(DELT, TSMULT,TOTIM, PERTIM, HNEW,HOLD,KSTP,
1
NCOL,NROW,NLAY1
C
C-----VERSION 1412 22FEB1982 BASlAD
C
******************************************************************
C
ADVANCE TO NEXT TIME STEP
C
********************~**************************~******************
C
C
SPECIFICATIONS:
C
C
-----------_-----------------------------------------------------DOUBLE PRECISIONHNEW
C
DIMENSION HNEW(NCOL,NROW,NLAY)r HOLD(NCOL,NROW,NLAY)
-----------------------------------------------------------------C
C
Cl----IF NOT FIRST TIME STEP THEN CALCULATE TIME STEP LENGTH.
IF(KSTP.NE.l) DELT=TSMULT*DELT
C
c2--ACCUMULATEELAPSED TIME IN SIMULATIONtTOTIM)
AND IN THIS
Q-----
l
STRESSPERIODtPERTIM).
TOTIM=TOTIM+DELT
PERTIM=PERTIM+DELT
C
c3------COPY HNEW TO HOLD.
DO 10 K=lrNLAY
DO 10 I=l,NROW
DO 10 J=l,NCOL
10 HOLD(J,I,K)=HNEW(J,I,K)
C
c4------RETURN
RETURN
END
4-37
List
Variable
of Variables
for
Module BASlAD
Definition
Range
DELT
Global
Length
of the current
time
step.
HNEW
Global
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
of
HNEWchanges at each iteration.
head in each cell.
HOLD
Global
DIMENSION (NCOL,NROW,NLAY), Head at the start
current
time step.
I
Module
Row index.
3
Module
Column index.
K
Module
Layer
KSTP
Global
Time step
period.
NCOL
Global
Number of columns
NLAY
Global
Number of layers
NROW
Global
Number of rows in the grid.
PERTIM
Package
Elapsed
time
during
the current
TOTIM
Package
Elapsed
time
in the
simulation.
TSMULT
Package
Multiplier
of the
index.
counter.
Reset at the
start
of each stress
in the grid.
in the
grid.
to get from one time
4-38
stress
step
period.
length
to the
next.
Narrative
b
This module initializes
and the
that
right
hand side
hi,j,k
on the
They are calculated
hand side
are the
every
For each cell,
cell
i,j,k
2.
right
hand side
sum of terms
its
initialize
related
the equations
functions
(set
(RHS)
equal
4-39
RHSi,j,k
which
on the
multiplies
The right-hand-side
term and
to many of the flow
components.
are formulated.
in the
RETURN.
a term
( h-coefficient)
HCOFi,j,k
accumulators.
D
the
contains
of the equation.
time
Module BASlFM performs
1.
for
and a coefficient
the h-coefficient
in which
are accumulated.
the equation
left
Module BASlFM
the arrays
h-coefficient,(HCOF)
Recall
for
following
to zero)
order:
the HCOF and RHS
SUBROUTINE BASlFM(HCOF,RHS, NODES)
C
C
C-----VERSION 1632 24JUL1987 BASlFM
:
C
C
C
C
C
********i*********************************************************
SET HCOF=RHS=O.
***+**~*t**************~******************************************
SPECIFICATIONS:
-----------------------------------------------------------------DIMENSIONHCOF(NODES),RHS(NODES)
------------------------------------------------------------------
El ------FOR
EACH CELL INITIALIZE HCOF AND RHS ACCUMULATORS.
DO 100 I=lrNODES
HCOF(I)=O.
RHS(I)=O.
100 CONTINUE
C
C2------RETURN
RETURN
END
4-40
List
Variable
of Variables
for
Module BASlFM
Definition
Range
I
Module
Index.
HCOF
Global
DIMENSION (NODES), Coefficient
(J,I,K) in the finite-difference
of head in cell
equation.
NODES
Global
Number of cells
finite-difference
RHS
Global
DIMENSION (NODES), Right
difference
equation.
of terms from several
(nodes)
4-41
in the
hand side of the finiteRHS is an accumulation
different
packages.
grid.
Narrative
for
Module BASlOC
Module BASlOC sets flags used by the budget and output procedures to
determine
what data should be printed
or recorded on disk.
There are
three individual
flags and one table of flags.
The individual
flags are
IHDDFL which indicates
that head or drawdown is to be printed
or recorded,
IBUDFL which indicates
that the overall
budget should be printed,
and
ICBCFL which indicates
that cell-by-cell
flow terms should be calculated
and printed
or recorded.
The table of flags called
IOFLG has four flags for
They correspond
to the four options:
print
heads, print
drawdown,
each layer.
save heads, and save drawdown.
The flags in IOFLG are used in conjunction
If IHDDFL is set, IOFLG is used to determine head and
with the flag IHDDFL.
drawdown on a layer-by-layer
basis.
If IHDDFL is not set, heads and drawdown
are not printed
or saved and IOFLG is ignored.
step;
flags
If the user is controlling
output,
if not, IOFLG is set at the start
are set at each time step.
Module BASlOC performs
its
the flags are read at each time
of the simulation
and the individual
functions
in the
following
order:
that he will
control
output.
1. Determine if the user has specified
He does so by coding a positive
integer
in the twelfth
element of the
That integer
is read by module BASlDF and is passed to this
IUNIT table.
module (BASlOC) under the name INOC. Go to either
2 or 3.
2. The user is not controlling
output.
Set flags for default-output
Flags IHDDFL and IBUDFL are set only at the last time
and then return.
step in each stress
period or when the iterative
procedure fails
to converge.
RETURN.
output.
Read and print
the code
3. The user has chosen to control
INCODE and flags IHDDFL, IBUDFL, and ICBCFL.
The code INCODE gives the
user several
options
for specifying
the flag table IOFLG.
4. Determine
greater
than zero.
whether INCODE is less
Go to 5, 6, or 7.
than
zero,
equal
to zero,
time
INCODE is
5.
step and print
Use the IOFLG flags used in the
less than zero.
a message to that effect.
Go to 8.
flags
INCODE is
6.
in all other
Read IOFLG for
equal to zero.
layers equal to those in layer
7.
the
the
INCODE is
greater
than
zero.
layer 1 and then
1. Go to 8.
Read IOFLG array.
RETURN.
4-42
previous
set
Go to 8.
of what the user has specified,
set the
8. Regardless
iterative
procedure failed
to converge or if the current
last time step in the stress period.
9.
or
flag IBUDFL if
time step is
Flow Chart
for
Module BASlOC
(x-)
INOC is the input unit for Output
Control
specifications.
It is
specified
by the user as the
twelfth
element of the IUNIT array.
If it is less than or equal to
zero, the user has chosen the
default
output.
If it is greater
than zero, the user has chosen to
control
output.
INCODE provides
the user with
for filling
the IOFLG array.
options
If INCODE < 0, IOFLG from the
last time step is reused.
READ INCODE
If INCODE = 0, IOFLG for layer 1
is read and all other layers
are
set equal to layer 1.
If
INCODE > 0, IOFLG is
read.
IOFLG is a table of flags with one
entry for each layer.
Each entry
has four flags:
1 ---head print
2 ---drawdown
print
3 ---head save
4 ---drawdown
save
If
REUSE IOFLG
FROM LAST
TIME STEP
a flag is set (equal to l), head
or drawdown for the corresponding
layer is either
printed
or saved on
disk.
READ IOFLG
FOR LAYER 1
AND SET ALL
OTHER LAYERS
EOUAL
I
‘I
IHDDFL is the head/drawdown flag.
If it is set, heads and drawdowns
will
be written
in accordance with
the flags in IOFLG.
IF LAST TIME
STEP IN STRESS
PERIOD OR FAILED
TO C~,NVl~~E.
SET
IBUDFL is the budget print
flag.
If
it is set, the overall
budget will
be printed.
ICBCFL is the cell-by-cell
flow term
If it is set, cell-by-cell
flag.
flow terms will
be printed
or
recorded on disk for those components of flow for which the CBC
flag (IWELCB, IRCHCB, IDRNCB, etc.)
is set.
4-43
READ IOFLG
1
c
SUBROUTINEBASlCC(NSTP,KSTP,ICNVG,IOFLGtNLAYt
IBUDFLrICBCFLrIHDDFLrINOCtIOUT)
1632 24JUL1987 BASlCC
******t**************************************~****************~***
C-----VERSION
C
OUTPUTCONTROLLERFOR HEAD, DRAWDOWN,
AND BUDGET
*********************************************~***~****************
C
C
C
SPECIFICATIONS:
-----------------------------------------------------------------DIMNSION IOFLG(NLAY,4)
----------------L-------------------------------------------------
C
Cl------TEST UNIT NUMBER(INCC (INOC=IUNIT(lP)))
Cl------OUTPUT CONTROLIS ACTIVE.
TO SEE IF
IF(INOC.NE.O)GO TO 500
n
k2 ------IF
OUTPUTCONTROLIS INACTIVE THEN SET DEFAULTS AND RETURN.
IHDDFL=O
IF(ICNVG.EQ.0 .OR. KSTP.EQ.NSTP)IHDDFL=l
IBUDFL=O
IF(ICNVG.EQ.0 .OR. KSTP.EQ.NSTP)IBUDFL=l
ICBCFL=O
GO TO 1000
-------READ
AND PRINT OUTPUT FLAGS AND CODE FOR DEFINING IOFLG.
500 READ(INOC,l) INCODE,IHDDFLrIBUDFL,ICBCFL
1 FORMAT(4110)
WRITE(IOUT,3) IHDDFLrIBUDFLrICBCFL
3 FORMAT(lHO,‘HEAD/DRAWDOWN
PRINTOUT FLAG =‘.12r
1
5X,‘TOTAL BUDGETPRINTOUTFLAG =‘112,
2
SX,‘CELL-BY-CELL FLOW TERM FLAG =‘,I21
C
C4------DECODE
INCQDE TO DETERMINEHOWTO SET FLAGS IN IOFLG.
IF(INCODE) 100,200,300
C
IOFLG FROMLAST TIt4E STEP.
100 WRITE(IOUT,lOl)
C5------USE
101 FORMATtlH #‘REUSING PREVIOUS VALUES OF IOFLG')
GO TO 600
W------READ
IOFLG FOR LAYER 1 AND ASSIGN SAMETO ALL LAYERS
200 REtW(INOC.201) (IOFLG(l,M)rM=l,4)
201 FORMAT(4110)
DO 210 K=l,NLAY
IOFLG(K,1)=IOFLG(lrl)
IOFLG(K,2)=IOFLG(1,2)
IOFLG(K,3)=IOFLG(1,3)
IOFLG(K,4)=IOFLG(lr4)
210 CONTINUE
WRITE(IOUT,Pll) (IOFLG(l,M),M=1,4)
211 FORMAT(~HDI’OUTPUT FLAGS FOR ALL LAYERS ARE THE SAME:‘/
1 1X,’ HEAD
DRAWDOWNHEAD DRAWDOWN’/
1X;‘PRINTOUT PRINTOUT SAVE
SAVE’/
1X.34(‘-0/1X,15r110,18,18)
GO TO 600
C
c7-----
READ IOFLG IN ENTIRETY
300 READ(INOCb301) ((IOFLG(K,I),I=1,4),K=l,NLAY)
301 FOlUdAT(4IlO)
WRITE(IOUT.302)
302 FORMAT(lH01 ‘OUTPUT FLAGS FOR EACH LAYER: ‘/
1 1X,'
HEAD
ORAWDOWNHEAD DRAWDOWN’/
2
lX,‘LAYER
PRINTOUT PRINTOUT SAVE
SAVE’/
3
1X.41(‘-‘))
-WRITEii&T,3U3)
(Kt(IOFLG(K,I),I=l,4),K=l,NLAY)
303 F0RMAT(1X,14,18,110,18,18)
C
CB------ME
LAST STEP IN A STRESS PERIOD AND STEPS WHEREITERATIVE
C&-----PROCEDURE FAILED TO CONVERGEGET A VOLUM-RIC BUDGET.
600 IF(ICNVG.EQ.0 .OR. KSTP.EQ.NSTP) IBUDFL=l
c
C9------RENRN
1000 RETURN
END
4-44
List
Variable
I
of Variables
for
Definition
Range
IBUDFL
Module
Package
ICBCFL
Global
I CNVG
Global
I HDDFL
Package
INCODE
Module
INOC
Package
I OFLG
Package
IOUT
K
KSTP
Global
Module
Global
M
NLAY
NSTP
Module
Global
Global
Module BASlOC
Index.
Flag.
= 0, volumetric
budget will
not be printed
for the
current
time step.
# 0, volumetric
budget should be printed
for the
current time step.
Flag.
= 0, cell-by-cell
flow terms will
not be recorded
or printed
for the current
time step.
# 0, cell-by-cell
flow terms will
be recorded or
printed
for the current
time step.
procedure
Flag is set equal to 1 when the iteration
has converged.
Flag.
= 0, neither
head nor drawdown will
be printed
at this time step.
# 0, head and drawdown may be printed
at the end of
the current
time step.
Code specified
by user.
< 0, reuse contents
of IOFLG from the last time step.
= 0, read IOFLG for layer 1 and set all other layers
to the same thing.
> 0, read IOFLG contents
for each layer.
Unit number from which input to output control
option
will
be read.
DIMENSION (NLAY,4), Flags to control
printing
and
recordina
of head and drawdown for each layer.
be printed.
(NLAY,l)"#
0, heads wi
11 be printed.
(NLAYJ) # 0, drawdown
be recorded.
(NLAY,3) # 0, heads wi
11 be recorded.
(NLAY,4) # 0, drawdown
printed
output.
IOUT = 6.
Primary unit number for a
Layer index.
of each stress
Time step counter.
Reset at the start
period.
Index.
Number of layers in the grid.
Number of time steps in the current
stress period.
4-45
Narrative
Module BASlOT invokes
Those results
summary.
which
include
Results
of flags
should
be written
module
drawdowns
step
(printer
results
which
that
If
the
results
flag
flag
the
its
If
set,
volumetric
functions
It controls
the
procedure
flag
which
which
IBUDFL is
flag
iterative
budget,
layers
budget.
a time
set
it
should
printing
failed
After
heads and
every
invoked
time
summary is printed.
order:
in this
of a time
to
be written.
SBASlV is
following
later
set,
heads and drawdown
submodule
in the
is
and a time
IHDDFL is
SBASlH and SBASlD to write
This
IPFLG.
simulation.
IHDDFL, IOFLG, and IBUDFL
to flags
have been printed,
If the head and drawdown flag
SBASlH and SBASlD to write
in the table
4.
calculate
5.
print
volumetric
and for
overall
of the
converge,
module if
any
summary.
print
a message
effect.
3.
flags
results
Control).
submodules
If
are printed.
2.
overall
according
or disk)
calls
and print
Clear
write
named IOFLG is used to determine
Module BASlOT performs
1.
which
drawdown,
are printed
respectively.
during
submodules
head,
(BASlOT)
to calculate
Module BASlOT
by module BASlOC (Output
are set
a table
This
for
If
If
the
heads and drawdowns
are set,
call
in accordance
submodules
with
the
IOFLG.
budget
and print
a time
6.
the
(IHDDFL)
the
printout
flag
(IBUDFL)
volumetric
flag
is
set,
call
submodule
SBASlV to
budget.
(IPFLG)
summary.
RETURN.
4-46
is
set,
call
submodule
SBASlT to
to
Flow Chart
for
Module BASlOT
IPFLG is the printout
flag.
It
is set when any results
are
If it is set, a
printed.
time summary is printed.
SBASlH is a submodule which
writes
heads.
SBASlD is a submodule which
writes
drawdown.
SBASlV is a submodule which
prints
the
volumetric
budget.
SBASlT is a submodule which
prints
a time
summary.
IHDDFL is the head/drawdown
If it is set, heads
flag.
and drawdown will
be written
in accordance with flag
settings
in IOFLG.
IBUDFL is the budget print
If it is set, volumetric
flag.
budget will
be printed.
NO
I
J
IOFLG is a table of flags with
one entry for each layer.
Each entry has four flags:
1 ---head print
2 ---drawdown
print
3 ---head save
save
4 ---drawdown
4A
I NO
IF IPFLG IS
SET, CALL
SBASlT TO PRINT
TIME SUMMARY
L
8
I
1
SUBROUTINE BASlOTt HNEW,STRT, ISTRT,BUFF, IOFLG,
MSUM,IBOUND,
VBNM,
VBVL, KSTP,KPER,DELT,PERTIM,TOTIM, ITMUNI,NCOL,NROW,NLAY, ICNVG,
2 IHDDFL,IBUDFL,IHEDFM,IHEDUN,IDDNFM,IDDNUN,IOUT~
-----VERSION 1522 12MAY1987 BASlOT
***************~****************************************~*********
OUTPUT TIME, VOLUMETRIC
BUDGET, HEAD, AND DRAWDOWN
*************+****************************************************
:
C
C
C
C
SPECIFICATIONS:
--------------------------
C
----------------------------------------
CHARACTER*4 VBNM
DOUBLE PRECISION HNEW
C
C
C
Cl---
C
CLEAR PRINTOUT FLAG
IPFLG=O
c2---
C
DIMENSION
HNEW(NCOL,NROW,NLAY),STRTtNCOL,NROW,NLAY),
VBNM(4,20),VBVL(4,20),10FLG(NLAY,4~,
1
IBOUND(NCOL,NROW,NLAY)rBUFF(NCOLINROW,NLAY~
2
-----------------------------------------------------------------(IPFLG)
f
IF ITERATIVEPROCEDUREFAILED TO CONVERGEPRINT MESSAGE
IF(ICNVG.EQ.0)WRITE(IOUT,l)KSTP,KPER
1 FORMAT(1HO,1OX,‘****FAILED TO CONVERGEIN TIME STEP'rI3,
' OFSTRESS PERIOD'rI3,'****')
1
C3-----C3------
IF HEAD AND DRAWDOWNFLAG (IHDDFL)
DRAWDOWNIN ACCORDANCEWITHFLAGS
IF(IHDDFL.EQ.0)GOTO 100
IS SET WRITEHEAD AND
IN IOFLG.
C
CALL SBASlH(HNEW,BUFF,IOFLG,KSTP,KPER,NCOL,NROW,
NLAY, IOUT, IHEDFM, IHEDUN, IPFLG,PERTIM,
TOTIM)
CALL SBASlD(HNEW,BUFF,IOFLG,KSTP,KPER,NCOL,NROW,NLAY,IOUT,
1 IDDNFM,IDDNUN,STRT,ISTRT, IBOUND,IPFLG,PERTIM,TOTIM)
1
C
c4------PRINT
TOTAL BUDGET IF REQUESTED
100 IF(IBUDFL.EQ.0)
GO TO 120
CALL SBASlVt MSUM,VBNM,VBVL, KSTP,KPER,
IPFLG=l
IOUT)
:5 ------END
PRINTOUT WITHTIME SUMMARYAND FORM FEED IF ANY PRINTOUT
c5 ------WILL BE PRODUCED.
120 IF(IPFLG.EQ.0) RETURN
CALL SBASlTt KSTP, KPER, DELT, PERTIMITOTIM, ITMUNI,IOUT)
WRITE(IOUT,lOl)
101 FORMATt1Hl)
C
C6------RETURN
RETURN
END
4-48
,
List
Variable
of Variables
for
Definition
Range
BUFF
Global
DELT
HNEW
Global
Global
I BOUND
Global
I BUDFL
Package
I CNVG
Global
IDDNFM
IDDNUN
Package
Package
IHDDFL
Package
I HEDFM
I HEDUN
Package
Package
I OFLG
Package
IOUT
I PFLG
Global
Package
I STRT
Package
ITMUNI
Package
Module BASlOT
DIMENSION (NCOL,NROw,NLAY), Buffer used to accumulate
information
before printing
or recording
it.
Length of the current
time step.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
of
HNEWchanges at each iteration.
head in each cell.
DIMENSION (NCOL,NR~W,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
Flag.
= 0, volumetric
budget will
not be printed
for the
current time step.
f 0, volumetric
budget should be printed
for the
current time step.
Flag is set equal to one when the iteration
procedure
has converged.
Code for format in which drawdown should be printed.
Unit number on which an unformatted
record containing
drawdown should be recorded.
Flag.
= 0, neither
head nor drawdown will
be printed
at
this time step.
# 0, head and drawdown may be printed
at the end of
the current
time step.
Code for the format in which head should be printed.
Unit number on which an unformatted
record containing
head should be recorded.
DIMENSION (NLAY,4),
Flags to control
printing
and
recording
of head and drawdown for each layer.
(NLAY,l) # 0, heads will
be printed.
(NLAY,2) # 0, drawdown will
be printed.
(NLAY,3) # 0, heads will
be recorded.
(NLAY,4) # 0, drawdown will
be recorded.
Primary unit number for all printed
output.
IOUT = 6.
Flag.
= 0 means nothing has been printed
this time step.
f 0 means something has been printed
this time
a time summary must be printed.
step; therefore,
Flag.
# 0, starting
heads will
be saved so that drawdown
can be calculated.
= 0, starting
heads will
not be saved.
Code for time units for this problem:
0 - undefined
lseconds
2 - minutes
3 - hours
4 - days
5 - years
4-49
List
Variable
of Variables
for Module BASlOT (Continued)
Definition
Range
KPER
Global
KSTP
Global
MSUM
NCOL
NLAY
NROW
PERTIM
STRT
TOTIM
VBNM
Global
Global
Global
Global
Package
Package
Package
Global
VBVL
Global
Stress
period
counter.
Time step counter.
Reset at the start of each stress
period.
Counter for budget entries
and labels in VBVL and VBNM.
Number of columns in the grid.
Number of layers in the grid.
Number of rows in the grid.
Elapsed time during the current
stress period.
DIMENSION (NcOL,NROW,NLAY), Starting
head.
Elapsed time in the simulation.
DIMENSION (4,20),
Labels for entries
in the volumetric
budget.
Entries
for the volumetric
budget.
, DIMENSION (4,20),
For flow component N, the values in VBVL are:
(l,N) Rate for the current
time step into the flow
field.
(2,N) Rate for the current
time step out of the flow
field.
(3,N) Volume into the flow field
during simulation.
(4,N) Volume out of the flow field
during simulation.
4-50
Narrative
for
Module SBASlD
Module SBASlD is called
by module BASlOT to calculate
and write drawdown'
for every cell in certain
layers in the grid.
The module is called
at the
end of each time step if the head and drawdown flag (IHDDFL) is set.
It
calculates
drawdown only if the user has specified
that starting
heads should
be saved.
The layers for which drawdown is to be written
are determined
by the
In IOFLG, there are four flags
settings
of flags in the table named IOFLG.
The second flag,
if it is set, causes drawdown to be printed.
each layer.
The fourth
flag,
if it is set, causes drawdown to be recorded.
Module SBASlD performs
1.
For each layer,
If flags indicate
2.
on to the next layer.
3.
4 or 5.
Test
flag
its
functions
do steps
that
in the
following
order:
2-5.
drawdown is
ISTRT to see if
starting
4.
Starting
heads were not saved.
5.
Starting
heads were saved.
not needed for
this
heads were saved.
Write
layer,
go
Go to either
a message to that
effect
drawdown for
layer.
and
STOP.
Calculate
if drawdown is to be printed,
6. For each layer,
or ULAPRW, depending on the format requested
(IDDNFM),
7.
to write
8.
if drawdown is to be recorded,
For each layer,
the drawdown to the unit specified
in IDDNUN.
RETURN.
4-51
this
call module ULAPRS
to print
drawdown.
call
module ULASAV
for
Flow Chart
IOFLG is a table containing
one entry for each layer.
Each element consists
of
four flags which, when
set. cause (1) head to be
printed,
(2) drawdown to
be printed,
(3) head to be
recorded,
and (4) drawdown
to be recorded.
for
Module SBASlD
(YE--)
FOR EACH LAYER
1
ULAPRW is a utility
module
which prints
a value for
each cell in a wrao format.
In the wrap format', all
values for one row are
printed
before any values
for the next row.
PRINT MESSAGE
SAYING STARTING
HEADS WERE NOT
SAVED
ULAPRS is a utility
module
which prints
a value for
each cell in the layer in
In the
a strip
format.
strip
format,
all values
in a group of N columns
are printed
before any
values in the next N
columns are printed.
CALCULATE
DRAWDOWN
FOR EACH LAYER
ULASAV is a utility
module
which records a value for
each cell in a layer.
IDDNUN is a unit number,
specified
by the user,
on which drawdown will
recorded.
I
6
CALL MODULES
ULAPRW OR
ULAPRS TO PRINT
DRAWDOWN
be
4-52
b
SUBRWTINE SBAS~D(HNEW~BUFF~IOFLG,KSTF’,KPERINCOL,NRCW,
1
NLAY,IOUT,IDDNFM,IDDNUN,STRT,ISTRTtIBWND,IPFLGt
2
PERTIMsTOTIM)
C-----VERSION 1630 lSMAY1987 SBASlD
*************************************************~*****
C
CALCULATEPRINT AND RECORDDRAWDOWNS
c
**+*******~***C*****~******~********~**********~*****~~
c
kC
SPECIFICATIONS
------------------------------------------------------CHARACTER*4TEXT
DOUBLEPRECISION HMW
C
1
2
DIMENSION HNEW(NCOLrNROW,NLAY),IOFLG(NLAY,4)rTEXT(4),
BUFF(NCOLrNRCW,NLAY),STRT(NCOL,NROW,NLAY),
IBCUND(NCOL,NRCW,NLAY)
c
DATA TEXT(l),TEXT(2)rTEXT(3l,TEXT(4)
1
'DOWN'/
------_------------------------------------------------
/’
‘,’
‘r’DRAW’r
c
C
Cl------FOR
EACH LAYER CALCULATEDRAWDOWN
IF PRINT OR RECORD
Cl------IS
REQUESTED
DO 59 K=l,NLAY
C
C2------IS
DRAWDOWN
NEEDEDFRO THIS LAYER?
IF(IOFLG(K,Z).EQ.O
.AND. IOFLG(Ks4).EQ.O) GO TO 59
n
B
i3 ------DRAWDOWN IS NEEDED. WERESTARTING HEADS SAVED?
IF(ISTRT.NE.0)
GO TO 53
C
a------STARTING
HEADS WERENOT SAVED. PRINT MESSAGEAND STOP.
WRITE(IOUT,52)
52 FORMATtlHOr’CANNOT CALCULATEDRAWDOWN
BECAUSESTART’,
1
’ HEADSWERENOT SAVED’)
STOP
C
CS------CALCULATE DRAWDOWN
FOR THE LAYER.
53 DO 58 I=l,NRW
DO 58 J=l,NCOL
HSING=HNEW(J,I,K)
E!UFF(J,I,K)=HSING
IF(IBCiJND(J,I,K).NE.O)
BUFF(J,I,K)=STFtT(J,I,Kl-HSING
58 CONTINUE
59 CONTINUE
C
C6------FOR
EACH LAYER: DETERMINEIF DRAWDOWN
SHOULDBE PRINTED.
IX------IF
SO THEN CALL ULAPRS OR ULAFRWTO PRINT DRAWDOWN.
DO 69 K=ltNLAY
KK=K
IF(IOFLG(K,Z).EQ.O)
GO TO 69
IF(IDDNFM.LT.0) CALL ULAPRS(BUFF(l,l,K),TEXT(l),KSTP,KPER,
1
NCOL,NRW,KK,-IDDNFM,IOUT)
IF(IDDNFM.GE.0) CALL ULAPRW(BUFF(lrlrK),TEXT(l),KSTP,KPER,
1
NCOL,NR~,KK,IDDNFM,IOUT)
IPFLG=l
69 CONTINUE
C
C7------FOR
EACH LAYER: DETERMINEIF DRAWDOWN
SHOULDBE RECORDED.
C7------IF
SO THEN CALL ULASAV TO RECORDDRAWDOWN.
IFIRST=l
IF(IDDNUN.LE.0) GO TO 80
DO 79 K=lrNLAY
KK=K
IF(IOFLG(K,4).LE.O)
GO TO 79
IF(IFIRST.EQ.l)
WRITE(IOUT,74) IDDNUN,KSTP,KF’ER
74 FO~AT(lHD,‘DRAWDOWN WILL BE SAVED ON llNIT’tI3,
1
’ AT END OF TIME STEP’rI3r’s
STRESS PERIOD’,131
IFIRST=O
CALL ULASAV(BUFF(lrltK),TEXT(l)rKSTP,KPER,PERTIM,TOTIM,~L,
1
NRCW,KK,IDDNUN)
79 CONTINUE
c
C8------RETURN
80 RETURN
END
4-53
List
Variable
for
Global
HNEW
Global
HSING
I
I BOUND
Module
Module
Global
I DDNFM
I DDNUN
Package
Package
IFIRST
Module
I OFLG
Package
IOUT
I PFLG
Global
Package
I STRT
Package
J
K
KK
Module
Module
Module
KPER
KSTP
Global
Global
NCOL
NLAY
NROW
PERTIM
STRT
TEXT
Global
Global
Global
Package
Package
Module
Package
Module SBASlD
Definition
Ranae
BUFF
TOTIM
of Variables
DIMENSION (NCOL,NROW,NLAY), Buffer used to accumulate
information
before printing
or recording
it.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
of
HNEWchanges at each iteration.
head in each cell.
Single-precision
temporary field
for HNEW (J,I,K).
Index for rows.
DIMENSION (NcOL,NR~W,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
Code for format in which drawdown should be printed.
Unit number on which an unformatted
record containing
drawdown should be recorded.
Flag to indicate
that a notice should be printed
when
drawdown is recorded.
DIMENSION (NLAY,4),
Flags to control
printing
and
recording
of head and drawdown for each layer.
(NLAY,l) # 0, heads will
be printed.
(NLAY,2) # 0, drawdown will
be printed.
(NLAY,3) # 0, heads will
be recorded.
(NLAY,4) # 0, drawdown will
be recorded.
Primary unit number for all printed
output.
IOUT = 6.
Flag.
= 0 means nothing has been printed
this time step.
f 0 means something has been printed
this time
step; therefore,
a time summary must be printed.
Flag.
# 0, starting
heads will
be saved so that drawdown
can be calculated.
= 0, starting
heads will
not be saved.
Index for columns.
Index for layers.
Temporary variable
set equal to K. KK is used as an
actual argument in subroutine
calls to avoid using
the DO loop variable
K as an argument, which causes
problems with some compilers.
Stress period counter.
Reset at the start
of each stress
Time step counter.
period.
Number of columns in the grid.
Number of layers in the grid.
Number of rows in the grid.
Elapsed time during the current
stress
period.
DIMENSION (NCOL,NROW,NLAY), Starting
head.
Label to be printed
or recorded with array data.
Elapsed time in the simulation.
4-54
Narrative
for
Module SBASlH
Module SBASlH prints
and records head for every cell in certain
layers
in the grid.
It is called by module BASlOT at the end of each time step if
the head and drawdown flag (IHDDFL) is set.
The layers for which head is
written
is controlled
by the settings
of flags in the table named IOFLG.
In IOFLG, there are four flags for each layer.
The first
flag,
if it is set,
causes head for the corresponding
layer to be printed.
The third
flag,
if it
is set, causes head to be recorded.
Module SBASlH performs
1.
For each layer,
its
functions
in the
following
order:
DO STEPS 2-4.
this
2. Test the flag table (IOFLG) to see if
If so, DO STEPS 3 AND 4,
layer.
heads should
array
3. Copy heads for this layer (which are contained
in the double-precision
(HNEW)) into the single-precision
buffer
array (BUFF).
code, call
4. Depending on the print-format
ULAPRS to print
the contents
of the buffer
array.
either
be printed
for
module ULAPRW or
5. Test the unit number for recording
heads (IHEDUN) to see if it is
If it is not positive,
heads will
not be recorded (SKIP STEPS
positive.
heads may be recorded in accordance with the setting
If it is positive,
6-9).
of flags in the IOFLG array.
DO STEPS 6-9.
6.
this
For each layer,
If
7.
layer,
DO STEPS 7-9.
flags in IOFLG indicate
that
move on to the next layer.
8. Copy heads from the HNEW array
(single-precision).
9.
10.
Call
module ULASAV to
record
RETURN.
4-55
heads are not to be recorded
(double-precision)
the
heads on unit
for
to the BUFF array
IHEDUN.
Flow Chart
for
Module SBASlH
IOFLG is a table
containing
one
Each
entry for each layer.
element consists
of four flags
which, when set, cause (1) head
to be printed,
(2) drawdown to be
printed,
(3) head to be recorded,
and (4) drawdown to be recorded.
NO
ULAPRW is a utility
module which
prints
a value for each cell in
the layer in a wrap format.
In
the wrap format,
all values for
one row are printed
before any
values for the next row.
COPY HEADS
INTO BUFFER
ULAPRS is a utility
module which
prints
a value for each cell in
the layer in a strip
format.
In
the strip
format,
all values in
a group of N columns are printed
before any values in the next N
columns are printed.
ULASAV is a utility
records a value
in a layer.
CALL ULAPRW
OR ULAPRS TO
PRINT HEADS
module which
for each cell
FOR EACH LAYER
IHEDUN is a unit number, specified
by the user, on which heads will
If IHEDUN is less
be recorded.
than or equal to zero, heads will
not be recorded.
I
I
YES
r6
Y
t
YES
COPY HEADS
RECORD HEADS
4-56
1
SUBROUTINE SBAS~H(HNEW,BIJFFIIOFLG,KSTPIKPERINCOL,NROW,
1
NLAY~IOUT,IHEDFMIIHEDUN,IPFLG,F'ERTIM,TOTIM)
C
C-----VERSION
1653 15MAY1987SBASlH
*******************************************************
c"
PRINT AND RECORD HEADS
*******************************************************
:
C
SPECIFICATIONS
-------------------------------------------------------
C
CHARACTER*4 TEXT
DOUBLE PRECISION HNEW
C
DIMENSIONHNEW(NCOL,NROW,NLAY),IOFLG(NLAY,4),TEXT(4),
1
BUFF(NCOL,NRCW,NLAY)
C
DATA TEXT(l),rrXT(2)rrrXT(3),TEXT(4)
‘HEAD’/
--_---------------------------------------------------
1
:
Cl---
/’
‘,’
1,’
‘,
FOR EACH LAYER: PRINT HEAD IF REQUESTED.
DO 39 K=lrNLAY
KK=K
C
CP------TEST
IOFLG TO SEE
IF(IOFLG(K,l).EQ.O)
IPFLG=l
C
C3------COPY
HEADS FOR
IF HEAD SHOULD BE PRINTED.
GOTO 39
THIS LAYER INTO BUFFER.
DO32 I-1rNROW
DO 32 J=lrNCOL
BUFF(J,I,l)=HNEW(J,I,K)
32 CONTINUE
C
c4 ------CALL
UTILITY MODULE TO PRINT CONTENTS OF BUFFER.
IF(IHEDFM.LT.0)
CALL ULAPRS(BLIFF,TEXT(l)rKSTP,KPER,NCOLrNRUV,KK,
1
-1HEOFMrIOUT)
IF(IHEDFM.GE.0) CALL ULAPRW(BUFFITEXT(~)~KSTPIKPERINCOL,NROW,KK,
IHEDFM,IOUT)
391CONTINUE
:5
C
------IF
UNIT FOR RECORDING HEADS <= 0: THEN RETURN.
IF(IHEDUN.LE.O)GOTO 50
IFIRST=l
C&-----FOR
EACH LAYER: RECORD HEAD IF REQUESTED.
DO 49 K=l,NLAY
KK=K
C
C7----- -CHECK IOFLG TO SEE IF HEAD FOR THIS LAYER SHOULD BE RECORDED.
IF(IOFLG(K,3).LE.O)
GO TO 49
IF(IFIRST.EQ.l) WRITE(IOUT,41) IHEDUNnKSTPrKPER
41 FORMAT(lHDs’HEAD WILL BE SAVED ON UNIT’rI3,’
AT END OF TIME STEP’,
1
13,‘s STRESS PERIOD’s131
C
IFIRST=O
HEADS FOR THIS LAYER INTO BUFFER.
DO44 I=l,NROW
DO 44 J=l,NCOL
BUFF(JrI,l)=HNEW(J,I,K)
44 CONTINUE
CB------COPY
C
C9------RECORD
CONTENTS OF BUFFER ON UNIT=IHEDUN
CALL ULASAV(BUFFITEXT(~),KSTP,KPER,PERTIM,TOTIM,NCOL~NROW,KK,
1
IHEDUN)
49 CONTINUE
C
ClD-----RETURN
50 RETURN
END
4-57
List
Variable
for
Global
HNEW
Global
I
I FIRST
Module
Module
I HEDFM
I HEDUN
Package
Package
I OFLG
Package
IOUT
I PFLG
Global
Package
3
Module
Module
Module
DIMENSION (NC~L,NR~W,NLAY), Buffer used to accumulate
information
before printing
or recording
it.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
of
HNEWchanges at each iteration.
head in each cell.
Index for rows.
Flag which, if set (equal to l), indicates
that a notice
should be printed
when head is recorded.
Code for format in which head should be printed.
Unit number on which an unformatted
record containing
head should be recorded.
DIMENSION (NLAY,4), Flags to control
printing
and
recording
of head and drawdown for each layer.
(NLAY,l) # 0, heads will
be printed.
(NLAY,2) # 0, drawdown will
be printed.
(NLAY,3) # 0, heads will
be recorded.
(NLAY,4) # 0, drawdown will
be recorded.
Primary unit number for all printed
output.
IOUT = 6.
Flag.
= 0 means nothing has been printed
this time step.
# 0 means something has been printed
this time
a time summary must be printed.
step; therefore,
Index for columns.
Index for layers.
Temporary variable
set equal to K. KK is used as an
actual
KPER
KSTP
Global
Global
NCOL
NLAY
NRCW
PERTIM
TEXT
TOTIM
Global
Global
Global
Package
Module
Package
Module SBASlH
Definition
Range
BUFF
K
KK
of Variables
argument
in
subroutine
the DO loop variable
K as an
problems with some compilers.
Stress period counter.
Reset at the
Time step counter.
period.
Number of columns in the grid.
Number of layers in the grid.
Number of rows in the grid.
Elapsed time during the current
Label to be printed
or recorded
Elapsed time in the simulation.
4-58
calls
to
argument,
start
avoid
using
which
causes
of each stress
stress period.
with array data.
Narrative
for
Module SBASlI
Module SBASlI initializes
the Output Control
System.
If the user does
not opt to control
output,
the formats for printing
head and drawdown are
set to the default
format and flags are set so that,
whenever heads or
drawdowns are printed,
they are printed
for all layers.
If the user does
opt to control
output,
the formats for printing
and the unit numbers for
recording
head and drawdown are read.
A table named IOFLG contains
one entry for each layer in the grid.
Each entry consists
of four flags corresponding
to four operations:
(1) head
print,
(2) drawdown print,
(3) head record,
and (4) drawdown record.
The
module BASlOT examines the table and, for each layer,
performs only the
operations
for which the corresponding
flags are set (equal to one).
This
module (SBASlI) sets the head-print
flag if the user opts for default
output.
If starting
heads are saved, it also sets the drawdown-print
flag.
If the
user opts to control
output,
the flags in IOFLG are read at each time step.
Module SBASlI performs
its
functions
in the
following
order:
(IUNIT (12)), which is known
1. Test the unit number for Output Control
If it is positive,
in this module by the name INOC, to see if it is positive.
the Output Control option is active
and output specification
will
be read
from the unit number contained
in INOC. If it is not positive,
the Output
Control
option is not active
and flags are set to defaults.
GO TO 2 OR 3.
is active.
Read and print
the head-print
format
2. Output Control
code (IHEDFM), the drawdown-print
format code (IDDNFM), the unit number to
record heads (IHEDUN), and the unit number to record drawdown (IDDNUN).
GO TO 6. Note: The formats and associated
codes are listed
in the Input
Instructions
for Output Control.
3.
Output
Control
is
4. Set the print-format
get the default
format.
all
5. Set the
layers.
6.
flags
inactive.
codes
Print
a message listing
(IHEDFM and IDDNFM) equal
in IOFLG so that
RETURN.
4-59
the defaults.
to zero to
head and drawdown are printed
for
Flow Chart
for
Module SBASlI
INOC is the input unit for
Output Control.
It is the
same as element 12 in the
IUNIT table.
When it is
greater
than zero, Output
Control
is active--the
user
will
provide output speciWhen it is less
fications.
than or equal to zero, Output
Control
is inactive--output
will
be controlled
by default.
ENTER
SBASl I
ci
IOFLG is a table
containing
one entry for each layer.
Each entry consists
of four
flags which, when set, cause
(1) head to be printed,
(2) drawdown to be printed,
(3) head to be recorded,
and
(4) drawdown to be recorded.
+4.
SET THE FORMAT
CODES EQUAL
’ l-
4-60
SET IOFLG FOR
HEAD PRINT IN
ALL LAYERS
B
SUBROUTINE
SBAS1I(NLAY,ISTRT,IOFLG,INOC,IOUT,IHEDFM,
1
IDDNFM, IHEDUN,IDDNUN)
-----VERSION 1531 12MAY1987SBASlI
**************************************************************
C
C
SET UP OUTPUT CONTROL
C
**************************************************************
SPECIFICATIONS:
C
DIMENSION
IOFLG(NLAYs4)
---------------------------------------------------------------
El ------TEST
UNIT NUMBERFROM IUNIT (INOC) TO SEE IF OUTPUT
Cl ------CONTROL IS ACTIVE.
IF(INOC.LE.0) GOTO 600
C
------READ
AND PRINT FORMATSFOR PRINTING AND UNIT NUMBERSFOR
:x ------RECORDING HEADS AND DRAWDOWN.THEN RETURN.
500 READ (INOC,l)IHEDFM,IDDNFM,IHEDUN,IDDNUN
1 FORMAT (4110)
WRITE (IOUT, 1IHEDFM, IDDNFM
3 FORMAT (lHO,‘HEAD PRINT FORMATIS FORMATNUMBER’rI4,
I
1
DRAWDOWN
PRINT FORMATIS FORMATNUMBER’,141
WRITE(IOUT,4)IHEDUN,IDDNUN
4 FORMAT (lHO,'HEADSWILL BE SAVED ON UNIT'rI3,
1
1
DRAWDOWNS
WILL BE SAVED ON UNIT',131
WRITE(IOUT,561)
561 FORMAT(lHO,‘OUTPUT CONTROLIS SPECIFIED EVERY TIME STEP’)
GO TO 1000
C
c3------OUTPUT CONTROLIS INACTIVE. PRINT A MESSAGELISTING DEFAULTS.
600 WRITE(IOUT,641)
641 FORMAT(lHO,‘DEFAULT OUTPUT CONTROL-- THE FOLLOWINGOUTPUT’,
1
’ COMESAT THE END OF EACH STRESS PERIOD:
'1
WRITE(IOUT,642)
642 FORMAT{1X, ‘TOTAL VOLUMETRICBUDGET’1
WRITE(IOUT,643)
643 FORMAT(lXrlOX,'HEAD')
IF(ISTRT.NE.O)WRITE(IOUT,644)
644 FORMAT(lX,lOX,'DRAWDOWN')
C
c4------SET
THE FORMATCODES EQUAL TO THE DEFAULT FORMAT.
IHEDFM=O
IDDNFM=O
C
------SET
DEFAULT FLAGS IN IOFLG SO THAT HEAD (AND DRAWDOWN)IS
FOR EVERY LAYER.
E ------PRINTED
ID=0
IF(ISTRT.NE.0)
ID=1
670 DO680 K=l,NLAY
IOFLG(K,l)=l
IOFLG(K,2)=ID
C
D
IOFLG(K,3)=0
IOFLG(K,4)=0
680 CONTINUE
GOTO 1000
C6------RETURN
1000 RETURN
END
4-61
List
Variable
of Variables
for
Module SBASlI
Definition
Range
ID
Module
Flag to show if
means no).
STRT was saved
IDDNFM
Package
Code for
in which
IDDNUN
Package
Unit number on which an unformatted
drawdown should be recorded.
IHEDFM
Package
Code for
IHEDUN
Package
Unit
INOC
Package
Unit number from which
will
be read.
IOFLG
Package
DIMENSION (NLAY,4),
Flags to control
printing
and
recording
of head and drawdown for each layer.
(NLAY,l) # 0, heads will
be printed.
(NLAY,Z) # 0, drawdown will
be printed.
(NLAY,3) # 0, heads will
be recorded.
(NLAY,4) # 0, drawdown will
be recorded.
IOUT
Global
Primary
I STRT
Package
Flag.
format
format
(one means yes;
drawdown should
in which
number on which an unformatted
head should be recorded.
unit
number for
input
all
f 0, starting
heads will
can be calculated.
= 0, starting
heads will
K
Module
Index for
NLAY
Global
Number of layers
layers
4-62
in the
grid.
containing
be printed.
record
to output
printed
be printed.
record
head should
zero
containing
control
output.
be saved so that
not be saved.
option
IOUT = 6.
drawdown
Narrative
Submodule SBASlT prints
length
and the elapsed
program
given
the
option
those
units
(ITMUNI)
other
If
are being
the conversion
units.
units
However,
that
convenient
days,
he is
units.
and years.
the
using
user
and the
The user
The
is
program
specifies
indicator
time
factor
(ITMUNI)
to determine
the
conversion
to seconds.
is equal
to zero,
nonstandard
time
units
used.
(a)
nonstandard
Print
the time-step
length
and the
elapsed
time
in the
units.
(b)
3.
hours,
of the time-step
in module BASlDF.
(CNV) needed to convert
2.
consists
minutes,
set of time
the time
to all
Use the time-unit
1.
factor
to specify
units
summary which
in seconds,
can use any consistent
converts
time
a time
time
Module SBASlT
for
RETURN.
Calculate
the
length
of the time
Calculate
the time-step
step
and the elapsed
times
in
seconds.
4.
hours,
days,
length
and the
elapsed
times
in minutes,
and years.
5.
Print
the time-step
6.
RETURN.
length
and the elapsed
4-63
times
in all
time
units.
SUBROUTINE SBAS1T(KSTP,KPER,DELT,PERTIM,TOTIM,ITMUNIrIOUT)
C
C
C-----VERSION
0837 09APRh982 SBASlT
******************************************************************
PRINT SIMULATION
TIME
C
cC
C
C
C
C
******************************************************************
SPECIFICATIONS:
-----------------------------------------------------------------_----------------------------------------------------------------WRITE(IOUTn199)
KSTPnKPER
199 FO~AT(lHO,///lOX,‘TIME
SUMMARY AT END OF TIME STEP’rI3r
' IN STRESS F'ERIOD'rI3)
1
C
Cl-----
C
a
USE TIME UNIT INDICATOR
TO GET FACTOR TO CONVERT TO SECONDS.
CNV=O.
IF(ITMUNI.EQ.l) CNV-1.
IF(ITMUNI.EQ.2)CNV=60.
IF(ITMUNI.EQ.3)CNV=3600.
IF(ITMUNI.EQ.4)CNV=86400.
IF(ITMUNI.EQ.5)CNV=31557600.
f-3---
IF FACTOR=0 THEN TIMEUNITS ARE NON-STANDARD.
IF(CNV.NE.0.)
GO TO 100
TIMESIN NON-STANDARD TIME UNITS.
WRITE(IOUTs301)
DELT,PERTIM,TOTIM
301 FORMAT( 21X,'
TIME STEP LENGTH =‘rG15.6/
1
21X,' STRESS PERIODTIME='rG15.6/
21X,'TOTALSIMULATION
TIME=',Gl5.6)
2
:2A -----PRINT
C
CPE?-----RETURN
RETURN
C
C3-----CALCULATE LENGTH OF TIME STEP 8 ELAPSED TIMESIN SECONDS.
100 DELSEC=CNV*DELT
TOTSEC=CNV*TOTIM
PERSEC=CNV*PERTIM
C
TIMESIN MINUTESIHOURSIDAYS AND YEARS.
c4 ------CALCULATE
DELMN=DELSEC/60.
DELHR=DELMN/BO.
DELDY=DELHW24.
DELYR=DELDY/365.25
TOTMN=TOTSEC/BO.
TOTHR=TOTMN/60.
TOTDY=TOTHW24.
TOTYR=TOTDY/365.25
PERMN=PERSEC/60.
PERHR=PERMN/60.
PERDY=PERHW24.
PERYR=PERDY/365.25
C
Cl+--PRINT TIME STEP LENGTH AND ELAPSED TIES IN ALL TIM UNITS.
WRITE(IOUT,POO)
C
200 FORMATt 27X, ’
SECONDS
MINUTES
1
‘DAYS
YEARS’/27X,75(‘-‘1)
WRITE (IOUT,
DELSEC,DELMN,DELHR,DELDY,DELYR
201 FOfU.fAT(lX,’
TIME STEP LENGTH',5X,5615.6)
WRITE(IOUT,POP)
PERSEC,PERMN,PERHR,PERDYrPERYR
202 FORMAT(lX,’
STRESS PERIOD TIME'rSX,5G15.6)
WRITE(IOUT,203)
TOTSEC~TOTMN~TOTHRITOTDYITOTYR
203 FORMAT(lX,‘TOTAL
SIMULATION
TIME',SX,5G15.6)
C6------RETURN
RETURN
END
4-64
HOURS',lOX,
a
List
Variable
Ranae
CNV
Module
DELDY
DELHR
DELMN
DELSEC
DELT
DELYR
IOUT
ITMUNI
Module
Module
Module
Module
Global
Module
Global
Package
KPER
KSTP
Global
Global
PERDY
PERHR
PERMN
PERSEC
Module
Module
Module
Module
Package
Module
Module
Module
Package
Module
Module
Module
PERTIM
PERYR
TOTDY
TOTHR
TOTIM
TOTMN
TOTSEC
TOTYR
of Variables
for
Module SBASlT
Definition
Factor to convert elapsed time from units,
specified
by the user, to seconds.
Length of the time step in days.
Length of the time step in hours.
Length of the time step in minutes.
Length of the time step in seconds.
Length of the current
time step.
Length of the time step in years.
Primary unit number for all printed
output.
IOUT = 6.
Code for time units for this problem:
0 - undefined
1 - seconds
2 - minutes
3 - hours
4 - days
5 - years
Stress period counter.
Reset at the start
of each stress
Time step counter.
period.
Elapsed time in the stress period in days.
Elapsed time in the stress period in hours.
Elapsed time in the stress period in minutes.
Elapsed time in the stress period in seconds.
Elapsed time during the current
stress period.
Elapsed time in the stress period in years.
Elapsed time in the simulation
in days.
Elapsed time in the simulation
in hours.
Elapsed time in the simulation.
Elapsed time in the simulation
in minutes.
Elapsed time in the simulation
in seconds.
Elapsed time in the simulation
in years.
4-65
Narrative
for
Module SBASlV
Module SBASlV calculates
and prints
the overall
volumetric
budget.
The individual
entries
for the budget, which are calculated
by the budget
packages, are passed to this
modules in each of the component-of-flow
module in a tab le named VBVL.
Each entry in VBVL corresponds
to a component-of-flow.
It consists
rate of inflow
for the current
time step, rate of outflow
of four values:
for the current
time step, accumulated
volume of inflow
since the beginning
of the simulation,
and accumulated
volume of outflow
since the beginning
of the simulation.
In this module, the total
of all inflow
rates (TOTRIN),
outflow
rates (TOTROT), inflow-accumulated
volumes (TOTVIN), and outflowaccumulated
volumes (TOTVOT) are calculated.
The percent differences
between those totals
are also calculated
and printed.
The labels
for the
entries
are supplied
by the budget modules in the component-of-flow
packages and passed in the table VBNM.
Module SBASlV performs
Use the
(MSUMl).
1.
terms
counter
its
functions
MSUM to determine
in the
the
following
order:
number of individual
budget
for rates and volumes.
The accumulators
2. Clear the four accumulators
are total
rate into the system (TOTRIN), total
rate out of the system
(TOTROT), accumulated
volume into the system (TOTVIN), and accumulated
volume
out of the system (TOTVOT).
3. For each source
calculated
by the budget
or sink,
modules,
add the budget entries
to the accumulators.
4.
Print
the
number of the time
5.
Print
the
individual
input
6.
Print
the
individual
output
step
rates
rates
and stress
and volumes
and volumes
(rates
and volumes),
period.
and their
and their
totals.
totals.
the difference
between flow into and out of the simulated7. Calculate
flow system.
Calculate
the percent difference
between input and output
rates (lOO*(TOTRIN-TOTROT)/((TOTRINtTOTROT)/2)).
Calculate
the percent
difference
between input and output accumulated
volumes (lOO*(TOTVIN-TOTVOT)/
((TOTVIN+TOTVOT)/2)).
8.
output
9.
Print the differences
rates and volumes.
and percent
RETURN.
4-66
differences
between
input
and
Flow Chart
for
Module SBASlV
The inflow
and outflow
rates for the
current
time step and accumulated
volumes since the beginning
of the
simulation
for each budget entry
(component-of-flow)
are added to
the four accumulators
to obtain the
total
inflow
and outflow
rates for
the current
time step and the total
accumulated
volume of flow in and
volume of flow out since the start
of the simulation.
ENTER
SBASlV
THE NUMBER
CLEAR THE FOUR
RATE AND VOLUME
ACCUMULATORS
FOR EACH
BUDGET ENTRY
ADD THE RATES
AND VOLUMES FOR
THE CURRENT TIME
STEP TO THE
ACCUMULATORS
i
FOR EACH
BUDGET ENTRY
4
PRINT THE NUMBER
OF THE TIME STEP
AND XFDRESS
-
PRINT INFLOW RATE
AND A;C$luM;ELATED
4-67
SUBROUTINE SBASlVt MSUM,VBNM,VBVL, KSl?, KPER, IOUT)
C
C
C-----VERSION 1531 12MAY1987SBASlV
*********************************************************~********
C
C
PRINT VOLUMETRIC BUDGET
********************************************************~*********
C
C
C
SPECIFICATIONS:
-------_----------------------------------------------------------
C
CHARACTER*4 VBNM
DIMENSION VBNM(4,20)rVBVL(4,20)
------------------------------------------------------------------
C
C
Cl---
DETERMINE NUMBEROF INDIVIDUAL BUDGET ENTRIES.
MSUMl=MSUM-1
IF(MSUMl.LE.0)
RETURN
C
C2----
CLEAR RATE AND VOLUME ACCUMULATORS.
TOlRIN=O.
TOTROT=O
.
TOTVIN=O.
TOTVOT=O.
C
C3------
ADD RATES AND VOLUMES (IN AND OUT) TO ACCUMULATORS.
DO 100 L=lrMSUMl
TOTRIN=TOTRIN+VBVL(3,L)
TOTROT=TOTROT+VBVL(4rL)
TOTVIN=TOTVIN+VBVL(lrL)
TOTVOT=TOTVOT+VBVL(Z,L)
100 CONTINUE
C
cx------PRINT TIME STEP NUMBERAND STRESS PERIODNUMBER.
WRITE(IOUT,260) KSTP,KPER
WRITE(IOUTp265)
C
C5------ PRINT INDIVIDUAL INFLOWRATES AND VOLUMES AND THEIR TOTALS..
DO 200 L=lrMSUMl
WRITE(IOUT,275) (VBNM(I,L)rI=l,4)rVBVL(lrL)r(VBNM(I,L),I=l,4~
l,VBVL(3,L)
200 CONTINUE
WRITE(IOUT,286) TOTVIN,TOTRIN
:6 ------PRINT
INDIVIDUAL OUTFLOWRATES
WRITE(IOUT,287)
DO 250 L=lrMSUMl
4-68
ANDVOLUMES AND MEIR TOTALS.
B
WRITE(IOUT,275) (VBNM(I,L)rI=lr4)rVBVL(2rL),(VBNM(I,L)rI=l,4~
lrVBVL(4rL)
250 CONTINUE
WRITE(IOUT,298) TOTVOT,TOTROT
------CALCULATE
THE DIFFERENCE BETWEEN INFLOW AND OUTFLOW.
C
C7A-m-s CALCULATE DIFFERENCE BETWEENRATE IN AND RATE OUT.
DIFFR=TOTRIN-TOTROT
C
c7 B-----
CALCULATE PERCENT DIFFERENCE BETWEENRATE
IN AND RATE OUT.
PDIFFR=100.*DIFFR/((TOTRIN+TOTROT)/2)
C
C7C-----
C
CALCULATE DIFFERENCE BETWEENVOLUME IN AND VOLUME OUT.
DI FFV=TOTVIN-TOTVOT
C7D----- GET PERCENT DIFFERENCE BETWEENVOLUME IN AND VOLUME OUT.
PDIFFV=100.*DIFFV/((TOTVIN+TOTVOT)/2)
C
(33--PRINT DIFFERENCES AND PERCENT DIFFERENCES BETWEENINPUT
C&--AND OUTPUT RATES AND VOLUMES.
WRITE(IOUT,299) DIFFVIDIFFR
WRITE(IOUTt300) PDIFFVIPDIFFR
C
c9------RETURN
l
RETURN
C
C
C
---FORMATS
260 FORMAT(lHO,///30X,‘VOLUMETRIC
BUDGET FOR ENTIRE MODEL AT END OF’
1,’ TIME STEP'rI3,' IN STRESS PERIOD',I3/30X,77('-'1)
265 FORMAT(lH0,19X,‘CUMULATIVE VOLUMES’r6X,‘L**3’,37X
1,'RATES FOR THIS TIME STEP’r6X,‘L**3/T’/20X,l8(‘-‘),47X,24(’-’)
2//26X,'IN:',68X,'IN:'/26X,'---'r68X,'---')
275 FORMAT(lX,18X,4A4,’
=‘,G14.5,39X,4A4,’
=‘,G14.5)
286 FORMAT(lHO,26X,‘TOTAL IN ='rG14.5,47X,'TOTAL IN =’
1,614.5)
287 FORMAT(lHO,24X,‘OUT:‘r67X,‘OUT:‘/25X,4(’-’),67X,4(‘-‘))
298 FORMAT(lH0,25X, ‘TOTAL OUT =‘,G14.5,46X,
‘TOTAL OUT =’
1,614.5)
299 FORMAT(lH0,26X,‘IN
- OUT =',G14.5,47X,'IN
- OUT =‘rG14.5)
300 FORMAT(lHO,15X,‘PERCENT DISCREPANCY =‘rF20.2
1,30X,‘PERCENT DISCREPANCY =‘,F20.2,///)
C
END
4-69
List
Variable
Range
DIFFR
Module
DIFFV
Module
I
IOUT
KPER
KSTP
Module
Global
Global
Global
L
MSUM
Module
Global
MSUMl
PDIFFR
PDIFFV
TOTRIN
TOTROT
TOTVIN
TOTVOT
VBNM
Module
Module
Module
Module
Module
Module
Module
Global
VBVL
Global
of Variables
for
Module SBASlV
Definition
Sum of all inflow
rates minus sum of all outflow
rates
(TOTRI N-TOTROT).
Sum of all inflow
volumes minus sum of all outflow
volumes (TOTVIN-TOTVOT).
Index.
Primary unit number for all printed
output.
IOUT = 6.
Stress period counter.
Reset at the start
of each stress
Time step counter.
period.
Index for individual
flows.
Counter for the budget entries
and labels
in VBVL and
VBNM.
MSUM-1.
Percent difference
between the rate in and rate out.
Percent difference
between the volume in and volume out.
Accumulator
for the total
of all inflow
rates.
Accumulator
for the total
of all outflow
rates.
Accumulator
for the total
of all inflow
volumes.
Accumulator
for the total
of all outflow
volumes.
DIMENSION (4,20),
Labels for entries
in the volumetric
budget.
DIMENSION (4,20),
Entries
for the volumetric
budget.
For flow component N, the values in VBVL are:
(l,N) Rate for the current time step into the flow
field.
(2,N)
Rate
(3,N)
(4,N)
field.
Volume into the flow field
during simulation.
Volume out of the flow field
during simulation.
for
4-70
the
current
time
step
out
of
the
flow
CHAPTER 5
I
BLOCK-CENTEREDFLOW PACKAGE
Conceptualization
The Block-Centered
components
adjacent
the
Flow (BCF) Package computes
of the finite-difference
It also
cells.
movement of water
it
and Implementation
a node is located
name Block-Centered
developed
computes the terms
Flow is
2, the equation
which
that
determine
determine
To make the
to and from storage.
is assumed that
In Chapter
equation
at the center
given
the conductance
flow
the
required
between
rate
of
calculations,
of each model cell;
thus
to the package.
of flow
for
each cell
in the model was
as
+CCi-1/2,j,khi-l,j,ktCRi,j-1/2,khi,j-l,k
Cvi,j,k-1/2hi,j,k-1
t (-Cvi,j,k-1/2’CCi-l/2,j,k-CRi,j-1/2,k-cRi,j+l/2,k
- CCi+l/2,j,k-CVi,j,k+1/2t~~~Fi,j,k)hi,j,kt~~i,jtl/2,khi,jtl,k
+ ~~i+l/2,j,khi+l,j,kt~~i,j,k+l/2hi,j,k+l
The CV, CR, and CC coefficients
called
"branch
of external
source
conductances
terms
that
partially
and storage
between nodes--sometimes
The HCOF and RHS coefficients
and storage
terms,
Besides
terms.
the BCF Package calculates
but
correct
downward flow
Under these
increases
rather
the flow
reaches
in proportion
a constant
equations,
to correspond
conditions
to this
aquifer
the flow
limiting
limiting
value.
reducing
value.
the
flow-correction
becomes
to the underlying
to the head difference
in effect
5-l
are composed
calculating
are added to HCOF and RHS when an underlying
no longer
aquifers,
terms
terms
unsaturated.
aquifer
are conductances
conductances."
(2%
= RHSi,j,k*
between
The additional
the expressions
for
The following
d scussion
is divided
of the BCF package
Equations,
Horizontal
Conductance
of the conceptualization
into
Conductance
Under Wat r Table
Vertical
Flow Calculation
Storage
Term Conversion,
nine
sections:
Basic
Under Confined
Conditions,
Applicability
Conductance
Conditions,
Vertical
Under Desaturating
and implementation
Horizontal
Conductance
Conditions,
Formulation,
Storage
and Limitations
Formulation,
of Optional
Formulations
and Data Requirements.
Basic
The concept
(equation
It
(9)).
of equivalent
of hydraulic
(figure
Darcy's
is
conductance
reviewed
conductance
Conductance
law.
is
Conductance
for
was introduced
here and extended
elements
a combination
law defines
Equations
arranged
of several
one-dimensional
flow
in Chapter
to cover
2
the calculation
in series.
parameters
in a prism
used in Darcy's
of porous
material
23) as
Q = KA(h2-hI)/L
(30)
where
Q is the
flow
(Lst-1);
K is the hydraulic
flow
conductivity
is the
L is the
Conductance,
in the direction
of
(Lt-1);
A is the cross-sectional
h2-hl
of the material
area perpendicular
head differences
length
of the flow
C, is defined
across
path
to the flow
the prism
parallel
(L*);
to flow
(L);
and
(L).
as
C = KA/L.
(31)
5-2
a
Q
Q
Explanation
K
Is Hydraulic
Conductivity
h,
Is the Head at the Left End of the Prism
hl
Is the Head at the Right End of the Prism
Q
Is the Flow Rate from the Left End to the Right End
L
Is the Length of the Flow Path
A
Is the Cross Sectional
Figure 23.-Prism
Area Perpendicular
to the Direction
of porous material illustrating
5-3
of Flow
Darcy’s law.
Therefore,
Darcy's
law can be written
as
Q = C(h2-hl).
Another
(32)
form of the conductance
definition
for
horizontal
flow
in a prism
is
C = TW/L
(33)
where
T is transmissivity
of flow
(L*t-1);
W is the width
Conductance
particular
three
If
a prism
series--that
24--and
representing
for
a particular
aligned
the entire
prism
is the
of flow
of a prism
differ.
in the direction
can be calculated.
is
of flow,
n
C
i=l
known, a conductance
The equ ivalent
in the prism
div ided
conductance
by the
(32))
(34)
of head across
each section
in series
gives
Ahi = hA-hD.
for
head change across
9i
--
i=l
Ci
the
identity
(35)
each section
gives
n
c
head
the prism.
continuity
Substituting
in
as shown in
c = Q/b/+$)
Assuming
a
by three
of two or more subprisms
of each subprism
rate
and for
the conductances
generally
consists
sequentially
of material
medium characterized
will
material
prism
prism
conductivity,
directions
the conductance
the entire
change across
for
of hydraulic
of porous
is,
in the direction
(L).
In an anisotropic
principal
of the prism)
and
is defined
directions
in these
thickness
of the prism
direction.
principal
figure
(K times
= hA-hg.
5-4
using
Darcy's
law (equation
C”
--
1
-=-1
c
Cl
L
-----m-s
1
+-+-+...+-
1
1
c2
C3
C"
Y
Explanation
Q
Is the Flow Rate
%l
Is Conductance of Prism m
hfn Is Head at the Right Side of Prism m
Ah,,, Is the Head Change Across Prism m
C
Figure
Is the Conductance of the Entire Prism
24.-Calculation
of conductance
in series.
5-5
through
several prisms
Since
flow
tion
is one-dimensional
all
in storage,
and we are assuming
qi are equal
to the total
hA-hB
n
-t = hA-hB and ----= 1
Ci
i=l
Q
Q;
i=l
By comparison
with
equation
no accumulation
flow
or deple-
Q; therefore,
1
--.
Ci
(34),.it
(37)
can be seen that
1
nl
m-s = c mm .
C
is1 Ci
Thus for
valent
a set of conductances
conductance
tances.
the
sum of the
inverses
of the
are only
two sections,
.
the
equations
between
rather
specify
the
subscript
the
conductance
of
conductances
terms,
horizontal
individual
equivalent
conduc-
conductance
presented
adjacent
ccl
defined
within
nodes.
CR terms
Conditions
in this
Is--i
CR and CC of equation
report
.e.,
(29),
"l/2"
between nodes i,j,k
25 illustrates
the conductance
two cells
For example,
conduc-
cells.
The
are calculated
along
within
CRi,j+l/2,k
rows and
Similarly,
same column.
as opposed to conductance
is used.
use equiva-
“branch
individual
are oriented
between two nodes in the
between nodes,
notation
Under Confined
between two nodes in the same row.
conductance
conductance
to calculate
nodes
conductance
specify
Figure
than
conductance
between adjacent
of the equi-
(39)
The finite-difference
conductances
inverse
+ C2).
Conductance
horizontal
nate
in series,
Horizontal
tances,"--
terms
arranged
the
to
c = ClC2/(Cl
thus
equals
When there
reduces
lent
(36)
CC
To desiga cell,
represents
and i,j+l,k.
along
between nodes.
5-6
a row, and the parameters
Two assumptions
are made:
used
(1)
I
I
I+----DELRi-fPDELRi+,-
T
i
TRi,j+l,k
I
I
& i,j+l,k
DELCi
I
I
1.
T*i
CRi Ij+x I k
= 2 DELCi x TR
Ij *k TRi 9j+l ?k
ijk
I 8 DELRj+, + TRi 9j+,*k DELRj
Explanation
TRi 1
j 1k
CRi 1
j+% ,k
Is Transmissivity in the Row Direction in Cell i,j,k
Is Conductance in the Row Direction Between Nodes i,j,k and i,j+l,k
Figure 25.-Calculation
of conductance between nodes using
transmissivity and dimensions of cells.
5-7
the nodes are in the
form over
center
conductance
(39)
gives
of two half
mi,j+1/2,k
Substituting
= ClC2/(Cl
the
cells
and (2) the transmissivity
Thus the conductance
each cell.
lent
of the
conductance
cells
between the
in series
is uni-
nodes is the
(Cl and C2).
equiva-
Applying
equation
(40)
+ CZ)*
for
each half
cell
from equation
(33)
gives
TRi,j,k
DELCi
TRi,j+l ,k DELCi
------------m-------------l/2 DELRj+l
l/2 DELRj
= ----------------------------------TRi,j,k
DELCi
TRi,j+l,k
DELCi
-------B----+ m----w--------l/2 DELRj+l
1/2 DELRj
CRi,j+1/2,k
where
TR is transmissivity
in the
row direction
DELR is the
grid
width
along
a row (L);
DELC is the
grid
width
along
a column
DELR and DELC are identical
which
were introduced
new notation
Centered
Simplification
mi,j+1/2,k
is
and
(L).
to the terms Ar and AC, respectively,
in figure
introduced
(L*t-l);
4 and equation
here to conform
(3),
to the
Chapter
input
2.
of the
The
Block-
Flow Package.
of the
above expression
= 2 DELCi
gives
the
final
equation
TRi,j,kTRi,j+l,k
-------------------------------TRi,j,kDELRj+l
+ TRi,j+l,kDELRj.
5-8
(41)
The same process
can be applied
to the calculation
of
cci+l/z,j,k
giving
TCi,j,kTCi+l,j,k
= Z DELRj ----------_-------------------TCi,j,kDELCi+I
+ TCi+I,j,kDELCi
cci+l/z,j,k
(42)
where
TC is the transmissivity
(41)
and (42)
are used in the
conductances
between
the transmissivity
in the cells
set equal
unconfined,
the
cell
dimensions
then
using
Transmissivity
one of the
if
following
HNEWi,j,k
then
if
TOPi ,j,k
then
as the
product
conductance
equations
(41)
within
a cell
three
equations
However,
where
between the nodes
conductance
is unconfined
start
horizontal
Conditions
horizontal
conductance
is done at the
is calculated
thickness;
a layer
Equations
the equations.
Under Water Table
of horizontal
This
head fluctuates.
saturated
If
the
conductance
invoking
is confined,
simulation.
new values
transmissivity
to zero without
which
(Lzt-1).
of the model.
the
is zero,
Conductance
In a model layer
for
each layer
of both cells
is
column direction
BCF Package to calculate
nodes within
Horizontal
constant
in the
will
or potentially
must be calculated
of each iteration.
of hydraulic
is calculated
be
as the
First,
conductivity
from transmissivity
and
and
and (42).
in the
row direction
is calculated
using
2 TOPi,j,k,
TRi,j,k
= (TOPi,j,k
> HNEWi,j,k
TRi,j,k
- BOTi,j,k)
HYRi,j,k;
(43)
> BOTi,j,k,
= (HNEWi,j,k
- BOTi,j,k)
5-9
HYRi,j,k;
(44)
if
HNEWi,j,k
then
2 BOTi,j,k,
TRi,j,k
= 0
(45)
where
HYRi,j,k
is the hydraulic
direction
conform
(Lt.-l);
to the
(this
input
of cell
notation
of the
is the elevation
of the top
BOTi,j,k
is the elevation
of the bottom
sivity
in the
user;
the
horizontal
When head drops
below the aquifer
model has no provision
errors
may arise
in water-level
heads occur
for
in attempts
occur.
during
Errors
iteration;
head to drop erroneously
to no flow
controlling
slowing
the
for
the
all
problem,
rate
of
the
equations
section
whether
on data
arise
botton
the
set to no flow;
the
cell.
oscillations
iterative
solvers
herein
a layer-type
actual
contain
reversals
of computed
the
steps.
a
Thus
oscillations
of the cell,
and time
and cell
(45)),
in which
if
by
each layer.
(equation
of a dewatered
situations
iterations
cell
cause
will
change
As a means of
provisions
for
convergence.
or not the simulation
(43)-(45)
bottom
such computational
below the
In the program described
specify
can also
if
succeeding
this
to simulate
specified
from transmissivity
and is permanently
resaturation
of transmis-
for
dimensions.
and
(L).
is a constant
are calculated
to be dewatered,
i,j,k
factor
in each direction
is cons idered
(L);
anisotropy
Conductances
cell
here to
is the product
factor
row
Flow Package);
i,j,k
of cell
and a horizontal
anisotropy
in the
introduced
of cell
in the column direction
row direction
is
i,j,k
Block-Centered
TOPi,j,k
Transmissivity
the
conductivity
a
is to be invoked.
of water
This
requirements.
5-10
table
flag,
LAYCON, is used to
conditions
is discussed
through
more fully
in the
a
Vertical
Vertical
conductance
from an input
conductivity
from cell
i,j,k
in a single
thicknesses
Azl,
Az2
horizontal
(or map) areas
calculated
g, in this
interval
to contain
between two nodes,
n geohydrologic
conductivities
KI,Kz
the vertical
conductance
area is given
around
nodes
of an individual
by
Kg DELRj*DELCi
= --------------
%
layers
. . . . Kn and
The map area of the cells
. . . . AZ,.
data
hydraulic
the vertical
hydraulic
the model using
and vertical
and using
is DELRj*DELCi;
layer,
within
both thickness
may be considered
vertical
and i,j,k+l
geohydrologic
incorporates
term,
Formulation
are calculated
In general,
dimensions.
having
terms
which
and and i,j,k+l,
or units,
i,j,k
array
Conductance
(46)
Azg
The equivalent
interval
between
geohydrologic
vertical
nodes i,j,k
layers
conductance,
and i,j,k+I
as conductances
1
----------
for
ci,j,k+l/z,
is found
in series;
the
by treating
this
full
the
vertical
n individual
yields
=
Ci,j,k+l/Z
1
91
i
rearranging
equation
n Azg
1
-----------------
---
= -----------
KgDELRj*DELCi
------------Azg
DELRj*DELCi
*I
g=l
Kg
(47)
(47)
Ci,j,k+l/Z
------------DELRj*DELCi
1
= ------mn AZ
c
g=l
5-11
-ii;
(48)
g
The quantity
----------has been termed the "vertical
DELRj*DELCi
Vcont. l,j,k+l/2
in this report;
thus we have
is designated
leakance
' and
1
vconti , j ,k+l/2
Vcont
herein.
(or
is the term
That is,
harmonic
node i,j,k
which
rather
than
mean) vertical
the
values
this
multiples
is generally
for
the
interval
it.
for
between
will
the
It foll ows that
a series
Vconti,j,k+l/2,
intervals
the
Although
to be given
t0
between
specifies
of the
hydraulic
cell
interval
and cell
Vcont
array
is not
the discussion
layers.
5-12
the Vcont
array,
leakance
for
and the
the
layer
lowermost
read into
program;
input
vertical
the
The
The Vcont
is,
read,
of three-dimensional
that
area,
The
to the
(49).
is the
read for
of Vcont are thus
cell
conductance.
externally
is
between
and thickness.
i,j,k+l--that
the array
fact
by the
of a two-dimensional
which
emphas ize the
interval
vconti,j,k+l/2,
of equation
for
in terms
the
vertical
of Vconti,j
arrays,
and an equivalent
divided
conductivity
an application
input
for
or determined
i,j,k
values
thickness
the term
area to obtain
Each value
layer
of two-dimensional
continue
a total
read as the elements
between
in the model described
conductivity
user
calculated
each layer.
interval
in the model .
both
done through
are actually
Vconti,j,
the
Vcont by cell
of Vcont must'be
values
specifying
conductance
and as such incorporates
used as input
hydraulic
and node i,j,k+l,
is actually
program
actually
(4%
=
below
layer
the model through
in this
array
va lues
section
notation,
refer
to the
b
Figure
within
a single
Kz i,j
which
application
hydrogeologic
is uniform
of equation
at least
where Azk+1/2,
the
*vk+l
m---w
in which
2
'
might be found,
Figure
represent
and i,j,k+l
represents
for
example,
fall
which
is again
for
unit
layer
thickness
where several
in order
adjacent
by its
Vcont in this
model layers
of these
so that
nodes i,j,k
Each
layers.
hydraulic
over the
are used to
cell
conductivity,
area.
The
case becomes
where Avk is the thickness
B
units,
situation
resolution.
model layers
of vertical
1
= -------------------
(51)
(*"k&2
+ ---mw-----
Kz i,j,k
Kz i,j,ktl
of model layer
is the thickness
layer
This
vertical
geohydrologic
at least
1.
and
are used to represent
greater
hydrogeologic
(4"k)/2
--------
i,j,k
case,
*vk
is the sum of --2-
as in figure
to provide
own value
Vcon+,i,j,ktl/2
KZ
For this
(50)
between nodes,
assumed to be uniform
Avk+l
conduct ivity
Kz i,j
= ------Bk+1/2
, j ,k+l/2
at the midpoints
is characterized
both fall
hydraulic
area.
27 shows a case in which two adjacent
layer
expression
the cell
within
distance
AV
two vertically
and i,j,k+l
(49) yields
vertical
geohydrologic
nodes i,j,k
hav ing a vertical
unit,
vconti
a single
in which
26 shows a situation
k
of model layer
is the vertical
in cell i,j,k
K, i j k+l is the vertical
lby&r in cell i,j,ktl
hydraulic
hydraulic
5-13
ktl
conductivity
conductivity
of the upper
of the
lower
,
I
DELRj
Single
Geohydrologic
Unit
I
I
I id,k
Az k+‘/;
A-----0’ I
/’
I
00
0
!
/0
I
I i,j,k+l
0
Avk+
0
0
0
0
0
0
0
.
&“I<
I .
I
I
A”k
Boundary
between
model layers
--
A”k+l
2
--
I
-------
/
Figure 26.-Diagram
for calculation of vertical
leakance, Vcont, between two nodes
which fall within a single geohydrologic unit.
5-14
DELRj
I
I
I
I
I
Boundary
between
model layers --(Coincident with
Geohydrologic
Boundary)
Geohydrologic
Unit A
0 Uk
0-t----/ /’ i
/’
I
/’
-
Kzi,j,k
-1-----
b”k+l
AT--Geohydrologic
/
Unit B
I
I
A”k+l
0
0
/
Kzi,j,k+l
0 i,j,k+l
----
------
0
/’
/
4’
Figure 27.-Diagram for calculation of vertical
leakance, Vcont, between two nodes
located at the midpoints of vertically
adjacent geohydrologic units.
5-15
-B--m-_
If
one value
larger
only
of K, is much smaller
K, value
the term
denominator
i,j,k+l
be negligible
involving
of
Figure
will
the
within
situation,
(51).
Thus for
this
need be retained
in the
upper
the
In this
unit.
summation
of equation
semiconfining
The resulting
in which
the
condition,
in the
node i,j,k
at the median depths
(i.e.,
by a semiconfining
be represented
aquifer.
KZ value
the term containing
(51).
are taken
aquifer,
in equation
smaller
28 shows a third
are separated
than the other,
unit,
expression
of)
case,
(49)--the
two aquifers
three
intervals
lower
half
and the upper half
for
and node
which
must
of the
of the
lower
Vcont is
1
.l
VCOnti,j,k+l/2
=
(52)
------~~~~~~~~~~-----
UL/2
&l/2
A-%
--m-m + --- t -me-Kzu
KZC
KZL
where
AZ~ is the thickness
of the upper aquifer
AZc is the thickness
of the confining
AZL is the thickness
of the
K,,
for
aquifer
vertical
hydraulic
conductivity
of the upper
Kzc is the
vertical
hydraulic
conductivity
of the semiconfining
K,L is the
vertical
hydraulic
conductivity
of the
(i,j)
is much smaller
involving
bed
is the
each of these
location
lower
a
K,,
terms
must in general
In many applications
of the nodes.
than
either
be considered
K,,
or K,L;
and K,L are negligible
in these
in equation
lower
to vary with
it
turns
situations
(52) so that
aquifer
unit
aquifer;
and
the map
out that
K,,
the terms
the
expression
Vcont becomes
Kzc
Vconti,j,ktl/Z
= ;;
(53)
-,
a
5-16
DELRj
Kzu
AZ,/2
I
Upper Aquifer vertical conductancx
of lower half = Cu
0 i,j,k
--
-N--L-
AzC
-
-/
Kzc
AZL/2
Semiconfining layer vertical conductance =C,
I
I
KZL
0 i,i,k+l
Lower Aquifer vertical conductance
of upper half = CL
---Be-
1
-=-+-+-=
%
1
1
CIJ
CC
1
CL
A 2,/2
+
VCONT..
+
KZL
1
I,j,k + l/2
=
AZ,/2
-IK zu
28.-Diagram
A 2~12
AZ,
Kzc
Kzu
Figure
--
/
for calculation
of vertical
Az,
-l-
K zc
leakance,
AZLI~
KZL
Vcont,
between two nodes located at the midpoints of aquifers
which are separated by a semiconfining unit.
5-17
Boundary
Between
Model
Layers
If
the formulation
in figure
28, and if
of equation
the
further
bed makes no measureable
storage
sents
the
capacity
the
confining
two model layers.
This
and is frequently
referred
In summary,
Vcont,
which
ness,
rather
program
requires
using
than
user to calculate
in the
interval
situations
also
if
used as input
spacing
figure
elevation
data.
terms,
to either
three-dimensional
for
data,
unconfined)
26-28.
it
formulation,
without
to the
storage
actually
of figure
layers
(51 1, (52)
approach
This
occur
or (53)
involves
the flexibility
vertical
the orthogonal
9-c,
simulation
of the
of
conductivity
coefficient
reads
either
modification
5-18
(50),
this
The
program,
(or hydraulic
three-dimensional
array,
and thick-
n hydrogeologic
transmissivity
mesh such as that
input
conductance.
increases
and layer
12,
approach.
vertical
While
actually
the model never
a direct
of figure
and conductivity.
or equat ions
nodes)
and
between the
conductivity
externally
case (where
k, repre-
aquifer,
a single
thickness
Vcont values
between
lower
conductance
utilizes
hydraulic
Thus the model can implement
9-b or a deformed
be adapted
herein
or the
model layer
to that
area to obtain
Because layer
model application.
equivalent
conductance
the
vertical
shown
the confining
"quasi-three-dimensional"
inputs
general
of input
represents
vertical
shown in figures
some preprocessing
and bottom
both
Vcont by cell
in the vertical
in effect
is
to as the
independent
(49)
then
as the
the model described
multiplies
the
simply
are made that
horizontal
k+l
formulation
incorporates
equation
in the
model layer
to the situation
to the
model layer,
bed is treated
is applied
assumptions
contribution
of either
upper aquifer,
(53)
are
gird
mesh of
and can similarly
or to the quasiprogram.
Vertical
The basic
given
Flow Calculation
finite
difference
- h!i,j,k)
+
In this
equation
cell
Qi,j,k
the term
i,j,k
(equation
i,j,k
through
where following
indicates
flow
cell.
its
into
however,
situations
unsaturated--for
to fall,
(24))
was
+
+
this
by a confining
value
value
indicates
that
the water
of the top of the cell.
of a confined
aquifer
below the top of the aquifer.
condition
is shown in figure
bed are simulated
between the two layers,
a positive
flow
that
level
is
using
and the confining
by cell
In terms
Two aquifers
i,j,k,
bed by the
Pumping from the
5-19
out of
cells
in each
may become
the
vertical
lower
levels
of
separated
the quasi-three-dimensional
represented
CVi,j,k+I/2.
29.
of qi,j,k+I/2
There are,
when drawdown due to pumpage causes water
locally,
i,j,k+l,
- i.e.,
a portion
the flow
(55)
and (55) are based on the assumption
in which
in which the upper aquifer
by cell
gives
- 'hy,j,k)
(24),
and a negative
saturated
(54)
i.e.
(hy,j,k+I
the elevation
example,
at least
simulation,
(54)
than
m
- hi,j,k)
of equation
i,j,k
are fully
higher
face,
= CVi,j,k+l/2
cell
Equations
stands
lower
the convention
and i,j,k+l
i,j,k
- hT,j,k)
+ CCi+I/2,j,k(h!i+I,j,k
CVi,j,k+I/2(hy,j,k+I
qi,j,k+1/2
aquifer
cell
- hl,j,k)
Pi,j,khy,j,k
cell
for
- hY,j,k)
+ CVi,j,k+I/Z(hT,j,k+I
m
m-l
hi j k - hi,j,k
= ssi,j,k(ArjACiAVk)
--Iii-~-;--;--m-
CVi,j,k-I/2(h!i,j,k-1
the
equation
Conditions
as
+ CCi-I/2,j,k(h!i-I,j,k
into
Under Dewatered
approach,
underlying
conductance
layer
has.
0
Cell i,j,k
Confining
Unit
Topi
Ij 9k+l
hi 3j Ik+l
-M-B
-w-B
Cell i,j,k+l
Figure 29.-Situation
in which a correction is required to limit the
downward flow into cell i,j,k+l, as a result of partial
desaturation of the cell.
5-20
b
lowered
the water
the cell,
area.
level
so that
the aquifer
An assumption
pressure
taken
unit
the top
of the
through
hi,j,k+l
lower
is simply
lower
cell.
in equation
If
will
level,
in the
in formulating
expression
given
of equation
(55).
However,
system
direct
substitution
solution
used.
would
of finite
process.
The flow
of equation
(54).
this
confining
the head is simply
Just
below the
at that
lower
prevail,
unit
that
surface
so that
the
is atmospheric--
point-i.e.,
elevation
from cell
base of the
the elevation
is designated
by substituting
of
TOPi,j,k+l,
the
TOPi,j,k+l
for
this
m
- hi,j,k)
the flow
lower
(56)
if
will
cell.
for
we consider
matrix
To avoid
this
term of equation
The flow
no longer
i,j,k
into
in
unsymmetric,
condition,
in place
into
cell
i,j,k
probelm
the
[A]
of the
of equation
the equation
problems
for
in the
on the
by this
(27)),
node
approach
to remain
as computed
flow
of the expression
an alternative
is allowed
5-21
to this
of coefficients
generating
(55)
on the water
be to substitute
(matrix
(56)
(i.e.,
be negative);
approach
the matrix
equations
i,j,k+l
be dependent
would
(54),
(56)
will
qi,j,k+l/z
equation
difference
to cell
The simplest
cell
into
i,j,k
(26),
of the expression
render
saturated
across
Thus the head at the
of equation
the equation
entire
i,j,k
B
in
fully
unit
= CVi,j,k+l/2(TOPi,j,k+l
be downward,
condition
hi,j,k+l,
remains
of the confining
this
the cell
(55),
the convention
but under this
layer
conditions
bed is obtained
qi,j,k+1/2
following
surface
the elevation
the confining
Thus the flow
unsaturated
in the model formulation.
confining
flow
however,
sensed on the
as zero
i,j,k--hi,j,k.
of the top of
within
the head difference
of the confining
in cell
unit,
unconfined
the confining
and we consider
in the upper aquifer
below the elevation
is effectively
At the upper surface
of the confining
i,j,k+l
is made that
from top to bottom,
unit.
in cell
is
left
term,
side
is
CVi,j,k+l/2(h~,j,k+l
(where in this
indicating
case,
since
hi,j,k
movement out of cell
c
- hy,j,k)
> hi,j,k+J,
i,j,k.)
the
computed
The "actual"
flow
can be obtained
qc,
by subtracting
equation
negative,
flow into cell i ,j,k
m
- hi ,j,k)
(where again
is given by equation
(56) as CVi,j,k+J/2(TOPi,j,k+J
m
indicating
movement out of the ce 11).
> TOPi,j,k+l
hi,j,k
term,
is
(56)
A correct
ion
from equation
(55)s
i.e.
qc = (computed
flow
into
- ("actual"
cell
flow
i,j,k)
into
all
i,j,k)
equation
the
(24),
(54),
operation
is
for
allowing
of the model,
qc is added to the
involving
circumvent
computed flow
the term qc is added to the
rearranged
introduces
the
equation
(54),
to the form of equation
right
a difficulty,
this
right
side
which
is
(26);
RHS, of equation
since
qc contains
difficulty,
from the preceding
to remain
side,
unknown heads must be kept
on the
qc is actually
interation,
rather
(57)
- TOPi,j,k+l)
CVi,j,k+l/2(h!J,j,k+l
To compensate
=
side
of equation
identical
(26).
This
side
of
(54).
In
to equation
the term
immediately
hF,j,k+J,
and all
of equation
computed using
than that
left
and in practice,
the term
left
on the
the
(26).
value
from the current
terms
to
of hF,j,k+J
iteration,
i.e.
m,n-1
qc,n
= CVi,j,,k+l/2(hi,j,k+l
(58)
- TOPi,j,k+l)
where qc,n is the value of qc to be added to RHS in the nth iteration,
m,n-1
is the value of hm
l,j,k+l
from the preceding
iteration,
n-l.
hi ,j,k+l
m,n-1
m,n
convergence is approached the difference
between hi,j,k+J
and hi,j,k+J
progressively
smaller,
and the approximation
5-22
involved
in
(58) thus
and
As
becomes
becomes
more accurate.
In the
Value Of hi ,j ,k+I
i,j,k
correction
cell
level
cell,
cell,
in formulating
To examine this
i,j,k-1.
minus
cell,
For this
flow,
should
be added to the
programming
point
of view,
is to add the term
while
adding
HCOF forms
case,
into
the computed
whereas
of equation
the
of the coefficient
(54)
left
TOPi,j,k)
of hy,j,k,
side
to the
which
of the coefficient
matrix,
this
symmetry
of the coefficient
matrix;
at the same time,
an unknown head value
on the
correction
right
cell
into
cell
i,j,k
flow
into
computed
m
- hi,j,k)
where q,'
or (26).
From a
this
correction
of equation
RHS term.
(26),
Because
on the main
does not affect
side
A
the
"actual"
falls
diagonal
in placing
flow
way to handle
to HCOF on the
l
for
from the
The difference,
the most efficient
(CVi,j,k,I/2
for
i,j,k
= CVi,j,k-I/E(TOPi,j,k
hand side
cvi,j,k-l/2
the term
part
right
trial
of the cell.
we now take
flow
- TOPi ,j,k)*
qc'
initial
equations
the equations
correction,
- hy,j,k)
is thus
the
below the top
and we consider
iS CVi,j,k-1/2(h~,j,k-l
"actual"
the
has "dewatered"-i.e.,
be applied
from above iS CVi,j,k-I/2(hy,j,k-I
the Cell
i,j,k+l,
has fallen
itself.
step,
q,.
in i,j,k+l
to be the dewatered
overlying
of each time
above is used in formulating
underlying
must also
dewatered
i,j,k
described
when the
when the water
iteration
is used in computing
The process
cell
first
the
the
problems
entailed
of the
equation
are
avoided.
In summary,
must be made--one
cell,
whenever
dewatering
in formulating
and one in formulating
of a cell
equation
equation
(26)
5-23
(26)
as it
occurs,
as it
two corrections
applies
applies
to the overlying
to the dewatered
cell
These two corrections
itself.
case using
(26)
the designation
It
is formulated.
i,j,k
is
are applied
corrections
has been developed
[A]
the
procedure
program
(27),
limiting
to be implemented.
This
discussed
in the
distinguishes
constant
between
throughout
flow
on data
may "convert"
as the water
This
from
described
in the
For a layer
the
simulation,
of the storage
applies
terms,
simulation,
value
in a cell
falls
the
storage
coefficient
and those
in which
to a water
section
requirements.
on data
storage
storage
expression
to an individual
coefficient
formulation
in equation
cell,
= ssi
,j,k
or not
conditions
is
LAYCON, as
i,j,k,
described
the
(24)
flag,
form
m
hi,j,k
of the cell.
LAYCON, as
is to remain
This
coefficient
or vice-versa,
above the top
or (54).
remain
storage
value,
layer
herein
values
is based upon a direct
constant
during
application
expression,
which
has the
AV
--
table
below or rises
the use of the
the
form of the
whether
type-flag,
program
is made through
in which
both
efficiency.
specifies
layer
that
of the coefficient
under dewatered
the
equation
Formulation
in which
a confined
level
distinction
layers
the
in each
requirements.
of storage
the
the user
is done through
formulation
and that
program
herein,
which
however,
and to maximize
Storage
In the
event,
above,
for
the symmetry
vertical
section
the cell
to preserve
described
for
separately
to keep in mind,
in any dewatering
of equation
In the
to represent
important
corrections
matrix
are discussed
(ArjACiAVk)
At
------v--------
m-l
- hi,j,k
tm - tm-l
5-24
033)
AV
where --
is the
rate
of accumulation
of water
in the cell,
and as such must
At
appear on the
storage
SiOnS;
right
side
of equation
(24) or (54);
of the material
in cell i,j,k;
m
hi,j,k is the head in cell i,j,k
is the head in cell
the end of time
In equation
(26)
i,j,k
step m; and tm,I
is the time
at the
the
"storage
capacity"
the
"primary"
or the
which
for
rate
"primary
storage
is used when storage
m-l
of accumulation
step m; hi,j,k
SCIi,j,k
capacity"
term
m-l.
is termed
i,j,k;
from a secondary
conversion
in storage
step
of cell
scli,j,k
Using the concept
section.
dimen-
where
the term
is used to distinguish
in the following
the expression
report
cell
end of time
was introduced,
scli,j,k
In this
designation
capacity
explained
notation
specific
m-l; tm is the time at
step
the
are the
at the end of time
end of time
ssi,j,kArjACihVk.
storage
and Avk
ACi
at the
=
SCIi,j,k
Arj,
is the
ssi,j,k
is invoked,
of storage
in cell
i,j,k
as
capacity,
can be
written
m-l
- hi,j,k)/(tm
scli,j,k(hy,j,k
This
expression
SCIi,j,k
through
is separated
hy,j,k/(tm-tm_I),
the term
in the term
to the
storage
a confined
these
storage
of the cell
ssi,j,k
Avk;
material
for
in the
and
on the
of dimensionless
layer
two terms
which
HCOFi,j,k,
RHSi,j,k
The input
into
right
side
an unconfined
layer
(26),
left
/(tm-tm-I),
side
which
of
(26)
is included
of (26).
values
coefficient
multiplied
in the
l
Flow Package requires
coefficient
material
cell.
hTIi,k
Block-Centered
storage
in equation
is incorporated
scli,j,k
- tm-1)
in each layer
values
by layer
they
The incorporation
5-25
are given
thickness
are equal
of layer
to the
thickness
specification
of the model;
for
by the specific
in the cell,
specific
into
yield
the
of the
confined
storage
term maintains
of varying
the flexibility
and to implement
thickness,
or "quasi-three-dimensional"
The storage
as array
values
in the
by the
cell
areas,
stored
in the
input
instructions.
ArjACi,
to create
the
simulations
during
cell
in which
of the
falls
in effect
the
versa,
possible,
cell
simulation.
capacity,
SCli,j,k
Values
through
of the cell
values,
and they
are
coefficient
is used to
of confined
for
storage
the two-dimensional
level
cell
specific
coefficient
area;
a secondary
yield
multiplied
array
sfl.
5-26
conditions,
the
the
represent
each cell
pumpage, or if
or
appear to be
for
will
saturated)
of the cell--then
conditions
is done,
of a cell
(fully
table
layer
for
throughout
of simulated
to water
remains
the top
above the top
When this
by cell
input
crosses
term conversion
in the
cell
in a confined
Where these
any cell
represent
level
from confined
flag.
multiplied
is adequate
scli,j,k
in each individual
rises
storage
layer-type
above,
as a result
cell
simulation.
user may invoke
use of the
SCzi,j,k
are designated
are then multiplied
capacity
the water
the water
"converts"
the
level
If
if
system
through
storage
they
or below the top of the
in an unconfined
during
the
storage
described
the water
of the
below the top
level
by layer;
discretization.
Term Conversion
capacity
a simulation--i.e.,
the water
vice
storage
above the top
course
three-dimensional
of vertical
These values
layers
SC1 array.
The primary
either
the direct
are read layer
Storage
for
either
conceptualizations
coefficient
sfl
of the program to represent
entire
primary
the
storage
by cell
in the
These confined
layer
layer
storage
confined
capacity,
area.
are read
storage
coefficient
values
capacities,
which
for
each cell
array
are stored
in the
layer
unconfined
expression
for
which
rate
in the
yield
storage
In a layer
by cell
areas
to obtain
SCl.
Values
array
are read through
These specific
sf2.
obtain
are multiplied
values
are multiplied
has been designated
of accumulation
areas
in array
for
storage
term
in storage
in cell
i,j,k
yield
input
by cell
are stored
storage
of specific
the two-dimensional
which
capacities,
confined
to
SC?.
conversion,
the
is formulated
as follows
AV
it
m
SCB (hi,j,k
- TOPi,j,k)
+ SCA (TOPi,j,k
= ------------------------------------------------tm - tm-l
Av
-- is rate of accumulation
At
as such must appear on the right side
where again
storage
capacity
SCB is the
effect
"current"
during
in cell
in effect
i,j,k
the
Since
time
the
step,
storage
given
storage
iteration
at the
the cell.
there
storage
the time
step
the following
for
(hy,j,k)
iteration
in process.
of time
is no free
capacity
is,
time
i,j,k
(24)
at the start
is,
the
also
or (54);
surface
at that
storage
and
SCA is the
of the time
step;
capacity
in the cell
time
at the
is taken
start
and
in
equal
to SCIi,j,k.
5-27
to SCIi,j,k;
of the
as the confined
If,
during
of head for
to be above the top of the cell,
set
i,j,k
a case in which the head
m-l
step m (hi,j,k)
is above the top of
step m, the computed value
is
in cell
Consider
SCA is set equal
is found
(61)
in storage
of equation
capacity--that
beginning
capacity--that
iteration
in cell
of water
m-l
- hi,j,k)
equation
a
the end of
SCB for
(61)
for
that
iteration
then
reverts
to the form of equation
in a given
value
i,j,k
of hm
cell,
as shown in figure
is set equal
computed
iteration
30, the
turns
value
to SCZ, the unconfined
rate
of release
of water
(60).
However,
if
the computed
out to be below the top of the
of SCB for
storage
the following
iteration
In this
case the
capacity.
from storage
in the time
step
has two
components:
scli
the
rate
of release
from confined
SC2i,j,k
the
rate
of release
If
top
of cell
i,j,k,
(61)
so that
is
a free
m, the computed
value
of head for
However,
if
the computed
to be above the top
to SCIi,j,k,
intervals
rate
or water
the
of the
confined
of rising
water
of accumulation
table
storage
cell,
storage
level,
of water
hi,j,k,
within
during
the
the end of the time
(61) again
head for
is
below the
cell,
SCA in
an iteration
SCB in the subsequent
and equation
t0 SCZi,j,k
9
m-l
step,
exists
If,
to SCZi,j,k.
equal
- tm-1)
of the time
surface
of the cell,
and
storage.
equal
(60).
the
table
Set
to be below the top
set
from water
storage;
- TOPi,j,k)/(tm
(h!i,j,k
9
- tm-1)
or compressive
the head at the beginning
equation
step
m-l
- hi ,j,k)/(tm
(TOPi ,j,k
,j,k
reverts
step
to the
SCB in the subsequent
and again
This
two components
in storage--one
and one corresponding
form of equation
step
turns
out
is set
occurs
equal
during
are computed
corresponding
to confined
out
is also
iteration
situation
time
turns
iteration
the end of the time
capacity.
for
for
to unconfined
or compressive
storage.
Equation
Av
ii
(61)
can be rearranged
SCB
m
= ~~~~~~~~~ hi ,j,k
tm - tm,1
as follows
m-l
SCA (TOPi,j,k
- hi,j,k)
- SCB*TOPi,j,k
+ ---__---------------__________________
tm - tm-l
5-28
(62)
m-l
hiJ,k
---_--
-m
--.
ToPi,j,k
m
hi,j,k
-
-
l
-
-
-
-
-
-
-
-
. ..*,
Interval wver wmch
Confined Storage
Coefficient Is Applied
Interval Over Which
Specific Yield Is Applied
0
i,j,k
Figure 30.-A
model cell which uses two storage factors during
one iteration.
5-29
Ai'
Again,
--
represents
At
on the
right
(26),
of accumulation
hand side,
while
on the
appear
right.
and Limitations
The options
for
conditions,
limitation
calculation
and storage
term
model layer
corresponds
these
horizons
these
options
of problems
conversion
table
table
incorrect
(and irreversible
is expected
may occur as iterations
the decision
is
the
units
are carried
by several
of cells
out.
to use any of the three
table
more than
) conversion
horizon,
each
and that
Use of
may lead to a variety
For example,
under water
to traverse
that
of low permeability.
are not satisfied
represented
conditions,
assumption
or permeable
in simulation.
aquifer
under water
under desaturating
aquifer
conditions
calculation
the water
flow
by distinct
Formulations
conductance
developed,on
to a distinct
where these
where a water
of horizontal
were all
are separated
conductance
of Optional
of vertical
and inaccuracies
horizontal
and as such would
(24) or (54).
In the formulation
of equation
SCB
the term --------is subtracted
from HCOFi,j,k
on-the left
tm - tm-l
m-l
SCA(TOPi,j,k
- hi,j,k)
- SCB*TOPi,j,k
the term ----_-------------------------------is added to
tm - tm-1
Applicability
table
in storage
in equation
therefore,
RHSi,j,k
rate
if
the option
conditions
is used
model- layers
one layer
to a no-flow
during
, and
simulation,
condition
Thus care should be exercised
options
noted above.
Data Requirements
The fundamental
variables
in the model are entered
These variables,
depending
controlling
through
on the
the
cell-to-cell
Block-Centered-Flow
options
5-30
which
flow
and storage
Package input.
are invoked,
for
may include
in
transmissivity,
hydraulic
coefficient,
vertical
elevation.
conductivity,
leakance,
Each of these
aquifer
variables
module UZDREL, which
is described
either
reads a two-dimensional
array
a single
throughout
value
provided
for
the array,
The model utilizes
the
simulation
indicates
transmissivities
hydraulic
conversion
code identifies
arrays
of data
required
set of two-dimensional
initially,
until
That is,
provides
layers
all
of the
then
all
input
process
of three-dimensional
the
layer
required
storage
for
for
than would be possible
corresponding
from
layer-type
indicates
each layer
parameter,
layer
layer
of
the data
for
This method of data
arrays
it
identifies
each required
of the arrays
or
flow
layer,
by layer;
arrays
code
term
Because the
in a given
for
layer-type
of vertical
and thus
to
as the product
whether
conditions.
layer,
according
are to be used,
limitation
one array
have been covered.
a simpler
of a series
the
arrays,
in sequence,
all
thickness;
to be employed
for
or
value
layers
at each iteration
The data are entered
to be read.
read in turn.
values
under dewatered
module
layer,
that
top
array-
This
a single
In particular,
and whether
the options
14.
code to classify
and saturated
above is to be invoked
and aquifer
layer.
transmissivity
is to be used;
the kinds
in the
are to be calculated
conductivity
for
storage
the utility
in Chapter
are used.
specified
elevation
using
confined
by the user and applies
cells
that
bottom
of data
a layer-type
options
whether
all
yield,
is entered
reader
accepts
specific
a
is
1 are read
2, and so on
organization
using
to the
the alternative
various
parameters.
Within
every
cell,
each layer
including
the
required
constant-head
parameters
should
and no-flow
cells.
5-31
be specified
For no-flow
for
cells,
the entered
values
be specified;
the other
are never
for
constant
parameters
used in calculation,
head cells,
the storage
and realistic
are,
and thus
values
for
any values
may
terms
are not used but
those
parameters
must be
entered.
transmissivity
Two parameters,
the designation
of two values
read for
To reduce
each of these
parameters,
direction;
these
row-direction
anisotropy
factor
to obtain
single
value
of the
layer,
through
layer
except
actually
layer.
the
apply
to the
For example,
layer
of layer
1 and the midpoint
In addition
Package input
whether
the
includes
simulation
whether
ISS flag
is
storage
skipped.
set
cell
coefficient
Thus for
above,
user
A
for
each
with
each
layer
next
during
lower
the
interval
between
the
Block-Centered
input
the midpoint
(DELR and DELC), a flag
or steady
state
(ISS),
terms
are to be saved
conditions
(ISS # 0),
or specific
steady-state
by an
2.
is transient
steady-state
row
values.
a given
and the
entered
to the
dimensions
flow
with
layer
values
mentioned
cell-by-cell
for
of Vcont
of layer
array
in the
multiplied
are associated
associated
applies
to the terms
indicate
for
1 actually
values
by the
and
a single
column-direction
or K,/Az)
values
row direction
only
the
each require
TRPY (NLAY).
between that
array
for
only
specified
array
the
sequence
is
(Vcont,
interval
the
effort,
are subsequently
factor
terms
lowermost;
input
the corresponding
anisotropy
leakance
in the
giving
values
the one-dimensional
Vertical
conductivity,
at each cell--one
one in the column direction.
is
and hydraulic
runs,
yield
and storage
arrays
5-32
of storage
Flow
to indicate
and a flag
(IBCFCB).
to
If
the
no space is allocated
calculations
coefficients
are
or
specific
yields
must not be included
the data
sequence will
or of a LAYCON value
Four types
combinations
be misread.
will
also
of layer
types
provided
layer
are stored
in the one-dimensional
O--In
of transmissivity
for
conditions,
will
fraction
present)
storage
the
entered
is the
in the
be specified
value
which
assigned
without
Tran
for
or specific
yield
row-direction
array
by providing
is applied
to all
level
cells
5-33
falls
confined
unconfined
to be a
layer
in the
are entered
leakance
Again,
values
parameter
or by providing
in this
(if
input
of layer
array
in the
unless
are
values
a single
The parameter
type
or
below the
the transmissivities,
of the layer.
the simulation.
conversion,
is transient,
are entered
vertical
array,
of a simulation
modification
in which
simulation
(NCOL, NROW).
the entire
at the beginning
change throughout
Vcont
for
term
transmissivities
in the model,
which
The code values
a layer
the
values
(NCOL, NROW); and following
input
codes,
from the overlying
If
to be negligible.
various
drawdowns are expected
and flow
sequence.
Package.
used to simulate
be used to simulate
ISS
below.
storage
is normally
thickness
lowermost
layer-type
water
of
array
Block-Centered-Flow
is no provision
provided
are included,
incoporating
are given
varies,
type
data
LAYCON (NLAY).
there
they
specification
of the
from above if
prevail,
of layer
NROW); then
layer
level
layer
always
coefficient
array
category
if
erroneous
by their
array
flow
also
is expected
sfl(NCOL,
input
This
but could
conditions
small
this
of vertical
cell.
by the
characteristics
as water
limitation
top of the
layer
data;
by the model,
are identified
corresponding
Layer-type
Note that
are recognized
of the options
input
cause misreading
These four
and the
in the
may
default
values
are retained
Layer-type
l--This
or in the uppermost
are expected
tion.
layer
assumption
that
is made for
water
table
flow
1 is used only
transmissivities
includes
yield
direction
If
layer
layer
Layer-type
between confined
and limitation
a high
layer
array
be inappropriate
except
equal
NROW).
to one,
given
indicating
of hydraulic
Thus the
elevation,
as transient,
NROW).
in the
in the
vertical
input
Row
array
array
BOT(NCOL,
leakance
values
Because use of this
in the uppermost
LAYCON is
However,
sfl(NCOL,
entered
one layer,
Vcont(NCOL,
since
layer.
indicated
are entered
more than
and no provision
bottom
array
are then
of the
conditions,
the
is
of simula-
by virtue
as the products
input
elevations
conditions
of a model.
within
model
period
prevail;
and cell
values
bottom
input
layer,
a value
a check of
of one;
the uppermost
if
the
model
message is printed.
Z--This
layer
type
and unconfined
of flow
of the
is used where the
conditions,
so that
from above under dewatered
but where the saturated
fraction
values
in the
number is made whenever
an error
desirable;
always
conductivity
are entered
number is not also
layer,
the entire
term conversion,
will
thickness
conductivity
in the
type would
layer
storage
the uppermost
the model contains
are entered
where unconfined
throughout
If the simulation
HY(NCOL, NROW) and cell
the
for
hydraulic
values
hydraulic
NROW).
layer
in a single-layer
from above under dewatered
than transmissivity.
specific
only
and only
conditions
and saturated
data
is utilized
are computed at each iteration
conductivity
rather
in the
is made for
limiting
layer-type
type
of a model,
to persist
No provision
input
layer
layer
thickness
thickness
storage
conditions
is expected
throughout
5-34
situation
the
to
period
may alternate
term
conversion
are both
remain
everywhere
of simulation,
so that
recalculation
tivity
and saturated
thickness
option
requires
both
yield
value
specified
limit
that
be specified
for
flow
confined
array
sfl(NCOL,
array
Tran(NCOL,
NROW).
leakance
Specific
yield
simulation
values
values
Flow options
3--This
associated
are recalculated
are next
used in the
values
are entered
values
layer
entered
and finally
elevation
If
the
in the array
layer
simulation
in the
lowermost
in the array
be
option
are then entered
is the
entered
bottom
layer
type
to
is
input
in the
in the model,
Vcont(NCOL,
sfZ(NCOL,
top elevations
with
water
incorporates
at each iteration
elevations,
and both
data
thus
includes
storage
vertical
leakances
are entered
coefficients
in the
are then
and layer
input
entered
(if
array
NROW).
NROW) if
are entered
hydraulic
in the
the model,
vertical
the
in
array
Specific
yield
conductivities
and
and limitation
are implemented.
layer
The re-
bottom
specific
yields
Confined
storage
(NCOL, NROW); hydraulic
elevations,
(if
the
layer
are next
values
5-35
is the
entered
are then
transient),
coefficients
conductivity
HY(NCOL, NROW), and aquifer
Unless
values
Block-Centered-
Transmissivities
term conversion
transient),
leakance
of the
conductivities,
sfl
in BOT(NCOL, NROW).
NROW).
using
top elevations.
elevations
Vcont(NCOL,
conditions.
conditions
hydraulic
all
table
storage
from above under dewatered
confined
values
the
the top
is also
term conversion
and a specific
conditions.
Transmissivity
Unless
coefficient
conduc-
TOP (NCOL, NROW).
Layer-Type
quired
elevation
of hydraulic
The storage
and that
coefficient
are then
is transient;
the array
of flow
storage
each cell,
the top
NROW).
vertical
layer
a confined
storage
product
is not necessary.
for
each cell;
as the
from above under dewatered
transient,
P
of transmissivity
lowermost
bottom
in
in the array
entered
in the
array
sfZ(NCOL,NROW);
array
aquifer
top elevations
are entered
in the
TOP(NCOL, NROW).
The input
the
and finally
utility
required
sequence
modules
formats
and in appendix
is outlined
which
in the following
are used are described
are illustrated
in the
"Sample
in
Input
section.
Chapter
to the
Both of
14, and the
BCF Package"
D.
a
a
5-36
Block-Centered
Flow Package Input
Input for the Block-Centered
specified
in IUNIT(1).
Flow (BCF) Package is
read from the
unit
FOR EACH SIMULATION
BCFlAL
1. Data:
Format:
ISS
110
IBCFCB
110
2. Data:
Format:
LAYCON(NLAY)
4012
(Maximum of 80 layers)
(If there are 40 or fewer
use two records.)
layers,
use one record;
otherwise,
BCFlRP
l
3. Data:
Module:
TRPY(NLAY)
UlDREL
4. Data:
Module:
DELR(NCOL)
UlDREL
5. Data:
Module:
DELC(NROW)
UlDREL
A subset of the following
two-dimensional
arrays are used to describe
The arrays needed for each layer depend on the layer type code
each layer.
[i-~~C~N~)and whether the simulation
is transient
(ISS = 0) or steady state
If an array is not needed, it must be omitted.
All of the
arrays (iiems 6-12) for layer 1 are read first;
then all of the arrays
for layer 2, etc.
IF THE SIMULATION IS TRANSIENT
6. Data:
Module:
sfl(NCOL,NROW)
UEDREL
IF THE LAYER TYPE CODE (LAYCON) IS ZERO OR TWO
7. Data:
Module:
Tran(NCOL,NROW)
UZDREL
IF THE LAYER TYPE CODE (LAYCON) IS ONE OR THREE
D
8. Data:
Module:
HY(NCOL,NROW)
UEDREL
9. Data:
Module:
BOT(NCOL,NROW)
UEDREL
5-37
IF THIS IS NOT THE BOTTOMLAYER
10. Data:
Module:
Vcont(NCOL,NROW)
U2DREL
IF THE SIMULATION IS TRANSIENT AND THE LAYER TYPE CODE (LAYCON) IS TWO OR THREE
11. Data:
Module:
sf2(NCOL,NROW)
U2DREL
IF THE LAYER TYPE CODE IS TWO OR THREE
12. Data:
Module:
Explanation
ISS--is
the
steady-state
TOP(NCOL,NROW)
U2DREL
of Fields
Used in
ISS # 0, the simulation
is steady
If
ISS = 0, the simulation
is transient.
a flag
Instructions
flag.
If
IBCFCB--is
Input
and a unit
state.
number.
If
IBCFCB > 0, it is the unit number on which cell-by-cell
flow
terms will
be recorded whenever ICBCFL (see Output
Control)
is set; the terms which are saved will
include
cell-by-cell
storage terms, cell-by-cell
constant
head flows,
and internal
cell-by-cell
flows.
If
IBCFCB = 0, cell-by-cell
recorded.
If
IBCFCB < 0, flow for each constant-head
cell will
be printed,
rather than saved on disk, whenever ICBCFL is set;
cell-by-cell
storage terms and internal
cell-by-cell
flows will
neither
be saved nor printed.
flow
terms
will
not be printed
or
Each element holds the code for the
LAYCON--is the layer type table.
Read one value for each layer.
There is a limit
respective
layer.
Leave unused elements blank.
of 80 layers.
o-
confined--Transmissivity
and storage coefficient
of the
layer are constant
for the entire
simulation.
l-
It is calculated
unconfined--Transmissivity
of the layer varies.
from the saturated
thickness
and hydraulic
conductivity.
The storage coefficient
is constant;
valid only for
layer 1.
5-38
3
of the layer is constant.
2 - confined/unconfined--Transmissivity
The storage coefficient
may alternate
between
Vertical
confined and unconfined
values.
leakage from above is limited
if the layer
desaturates.
of the layer varies.
It
3 - confined/unconfined--Transmissivity
is calculated
from the saturated
thickness
and hydraulic
conductivity.
The storage
coefficient
may alternate
between confined
Vertical
leakage from
and unconfined
values.
above is limited
if the aquifer
desaturates.
TRPY--is a one-dimensional
array containing
an anisotropy
factor
for each
It is the ratio of transmissivity
or hydraulic
conductivity
layer.
(whichever
is being used) along a column to transmissivity
or
hydraulic
conductivity
along a row.
Read one value per layer.
Set to 1.0 for isotropic
conditions.
NOTE: This is one array with
one value for each layer.
D
Read one value
DELR--is the cell
columns.
width
along
rows.
DELC--is the cell
rows.
width
along
columns.
for
Read one value
each of the NCOL
for
each of the NROW
Read onlv for a transient
simulation
sfl--is
the orimarv storaae coefficient.
always
(steady'-statbflag,
iSS, is 0).
Note that f& Laycon= 1 sfl will
be specific
yield,
while for Laycon= or 3, sfl will
a 1'iays be confined
be confined
For Laycon=O, sfl would normally
storage coefficient.
however, layer-type
0 can also be used for simulation
storage coefficient;
of water table conditions
where drawdowns are expected to remain everywhere a small fraction
of the saturated
thickness,
and where there is
no layer above, or flow from the layer above is neglig i ble; and in
this case specific
yield
values would be entered in sfl.
Tran--is
the transmissivity
along
obtain transmissivity
along
LAYCON is zero or two.
rows.
Tran is multiplied
Read only for
columns.
by TRPY to
layers where
HY--is the hydraulic
conductivity
along rows.
TRPY to obtain the hydraulic
conductivity
for layers where LAYCON is one or three.
HY is multiplied
along columns.
BOT--is the elevation
of the aquifer
LAYCON is one or three.
Read only
Vcont--is
bottom.
for
by
Read only
layers
where
the vertical
hydraulic
conductivity
divided
by the thickness
from
Since there is not a layer beneath
a layer to the layer beneath it.
Vcont cannot be specified
for the bottom layer.
the bottom layer,
5-39
Read it only for layers where
sf2--is
the secondary storage coefficient.
LAYCON is two or three and only if a transient
simulation
(steadyThe secondary storage coefficient
is always
state flag,
ISS, is zero).
specific
yield.
TOP--is the elevation
of the aquifer
LAYCON is two or three.
5-40
top.
Read only
for
layers
where
I--I-wcnl-I-wu-lwm
mmmmmmmmmm
NNNNNNNNCIN
I II
I III
III
l-l
0
.
N
!
i
t
4:
:‘P
32
>”
5-41
Module Documentation
for
the
Block-Centered
Flow Package
The Block-Centered
Flow Package (BCFl) has four primary modules and
The relationship
of the modules to MAIN and to each
three submodules.
other is shown in figure
31. The flow of information
used to calculate
horizontal-hydraulic
conductances
(CC and CR) is shown for several of the
For example, BCFlRP passes transmissivity
(T) and cell dimensions
modules.
(DELR and DELC) to SBCFlN. Module SBCFlN then returns
CC and CR to BCFlRP.
The modules are:
Primary
Modules
BCFlAL
Allocates
BCFlRP
Reads all data needed by the package, invokes
SBCFlN to reconcile
input transmissive
values
with the IBOUND array,
and calculates
storage
capacities
and constant
conductances.
BCFlFM
Calculates
all coefficients
of the system of
equations
that are not constant
and invokes
SBCFlH to calculate
horizontal-branch
conductances
in partially
saturated
layers.
BCFlBD
Calculates
flow rates and accumulated
flow volumes
into and out of storage and constant-head
boundaries.
When cell-by-cell
flow is specified,
flow across
all sides of each cell is also calculated.
space for
data
arrays.
Submodules
SBCFlN
Reconciles
input transmissive
values with the IBOUND
array and calculates
storage capacities
and constant
Invokes SBCFlC to calculate
horizontalconductances.
branch conductances
for layers where transmissivity
is constant.
SBCFlH
Calculates
transmissivity
for cells
in layers where it
depends on heads and invokes SBCFlC to calculate
horizontal-branch
conductances.
SBCFlC
Calculates
horizontal-branch
transmissivity.
SBCFlB
Calculates
SBCFlF
Calculates
flow terms (both cell-by-cell
and entries
to overall
budget) for flow to and from constanthead cells.
cell-by-cell
conductance
flow
5-42
terms
across
from cell
cell
faces.
/[-1
BCFl AL
FOR LAYER
TYPES 0 AND 2
/
I
BCFl BD
Explanation
HY
Hydraulic
TOP
Elevation of the Top of a Layer
Transmissivity
BOT
Elevation of the Bottom of a Layer
Grid Spacing in the Row Direction
DELC
Grid Spacing in the Column
cc
Conductance
in the Column
Direction
CR
Conductance
in the Row Direction
T
DELR
among the modules
Figure 31. -Relationship
Centered Flow Package.
5-43
Conductivity
in the Block-
Direction
Narrative
This
module allocates
It
Package.
Print
2.
Read and print
unit
and flag
are flow
to the
right,
3.
which
data
following
the
for
flag
ISS and the
Cell-by-cell
(IBCFCB).
the Block-Centered
Flow
the package.
steady-state
flow
arrays
order:
the message identifying
flow-term
to constant
space for
is done in the
1.
Module BCFlAL
for
forward,
flow
flow
cell-by-cell
terms
down, increase
for
the BCF Package
in storage,
and flow
heads.
Read and print
need the TOP array
(a)
Read the
the
layer-type
code and count
the
number of layers
and the BOTTOM array.
layer-type
codes.
0 = confined
1 = unconfined
(b)
layers
needing
(c)
and/or
print
2 = confined/unconfined
but transmissivity
is
3 = confined/unconfined
but transmissivity
depends on head
Initialize
KT and KB in which
the
numbers of
the TOP and BOTTOM are accumulated.
For each layer,
BOTTOM arrays
an error
the counters
constant
print
the
layer-type
code and determine
if
TOP
(type
= l),
are needed.
(1)
Print
(2)
If
the
a layer
layer
other
number and the
than
message and STOP.
5-44
the top
layer-type
layer
is
code.
unconfined
counter,
counter,
(3)
If
the
layer
type
is one or three,
add one to the BOTTOM
(4)
If
the
layer
type
is two or three,
add one to the TOP
KB.
KT.
4.
Calculate
5.
Allocate
the
number of elements
space for
the following
SC1
Primary
SC2
Secondary-storage
TRPY
Horizontal
BOT
Bottom of layers
TOP
Top of layers
HY
Hydraulic
The following
If
notes
in the
storage
grid
and in a layer.
arrays:
capacity;
capacity
anisotropy
conductivity
type
2 or 3 only);
factor;
(layer
(layer
(layer
type
type
2 or 3 only);
2 or 3 only);
(layer
type
and
1 or 3 only).
apply:
the simulation
is trans ient
(ISS = 0),
storage
coeff icients
needed.
The number of vertical
conductance
arrays
is one less
number of layers.
6.
Print
the amount of space used by the BCF Package.
7.
RETURN.
5-45
than
the
are
Flow Chart
ISS is the steady-state
flag.
If
is set (ISS = l), the simulation
is steady state
(storage is not
considered).
IBCFCB is
a flag
and a unit
for
Module BCFlAL
(y-z--)
it
number.
If IBCFCB > 0, it is the unit number
on which cell-by-cell
flow terms
will
be recorded whenever ICBCFL
is set.
If IBCFCB = 0, cell-by-cell
terms will
not be printed
recorded.
IDENTIFYING
THIS PACKAGE
flow
READ AND PRINT
ISS AND IBCFCB
or
If IBCFCB < 0, flow from constantbe printed
whenever
head cells will
ICBCFL is set.
LAYCON is a layer-type
each layer).
READ LAYERTYPE CODES
code (one for
4-i
1
INITIALIZE TOP
1
AND BOTTOM
COUNTERS KT AND
KB
I
I
I
I
confined
lunconfined
but
2 - confined/unconfined
transmissivity
is constant
3 - confined/unconfined
O-
t,
TYPES AND
COUNT
LAYERS THAT
NEED TOP
OR BOTTOM
KT is a counter for the number of
layers
for which TOP is needed.
(It is also, the number of layers
for which a secondary storage
factor
is needed.)
CALCULATE
KB is a counter for the number of
layers
for which BOTTOM is needed.
(It is also the number of layers
for which hydraulic
conductivity
is needed.)
ALLOCATE
SPACE FOR
PRINT THE
5-46
SUBROUTINE BCFlAL(ISUM,LENX,LCSClrLCHY,LCBOT,
LCTOP, LCSCZ,LCTRPY, IN, ISS, NCCL, NROW,NLAY, IOUT,IBCFCB)
1
C
C-----VERSION 1542 12MAY1987BCFlAL
************************************************************~*****
ALLOCATE ARRAY STORAGE FOR BLOCK-CENTEREDFLOW PACKAGE
*****+************************************************************
E
C
C
C
C
SPECIFICATIONS:
------------------_-----------------------------------------------
C
COMMON/FLWCOM/LAYCON(80)
----------_-----L------------------------------------------------C
C
Cl ------IDENTIFY PACKAGE
WRITE(IOUT,l)IN
1 FORMATtlHO, ‘BCFl -- BLOCK-CENTEREDFLOW PACKAGE,
l'r 9/l/87','
INPUT READ FROM UNIT',131
C
C2---C2-----
2
3
B
4
9
C
88
VERSION1' ,
ISS (STEADY-STATE FLAG) AND IBCFCB (FLAG FOR
PRINTINGOR UNITf FOR RECORDINGCELL-BY-CELL FLOW TERMS)
READtIN, ISS,IBCFCB
FORMAT(2110)
IF(ISS.EQ.0) WRITE(IOUT,3)
FORMAT(lX,‘TRANSIENT SIMULATION')
IF(ISS.NE.0) WRITE(IOUT,4)
FORMAT(lX,‘STEADY-STATE SIMULATION')
IF(IBCFCB.GT.0) WRITE(IOUT,9) IBCFCB
FORMAT(lX,‘CELL-BY-CELL
FLOWS WILL BE RECORDEDON UNIT',131
IF(IBCFCB.LT.0)
WRITE(IOUT,88)
FORMAT(lX,‘CONSTANT HEAD CELL-BY-CELL FLWS WILL BE PRINTED')
READ AND PRINT
c3 ------READ
TYPE CODE FOR EACH LAYER AND COUNT TOPS AND BOTTOMS
IF(NLAY.LE.80)
GO TO 50
WRITE(IOUT,ll)
11 FORMAT(lHO,‘YOU HAVE SPECIFIEDMORE THAN 80 MODEL LAYERS’/lX,
1 ‘SPACE IS RESERVED FOR A MAXIMUM OF 80 LAYERS IN ARRAY LAYCON’)
STOP
C
C3A---emREAD LAYER TYPE CODES.
50 READtIN,
(LAYCON(I)rI=l,NLAY)
51 FORMAT(40121
C
BOTTOMIS READ FOR TYPES lr3
TOP IS READ FOR TYPES 2r3
WRITE(IOUT,52)
52 FORMAT(lX,SX,‘LAYER
AQUIFERTYPE'r/lX,SXr19('-')I
C
c3B----- INITIALIZE TOP AND BOTTOMCOUNTERS.
NBOT=O
NTOP=O
C
C3C------
B
PRINT LAYER TYPE AND COUNT TOPS AND BOTTOMSNEEDED.
DO 100 I=lrNLAY
C
5-47
C3Cl----
PRINT LAYER NUMBERAND LAYER TYPE CODE.
L=LAYCON(I)
WRITE(IOUT,7) 1,L
7 FORMAT(lX,I9,110)
:3C2----ONLY
THE TOP LAYER CAN BE UNCONFINED(LAYCON=l).
.OR. I.EQ.l) GOTO 70
IF(L.NE.l
WRITE(IOUTn8)
8 FORMAT(lHO,‘AQUIFER TYPE 1
STOP
C
c3c3----
IS ONLY ALLOWEDIN TOP LAYER’)
1 AND 3 NEED A BOTTOM. ADD 1 TO KB.
.OR. L.EQ.3) NBOT=NBOT+l
LAYER TYPES
70 IF(L.EQ.l
:3C4 ----LAYER
TYPES 2 AND 3 NEED A TOP. ADD 1 TO KT.
NTOP=NTOP+l
IF(L.EQ.2 .OR. L.EQ.3)
100 CONTINUE
C
C
E4------COMPUTE
DIMENSIONS FOR ARRAYS.
NRC=NROW
*NCOL
ISIZ=NRC*NLAY
C
SPACE FOR ARRAYS. IF RUN IS TRANSIENT(ISS=O)
c5------ALLOCATE
C5------ THEN SPACE MUST BE ALLOCATED FOR STORAGE.
ISOLD=ISUM
LCSCl=ISUM
IF(ISS.EQ.0) ISUM=ISUM+ISIZ
LCSCZ=ISUM
IF(ISS.EQ.0) ISUM=ISUM+NRC*NTOP
LCTRPY=ISUM
ISUM=ISUM+NLAY
LCBOT=ISUM
ISUM=ISUM+NRC*NBOT
LCHY=ISUM
ISUM=ISUM+NRC*NBOT
LCTOP=ISUM
ISUM=ISUM+NRC*NTOP
ii6------PRINT
ME AMOUNTOF SPACE USED BY THE BCF PACKAGE.
ISF'=ISUM-ISOLD
WRITE(IOUT,lOl) ISP
101 FORMAT(lX,I8,' ELEMENTS IN X ARRAY ARE USED BY BCF’)
ISUMl=ISUM-1
WRITE(IOUT,102) ISUMlrLENX
102 FORMAT(lX,I8,’
ELEMENTS OF X ARRAY USED OUT OF’,181
IF(ISUMl.GT.LENX) WRITE(IOUT,103)
103 FORMAT(1X, ’
***X ARRAY MUST BE DIMENSIONED
LARGER***‘)
C
C7------RETURN
RETURN
END
5-48
List
Variable
I
for
Range
IBCFCB
Module
Package
IN
Package
IOUT
ISOLO
Global
Module
Package
ISP
ISS
Module
Package
ISUM
Global
ISUMl
L
LAYCON
Module
Module
Package
LCBOT
LCHY
LCSCl
LCSCZ
LCTOP
LCTRPY
LENX
Package
Package
Package
Package
Package
Package
Global
NBOT
Module
NCOL
-NLAY
NRC
NROW
NTOP
Global
Global
Module
Global
Module
ISIZ
of Variables
Module BCFIAL
Definition
Index.
Flag and a unit number.
> 0, unit number on which cell-by-cell
flow terms
will
be recorded whenever ICBCFL is set.
= 0, cell-by-cell
flow terms will
be not be printed
or recorded.
< 0, flow from each constant-head
cell will
be
printed
whenever ICBCFL is set.
Primary unit number from which input for this package
will
be read.
Primary unit number for all printed
output.
IOUT = 6.
Number-of cells
in the grid..
Before this module allocates
space, ISOLD is set equa 1
ISOLD is subtracted
to ISUM. After allocation,
from ISUM to get ISP, the amount of space in the
X array allocated
by this module.
Number of words in the X array allocated
by this module.
Flag.
= 0, simulation
is transient.
f 0, simulation
is steady state.
Index number of the lowest element in the X array which
has not yet been allocated.
When space is allocated
the size of the array is added to ISUM.
for an array,
ISUM-1.
Temporary storage for LAYCON(
DIMENSION (80) Layer type code:
0 - Layer strictly
confined.
1 - Layer strictly
unconfined.
2 - Layer confined/unconfined
(transmissivity
is
constant).
3- Layer confined/unconfined
(transmissivity
varies).
Location
in the X array of the first
element of array BOT.
Location
in the X array of the first
element of array HY.
Location
in the X array of the first
element of array SCl.
Location
in the X array of the first
element of array SC2.
Location
in the X array of the first
element of array TOP.
Location
in the X array of the first
element of array TRPY.
Length of the X array in words.
This should always be
equal to the dimension of X specified
in the MAIN
program.
Counter for the number of layers which need elevation
of
Layers for which LAYCON = 1 or 3.
the bottom.
Number of columns in the grid.
Number of layers in the grid.
Number of cells
in a layer.
Number of rows in the grid.
Counter for the number of layers which need elevation
of
the top.
LAYCON = 2 or 3.
5-49
Narrative
for
Module BCFlRP
This module reads transmissivity
along rows, hydraulic
conductivity
vertical
conductance,
elevation
of top
along rows, storage coefficients,
It also calls
SBCFlN to
of layer,
and elevation
of bottom of layer.
It does
calculate
parameters which are constant
throughout
simulation.
this in the following
order:
module UlDREL to read DELR, DELC, and TRPY which
1. Call utility
TRPY is the
one value for each column, row, and layer,
respectively.
ratio
of transmissivity
along columns to transmissivity
along rows for
each layer.
,’
have
use utility
module UPDREL to read the properties
2. For each layer,
The data requirements
for each layer are determined
of the porous medium.
by the layer-type
code.
(a)
storage
Find the address
If the
(b)
coefficient.
simulation
(c)
For constant
the transmissivity.
hydraulic
of the
layer
in the
is transient
(ISS = 0),
arrays.
read the primary
transmissivity
layers
(LAYCON = 0 or 2),
read
(d)
For variable
transmissivity
conductivity
and bottom.
layers
(LAYCON = 1 or 3),
read
(e)
Read vertical-hydraulic
These values will
be multiplied
For each
vertical
conductance.
next lower layer is calculated.
calculated
for the lowest layer
conductivity
divided
by thickness.
in the program by cell areas to get
layer,
the vertical
conductance
to the
Therefore,
no vertical
conductance
is
in the mesh.
(f)
If the simulation
is transient
read the secondary storage coefficient
three,
three-dimension
(g)
Read the top
elevation
if
the
and the layer type
(specific
yield).
layer
type
is two or
is two or three.
conductance
and storage terms which are
3. Call SBCFlN to calculate
constant
during the simulation
and check to see that branch conductances
agree with boundaries
specified
in the IBOUND array.
4.
RETURN.
5-50
Flow Chart for Module BCFl RP
DELR is the grid spacing in the row direction.
DELC is the grid spacing in the column
direction.
TRPY is the ratio of transmissivity in the column
direction to transmissivity in the row
direction.
FOR EACH LAYER
LAYCON is a layer-type code (one for each
layer).
+
0 - confined
1 - unconfined
2 - confined/unconfined
but
transmissivity is constant
3 - confined/unconfined
I
2
IF TRANSIENT
SIMULATION,
READ
PRIMARY STORAGE
COEFFICIENT
1
I
pii&
2c
Secondary Storage coefficient is relevant
only for convertible layers
(LAYCON = 2 or 3); then it is equal to
specific yield.
IF&;y3CgIAl;
1
HYDdAULlC
CONDUCTIVITY
AND BOTTOM
2E
.
IF TRANSIENT AND
LAYCON IS 2 OR 3,
READ SECONDARY
STORAGE COEFFICIENT
I
I
IF LAYCCN IS 2
OR 3. READ TOP
PREPARE AND CHECK
BCF DATA
5-51
I
I
1
\
SUBROUTINE BCF~RP(IBOUND,HNEW,SC~,HY,CR,CC,CVIDELRIDELC,
BOT, TOP, SCZ,TRPY, IN, ISS, NCOL,NROW,NLAY, NODES,IOUT)
C
.---VERSION 1636 15MAY1987 BCFlRP
CMm
C
***********************~*****************~************************
C
C
READ AND INITIALIZE DATA FOR BLOCK-CENTERED FLOW PACKAGE
******************************************************************
C
C
SPECIFICATIONS:
C
--------_--------------------------------------------------------C
CHARACTER*4 ANAME
DOUBLE PRECISION HNEW
C
DIMENSIONHNEW~NODES~rSC1~NODES~,HY~NODES~rCR~NODES~,CC~NODES~,
CV.(NODES)rANAME(6,10),DELR(NCOL),DELC(NROW)rBOT(NODES)r
1
1
TOP(NODES),SC2(NODES),TRPY(NLAY),IBOUND(NODES~
C
COMMON/FLWCOM/LAYCON( 80 1
C
C
C
DATA AN~E~lrl~,ANAME~2rl~,ANAME~3,l~,~~E~4,l~,ANA~~5,l~,
','PRIM','ARY ‘r’STOR’,‘AGE
‘r’COEF’/
1 ANAME(6,l) /’
DATA ANAME(lr2),ANAME(2,2)rANAME(3,2),~~(4,2),AN~E(5,2),
AL’r’ONG ‘,‘ROWS’/
‘,‘TRAN’r’SMIS’r’.
1 ANAME(6r2) /’
DATA ANAME(l,3),ANAME(2,3),ANAME(3,3),~~(4,3),~~E(5,3),
AL’,‘ONG ‘,‘ROWS’/
‘,‘COND’,‘.
1 ANAME(6r3) /’
H’r’YD.
DATA ANAME(lr4),ANAME(2,4)rANAME(3,4)rANAME(4,4),ANAME(5r4)r
1 ANAME(6,4) /‘VERT’,’
HYD’,’ CON’r’D /T'r'HICK','NESS'/
DATA ANAME(lr5),ANAME(2,5)rANAME(3,5)rANAME(4,5),AN~E(5,5),
‘,’
BO’,‘TTOM’/
1 ANAME(6,5) /’
DATA ANAME~l,6~,AN~;2,6~:~AME~;:~~rAN~~4,6~,ANAME~5,6~,
‘,’ TOP’/
1 ANAME(6r6) /’
‘,’
1,’
1,’
‘8’
DATA ANAME(1,7),ANAME(2,7)rANAME(3,7),~~(4,7),~~(5,7),
SE’r’COND’r’ARY
‘r’STOR’,‘AGE
‘,‘COEF’/
1 ANAME(6,7) /’
DATA ANAME(1,8),ANAME(2,8),ANAME(3,8),~~(4,8),~~(5,8),
1 ANAME(6,8) /‘COLU’r’MN
T’,‘O RO’r’W AN’r’ISOT’,‘ROPY’/
DATA ANAME(lr9),ANAME(2,9)rANAME(3,9),~~(4,9),~~(5,9)~
‘r’DELR’/
1 ANAME(6,9) /’
‘,’
‘,’
‘,’
‘,’
DATA ANAME~1r.~0~,ANAME~2,10~,ANAME~3,10~,~~~4,10~,~~~5,10~,
‘r’DELC’/
1 ANAME(6rlO) /'
','
','
','
','
------------------------------------------------------------------
Cl- -----CALCULATE
NUMBEROF NODES IN A LAYER AND READ TRPY, DELR,DELC
NIJ=NCOL*NROW
C
CALL UlDREL(TRPY,ANAME(lr8) ,NLAY, IN, IOUT)
CALL U1DREL(DELR,ANAME(lr9),NCOL,IN,IOUT)
CALL U1DREL(DELC,ANAME(lrlO~,NRW,IN,IOUT)
5-52
C
C2-----
READ ALL PARAMETERSFOR EACH LAYER
KT=O
KB=O
DO 200 K=lrNLAY
KK=K
C
C2/+--
C
c2B-----
FIND ADDRESS OF EACH LAYER IN THREE DIMENSION ARRAYS.
IF(LAYCON(K1.EQ.l
.OR. LAYCON(K1.EQ.3) KB=KB+l
IF(LAYCON(Kl.EQ.2
.OR. LAYCON(K1.EQ.3) KT=KT+l
LOC=l+(K-l)*NIJ
LOCB=l+(KB-l)*NIJ
LOCT=l+(KT-l)*NIJ
READ PRIMARY STORAGECOEFFICIENT INTO ARRAY SC1 IF TRANSIENT
IF(ISS.EQ.O)CALL
U2DREL(SC1(LOC),ANAMEME(lrl)rNROW,NCOL,KK,IN,IOUT~
C
c2c---.
READ TRANSMISSIVITY INTO ARRAY CC IF LAYER TYPE IS 0 OR 2
IF(LAYCON(K1.EQ.3 .OR. LAYCON(K1.EQ.l) GO TO 100
CALL U2DREL(CC(LOC),ANAME(lr2),NR~,NCOL,KK,IN,IOUT~
GO TO 110
:2D -----READ HYDRAULIC CONDUCTIVITYtHY) AND BOTTOMELEVATIONtBOT)
C2D-w-m IF LAYER TYPE IS 1 OR 3
100 CALL U2DREL(HY(LOCB),ANAMEME(lr3)rNROW,NCOL,KK,IN,IOUT~
CALL U2DREL(BOT(LOCB)rANAME(lr5)rNROWINCOLIKK,IN,IOUT~
C
C2E-----READ
VERTICAL HYCOND/THICK INTO ARRAY CV IF NOT BOTTOMLAYER
(32E--READ AS HYCOND/THICKNESS -- CONVERTEDTO CONDUCTANCELATER
110 IF(K. EQ. NLAY) GO TO 120
CALL U2DREL(CV(LOC)rANAME(1,4),NROW,NCOL,KK,IN,IOUT~
C
(32F--w-w READ SECONDARYSTORAGECOEFFICIENT INTO ARRAY SC2 IF TRANSIENT
C2F-----AND
LAYER TYPE IS 2 OR 3
120 IF(LAYCON(K1.NE.3
.AND. LAYCON(K1.NE.2) GO TO 200
IF(ISS.EQ.O)CALL
U2DREL(SC2(LOCT)rANAME~l,7),NROW,NCOL,KK,IN,IOUT~
C
C2G ----READ TOP ELEVATIONtTOP) IF LAYER TYPE IS 2 OR 3
CALL U2DREL(TOP(LOCT)rANAMEME(lr6)rNROW,NCOL,KK,IN,IOUT~
200 CONTINUE
C
c3 ------PREPARE
AND CHECK BCF DATA
CALL SBCFlN~HNEW,IBOUND,SClrSC2,CR,CC,CV,HY,TPY,DELR,DELC,ISS,
1
NCOL,NROW,NLAY, IOUT)
C
c4 ------RETURN
RETURN
END
5-53
List
Variable
Range
ANAME
BOT
Module
Package
cc
Global
CR
Global
cv
Global
DELC
Global
DELR
Global
HNEW
Global
HY
Package
I BOUND
Global
IN
Package
IOUT
ISS
Global
Package
K
KB
Module
Module
KK
Module
KT
Module
LAYCON
Package
of Variables
for
Module BCFlRP
Definition
Label for printout
of input array.
DIMENSION (NCOL,NROW,NBOT), Elevation
of the bottom of
each layer.
(NBOT is the number of layers for which
LAYCON = 1 or 3.)
DIMENSION (NCOL,NROW,NLAY), Conductance in the column
CC(J,I,K)
contains
conductance
between
direction.
nodes (J,I,K)
and (J,I+l,K),
This array is used to
temporarily
hold transmissivity.
DIMENSION (NCOL,NROW,NLAY), Conductance in the row
CR(J,I,K)
contains
conductance
between
direction.
nodes (J,I,K)
and (J+l,I,K).
DIMENSION (NCOL,NROW,NLAY-l),
Conductance in the
CV(J, I ,K) contains
conductance
vertical
direction.
between nodes (J,I,K)
and (J,I,K+l).
This array is
used to temporarily
to hold Vcont.
DIMENSION (NROW), Cell dimension in the column direction.
DELC(1) contains
width of row I.
DIMENSION (NCOL), Cell dimension in the row direction.
DELR(J) contains
the width of column J.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
of
HNEWchanges at each iteration.
head in each cell.
DIMENSION (NCOL,NROW,NBOT), Hydraulic
conductivity
of
(NBOT is the number of layers where
a cell.
LAYCON = 1 or 3.)
DIMENSION (NCOL,NROW,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
Primary unit number from which input for this package
will
be read.
Primary unit number for all printed
output.
IOUT = 6.
Flag.
= 0, simulation
is transient.
# 0, simulation
is steady state.
Index for layers.
Counter for the number of layers for which the bottom
elevation
is needed (LAYCON = 1 or 3).
Temporary variable
set equal to K. KK is used as an
actual argument in subroutine
calls
to avoid using
the DO loop variable
K as an argument, which causes
problems with some compilers.
Counter for the number of layers for which the top
elevation
is needed (LAYCON = 2 or 3).
DIMENSION (80) Layer type code:
confined.
o- Layer strictly
Layer strictly
unconfined.
l(transmissivity
is
Z- Layer confined/unconfined
constant).
(transmissivity
3- Layer confined/unconfined
5-54
b
List
Variable
Module
LOCB
Module
LOCT
Module
NCOL
tsc1
Global
Module
Global
Global
Global
Package
tsc2
Package
NIJ
B
for
Module RCFlRP (Continued)
Definition
Range
LDC
NLAY
NODES
NROW
of Variables
TOP
Package
TRPY
Package
Pointer to parts of the conductance
arrays corresponding
to particular
layers.
Pointer to parts of the BOT and HY arrays corresponding
to
particular
layers.
Pointer to parts of the TOP and SC1 arrays corresponding
to particular
layers.
Number of columns in the grid.
Number of cells
in a layer.
Number of layers in the grid.
Number of cells
(nodes) in the finite-difference
grid.
Number of rows in the grid.
DIMENSION (NCOL,NROW,NLAY), Primary storage capacity
of each cell (S*DELC*DELR).
DIMENSION (NCOL,NROW,NTOP), Secondary storage capacity
(NTOP is the number of
of each cell in the grid.
layers for which LAYCON = 2 or 3.)
DIMENSION (NCOL,NROW,NTOP), Elevation
of the top of
the layers.
(NTOP is the number of layers for
which LAYCON = 2 or 3.)
DIMENSION (NLAY), Ratio of transmissivity
in the column
direction
to transmissivity
in the row direction.
tInitially,
storage coefficient
values are multiplied
by cell
capacities.
values are read into these arrays;
areas in submodule SBCFlN to yield
5-55
these
storage
Narrative
for
Module BCFlFM
This module calculates
branch conductances
which are not constant
adds storage terms to the accumulators
in which
throughout
the simulation,
HCOF and RHS are formed, and adds terms to RHS and HCOF which correct
for
overestimation
of flow down into partially
saturated
cells.
1.
or 3),
for
For each layer in which transmissivity
varies with head (LAYCON = 1
call submodule SBCFlH to calculate
branch conductance.
If the simulation
is transient,
calculate
2.
each layer.
If the simulation
is steady state,
t3.
Determine
if
there
is one storage
If there is only one storage factor
t4.
calculate
storage terms and add them to the
h-coefficient
(HCOF).
factor
storage terms (STEPS 3-5)
GO TO STEP 6.
or two.
(LAYCON = 0 or l), use it to
right hand side (RHS) and the
then, using head at the beginning
If there are two storage factors,
t5.
of the time step (HOLD), determine the storage factor
at the beginning
of
the time step (SOLD) and use the latest
estimate
of head at the end of the
time step (HNEW) to determine the storage factor
at the end of the time
the storage terms to add to
step (SNEW). Use SOLD and SNEW to calculate
RHS and HCOF.
down F&o
For each layer
determine
if
a partially
skurated
layer
7.
calculate
If the layer is partially
saturated
and there
correction
terms and add to RHS and HCOF.
8.
saturated,
If
9.
this is not the bottom
calculate
the correction
are needed for
is flow
flow
from above,
layer and the layer below is partially
terms and add to RHS and HCOF.
RETURN.
tThe term storage
capacity
divided
SCA/(tm-tm,l),
equivalent
correction
terms
(STEPS 7-8).
factor,
by time
as used in Subroutine
BCFlFM, refers
SOLD is thus equivalent
step length.
in the notation
of equations
to SCB/(tm-tm,1).
5-56
(61) and (62),
to storage
here to
while
SNEWis
Flow Chart
LAYCON is a layer-type
(one for each layer).
0 - confined
1 - unconfined
2 - confined/unconfined
but transmissivity
is constant
3 - confined/unconfined
for
Module BCFlFM
code
(-E--)
FOR EACH LAYER
1
IF T VARIES,
CALCULATE
HORIZONTAL
CONDUCTANCES
FOR EACH LAYER
ADD STORAGE
TERMS TO RHS
AND HCOF
ADDSTORAGE
TE;t$
&FtIHS
I
I
FOR EACH LAYER
IF LAYCON IS
2 OR 3, GET
CORRECTION
TERMS FOR FLOW
FROM ABOVE
,
*
I
IF LAYCON FOR
LAYER BELOW IS
2 OR 3. GET
CORRECTION TERMS
FOR FLOW DOWN
5-57
SUBROUTINE BCF~FM(HCOFIRHS,HOLOISC~~HNEW~IBOUND,CR,CC,CV~HY,TR~‘YI
BOT,TCP~SC~~DELRIDELC,DELT,ISSIKITERIKSTP~KPERI
2
NCOL,NRC%V,NLAY,IOUT)
1640 15MAY1987 BCFlFM
C-----VERSION
C
******************************************************************
C
ADD LEAKAGE CORRECTION AND STORAGE TO HCOF AND RHS, AND CALCULATE
C
CONDUCTANCE AS REQUIRED
C
*********************************~~*******************************
E
SPECIFICATIONS:
C
1
”
DOUBLE PRECISION HNEW
C
DIMENSION HCOF(NCOL~NR~,NLAY)~RHS(NCOL,NRUVINLAY)~
1
2
3
4
5
HOLD(NCOLrNROW,NLAY),SCl(NCOLrNROW,NLAY)rHNEW(NCOLrNROW,NLAY),
IBOLIND(NCOL,NROW,NLAY),CR(NCCL.NROW,NLAY)r
CC(NCOL,NROW,NLAY)rCV(NCOL,NROW,NLAY)rHY(NCOL,NROW,NLAY)r
TRPY(NLAY),BOT(NCOL,NROW,NLAY)rTOP(NCOL,NRaJ,NLAY)rDELR(NCOL)r
DELC(NROW)rSC2(NCOLrNRCW,NLAY)
COMMON/FLWCON/LAYCON(BO)
-----------------------------------------------------------------KB=O
KT=O
C
C
Cl---
C
ClA---
FOR EACH LAYER: IF T VARIES CALCULATE HORIZONTAL CONDUCTANCES
DO 100 K=lrNLAY
KK=K
IF(LAYCON(K1.EQ.3
.OR. LAYCON(Kl.EQ.2)
KT=KT+l
IF LAYER TYPE IS NOT 1 OR 3 THEN SKIP THIS LAYER.
IF(LAYCON(K).NE.3
.AND. LAYCON(Kl.NE.1)
GO TO 100
KB=KB+l
----FOR
LAYER TYPES 1 6 3 CALL SBCFHl TO CALCULATE
HORIZONTAL CONDUCTANCES.
CALL SBCFlH~HNEW,IBOUND,CR,CC,CV,HY,TRPY,DELR,DELC,BOT,TOP,
KK,KB,KT,KITER,KSTP,KPER,NCOLrNR(XJ,NLAY,IOUT)
IOO’CONTINUE
ClB-----
C
CZ------IF
THE
SIMULATIONIS TRANSIENTADD STORAGE TO HCOF AND RHS
IF(ISS.NE.0)
TLED=l ./DELT
GO TO 201
KT=O
DO 200 K-1rNLAY
------SEE
IF THIS LAYER IS CONVERTIBLE OR NON-CONVERTIBLE.
IF(LAYCON(K1.EQ.3
.OR. LAYCON(Kl.EQ.2)
GO TO 150
c4 ------NON-CONVERTIBLE
LAYER, SO USE PRIMARY STORAGE
DO 140 I=l,NROW
DO 140 J=lrNCOL
IF(IBOlJND(J,I,K).LE.O)
GO TO 140
RHO=SCl(J,I,K)*TLED
HCOF(JrI,K)=HCOF(J,I,K)-RHO
RHS(J,I,K)=RHS(J,I,K)-RHO*HOLDtJ,I,K)
C
140 CONTINUE
GO TO 200
C5-----A CONVERTIBLE LAYER, SO CHECK OLD AND NEW HEADS TO DETERMINE
c5 ------WHEN
TO USE PRIMARY AND SECONDARY STORAGE
150 KT=KT+l
DO 180 I=l,NRW
DO 180 J=lrNCOL
C
C5A---mm IF THE CELL IS EXTERNAL THEN SKIP IT.
IF(IBOlJND(J,I,K).LE.O)
GO TO 180
TP=TOP(J,I,KT)
RHOZ=SC2(J,I,KT)*TLED
5-58
RHOl=SCl(J,I,K)*TLEO
C
Q B---
FIND STORAGEFACTOR AT START OF TIME STEP.
SOLD=RHOZ
IF(HOLD(J,I,K).GT.TP)
SOLD=RHOl
E5c
-----FIND
STORAGEFACTOR AT END OF TIME STEP.
HTMP=HNEW(J,I,K)
SNEW=RHM
IF(HTMP.GT.TP) SNEW=RHOl
C
pJJ---
ADD STORAGETERMS TO RHS AND HCOF.
HCOF(J,I,K)=HCOF(J,I,K)-SNEW
- SOLD*(HOLD(J,I,K)-TP)
RHS(J,I,K)=RHS(J,I,K)
- SNEW*TP
C
180 CONTINUE
C
200 CONTINUE
C
c6 ------FOR
EACH LAYER DETERMINE IF CORRECTIONTERMS ARE NEEDED FOR
c6 ------FLOW DOWNINTO PARTIALLY SATURATEDLAYERS.
201 KT=O
DO 300 K=l,NLAY
C
C7------
SEE IF CORRECTION IS NEEDED FOR LEAKAGE FROM ABOVE.
IF(LAYCON(K1.NE.3 .AND. LAYCON(K1.NE.P) GO TO 250
KT=KT+l
IF(K.EQ.l)
GO TO 250
n
:7A -----FOR EACH CELL MAKE THE CORRECTIONIF NEEDED.
DO 220 I=lrNRw
DO 220 J=lrNCOL
C
c75---IF THE CELL IS EXTERNAL(IBOUND<=O) THEN SKIP IT.
IF(IBOUND(J,I,K).LE.0)
GO TO 220
HTMP=HNEW(JrIrK)
k7c -----IF
HEAD IS ABOVE TOP THEN CORRECTIONNOT NEEDED
IF(HTMP.GE.TOP(J,I,KT))
GO TO 220
:7D -----WITH
HEAD BELOWTOP ADD CORRECTIONTEMS TO RHS AND HCOF.
RHS(J,I,K)=RHS(J,I,K)
HCOF(J,IrK)=HCOF(J,I,K)
220 CONTINUE
+ CV(J,I,K-l)*TCf’(J,I,KT)
+ CV(J,I,K-1)
C
ca------SEE
IF THIS LAYER MAY NEED CORRECTION FOR LEAKAGE TO BELOW.
250 IF(K.EQ.NLAY) GO TO 300
IF(LAYCON(K+l).NE.3
.AND. LAYCON(K+l).NE.Z) GO TO 300
KTT=KT+l
&A -----FOR EACH CELL MAKE THE CORRECTIONIF NEEDED.
DO 280 I=lrNROW
DO 2&l J=l,NCOL
El35 ----IF
CELL IS EXTERNAL (IBOUND<=
IF(IBOUND(J,I,K).LE.O)
GO TO 280
THEN SKIP IT.
C
C8C---
IF HEAD IN THE LOWERCELL IS LESS THAN TOP ADD CORRECTION
C8C-----TEfW TO RHS.
HTMP=HNEW(J,I,K+l)
IF(HlMP.LT.TOF’(J,I,KTT))
1
RHS(J,I,K)=RHS(J,I,K)
- CV(J,I,K)*(TOP(J,I,KTT)-HIMP)
280 CONTINUE
300 CONTINUE
C
c9 ------RETURN
RETURN
END
5-59
List
of Variables
for
Module
BCFlFM
Definition
Variable
Range
BOT
Package
cc
Global
CR
Global
cv
Global
DELC
Global
DELR
Global
DELT
HCOF
Global
Global
HNEW
Global
HOLD
Global
HTMP
HY
Module
Package
I
I BOUND
Module
Global
IOUT
ISS
Global
Package
J
K
KB
Module
Module
Module
KITER
KK
Global
Iteration
Module
KPER
KSTP
Global
Global
KT
KTT
Module
Module
Temporary variable
set equal to K. KK is
actual argument in subroutine
calls
to
the DO loop variable
K as an argument,
problems with some compilers.
Stress period counter.
Reset at the start
of
Time step counter.
period.
Counter for layers for which top elevation
Pointer to TOP array of layer immediately
DIMENSION (NC~L,NROW,NB~T), Elevation
of bottom of
each layer.
(NBOT is the number of layers for
which LAYCON = 1 or 3.)
DIMENSION (NCOL,NROW,NLAY), Conductance in the column
direction.
CC(J,I,K)
contains
conductance
between
nodes (J,I,K)
and (J,I+l,K).
DIMENSION (NCOL,NROW,NLAY), Conductance in the row
direction.
CR(J, 1,K) contains
conductance
between
nodes (J,I,K)
and (J+l,I,K).
DIMENSION (NCOL,NROW,NLAY-l),
Conductance in the vertical
direction.
CV(J,I,K)
contains
conductance
between
nodes (J,I,K)
and (J,I,K+l).
DIMENSION (NROW), Cell dimension in the column direction.
DELC(1) contains
the width of row I.
DIMENSION (NCOL), Cell dimension in the row direction.
DELR(J) contains
the width of column J.
Length of the current
time step.
DIMENSION (NCOL,NROW,NLAY), Coefficient
of head in cell
(J,I,K)
in the finite-difference
equation.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
of head
in each cell.
HNEWchanges at each iteration.
DIMENSION (NCOL,NROW,NLAY), Head at the start
of the
current
time step.
Temporary single
precision
HNEW(J,I,K).
DIMENSION (NCOL,NROW,NBOT), Hydraulic
conductivity
of
a cell.
(NBOT is the number of layers where
LAYCON = 1 or
3.)
Index for rows.
DIMENSION (NCOL,NROW,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
Primary unit number for all printed
output.
IOUT = 6.
Flag.
= 0, simulation
is transient.
f 0, simulation
is steady state.
Index for columns.
Index for layers.
Counter for layers for which bottom elevation
is needed.
counter.
5-60
Reset
at
the
start
of
each
time
step.
used as an
avoid using
which causes
each stress
is needed.
below layer
K.
List
Variable
Package
NCOL
NLAY
NROW
RHO
Global
Global
Global
Module
Module
Module
Global
SC1
Package
SC2
Package
tSNEW
Module
tSOLD
Module
TLED
TOP
Module
Package
TP
TRPY
Module
Package
tstorage
divided
for
Module BCFlFM (Continued)
Definition
Range
LAYCON
tRHO1
tRH02
RHS
l
of Variables
factor,
by time
DIMENSION (80) Layer type code:
0 - Layer strictly
confined.
1 - Layer strictly
unconfined.
2 - Layer confined/unconfined
(transmissivity
is
constant).
3 - Layer confined/unconfined
(transmissivity
varies).
Number of columns in the grid.
Number of layers in the grid.
Number of rows in the grid.
Storage coefficient
for strictly
confined
or strictly
unconfined
layers.
Confined storage factor
for convertible
layers.
Unconfined storage factor
for convertible
layers.
DIMENSION (NCOL,NROW,NLAY), Right hand side of finiteRHS is an accumulation
of
difference
equation.
terms from several different
packages.
DIMENSION (NCOL,NROW,NLAY), Primary storage capacity
0f
each cell (S*DELC*DELR).
DIMENSION (NCOL,NROW,NTOP), Secondary storage capacity
(NTOP is the number of
of each cell in the grid.
layers for which LAYCON = 2 or 3.)
Storage factor
at the end of the time step for
convertible
layers.
Storage factor
at the start
of the time step for
convertible
layers.
l/DELT.
DIMENSION (NCOL,NROW,NTOP), Elevation
of top of layers.
(NTOP is the number of layers for which LAYCON = 2 or 3.)
Temporary variable
for TOP(J,I,K).
DIMENSION (NLAY), Ratio of transmissivity
in the column
direction
to transmissivity
in the row direction.
as used in Subroutine
step length.
BCFlFM, refers
5-61
to storage
capacity
Narrative
for
Module BCFlBD
Module BCFlBD calculates
flow rates within
the porous medium for use
in the overall
volumetric
budget and calculates
cell-by-cell
flow terms
for recording
on disk.
Flow rates to constant
heads and from storage are
in the budget.
accumulated
and passed to the module BASlOT for inclusion
They are accumulated
by sign so that flow into constant-head
cells
is separate
from flow out of constant-head
cells,
and flow into storage is separate from
Flow rates to constant-head
cells
and from storage as
flow out of storage.
well as flow across cell boundaries
can be recorded on a cell-by-cell
basis
for use by other programs.
Flow from storage is calculated
inside
BCFlBD.
flow to constant-head
and across cell boundaries
is calculated
in submodules SBCFlF and
SBCFlB, respectively.
cells
Module BCFlBD performs
its
tasks
in the following
Clear the fields
STOIN and STOUT in which
respectively,
are accumulated.
1.
storage,
_
order:
flow
out of and into
If the user has specified
that cell-by-cell
flow terms should
2.
be recorded this time step (ICBCFL #O) and has specified
a unit number
(IBCFCB) for cell-by-cell
flow terms for the BCF Package, set the cell-bycell flag (IBD).
for
If this is steady-state
from storage.
3.
flow
If cell-by-cell
4.
in STEP Z), clear the
prior
to
skip
all
of the
calculations
flow terms are to be saved (i.e.,
if IBD was set
buffer
(BUFF) in which they will
be accumulated
printing.
accumZiator
6.
simulation,
For each cell in the
(STEPS 6 AND 7).
Calculate
flow
grid,
calculate
from storage
flow
from storage
and move to
in the cell.
If the cell-by-cell
rates are being recorded,
store flow rate from
7.
storage in the buffer.
Depending on the sign, add the flow from storage
to the accumulators
STOIN or STOUT.
a.
If the cell-by-cell
9.
Store
flag
(IBD)
is set,
record
the
contents
of the
buffer.
the
accumulated
table VBVL for inclusion
appropriate
label in the
and volumes
Call
11.
If the cell-by-cell
flag (IBD) is set, call
and record the flow across cell boundaries.
12.
SBCFlF
to
of
flow
from
storage
in
volumetric
budget.
Store an
location
in the table VBNM.
10.
calculate
submodule
rates
in the overall
corresponding
calculate
RETURN.
5-62
flow
from
constant-head
submodule
cells.
SBCFlB to
Flow Chart
for
Module BCFlBD
STOIN is an accumulator
for flow
terms having a positive
sign
(flow from storage into the
flow system) for inclusion
in
the volumetric
budget.
ACCUMULATORS
FOR BUDGET
ENTRIES (STOIN
STOUT is an accumulator
for flow
terms having a negative
sign
(flow into storage and out of
the flow system) for inclusion
in the volumetric
budget.
TERMS
ARE NEEDED,
IBD is a flag which indicates
that
for this time step, BCF cellby-cell
flow terms should be
recorded.
BUFF is a buffer where flow terms
are gathered prior to recording
them.
I
IF CELL-BY-CELL
TERMS ARE NEEDED,
CLEAR BUFF
I
FOR EACH LAYER 1
5
FOR EACH CELL
VBVL is a table of budget entries
calculated
by component-of-flow
packages for use in calculating
the volumetric
budget.
VBNM is a table
budget terms.
of labels
6
CALCULATE
FLOW
FROM SCEy;AGE IN
for
STORE STOIN
AND STOUT IN
VBVL AND LABELS
IN VBNM
I
CALL MODULE
SBCFIF TO GET
FLOW FROM
CONSTANT
HEADS
I
CALL MODULE
SBCFlB TO
GET AND RECORD
FLOW ACROSS
CELL WALLS
I
I
5-63
RETURN
SUBROUTINE BCFlBDt VBNM,VBVL, MSUM,HNEW,IBOUND, HOLD, SClrCR,CC,CV,
TOP,SCZ,DELT, ISS, NCOL, NRW, NLAY,KSTP,KPER, IBCFCB,
ICBCFL, BUFF, IOUT)
C-----VERSION 1546 12MAY1987BCFlBD
1
2
C
C
C
C
C
C
C
C
***+****+++**tt**Y*t~~*~~**~~~***~*~**~**~****~**~~*~*~~~~****~***
COMWTE BUDGET FLOW TERMS FOR BCF -- STORAGE, CONSTANT HEAD, AND
FLOW ACROSS CELL WALLS
*~+~l**II*I*******************************************************
SPECIFICATIONS:
------_-----L----------------------------------------------------CHARACTER*4 VBNM,TEXT
DOUBLE PRECISION HNEW
C
DIbfiNSION HNEW(NCOL,NROW,NLAY)r IBOUND(NCOL,NRCW,NLAY)r
HOLD(NCOL,NR~,NLAY),
SCl(NCOL,NR~,NLAY)r
CR(NCOL,NRCJfrNLAY)r CCtNCOLrNRCWrNLAY),
2
3
CVtNCOLrNRCWrNLAY), VBNM(4rZO)r VBVL(4,201,
4
SC2tNCOLrNRanlrNLAY)r
TOP(NCOL,NROW,NLAY)rBUFF(NCOLINROWINLAY)
5
1
C
COMMON/FLWCOM/LAYCON(801
C
DIMENSION TEXT(4 1
C
C
C
Cl---
DATA TEXT(l)rTEXT(Z)rTEXT(3)rTEXr(4)
-----------------------------------------------------------------INITIALIZE
STOIN=O.
STOUT=O.
/’
‘,’
‘,’
STO’r’RAGE’/
BUDGET ACCUMULATORS
CELL-BY-CELL FLOWS ARE NEEDED THEN SET FLAG IBD.
:2 ------IF
IBD=O
IF(ICBCFL.NE.0
.AND. IBCFCB.GT.01 IBD=l
C
C3-----IF STEADY STATE THEN SKIP ALL STORAGE CALCULATIONS
IF(ISS.NE.01
GO TO 305
C
CELL-BY-CELL FL@iS ARE NEEDED (IBD IS SET) CLEAR BUFFER
c4 ------IF
IF(IBD.EQ.0)
GO TO 220
DO 210 K=lrNLAY
DO 210 I=lrNRW
DO 210 J=l,NCOL
BUFF(J,I,K)=O.
210 CONTINUE
C
c5------RUN
THROUGH EVERY CELL IN ME GRID
220 KT=O
DO 300 K=lrNLAY
LC=LAYCON(K)
IF(LC.EQ.3 .OR. LC.EQ.2) KT=KT+l
DO 300 I=lrNRW
C
DO 300 J=lrNCOL
C6------CALCULATE
FLW FROM STORAGE (VARIABLEHEAD CELLS ONLY)
5-64
IF(IBWND(J,I,K).LE.O)
HSING=HNEW(JrIrK)
c
C6A----
GO TO 300
CHECK LAYER TYPE TO SEE IF ONE STORAGE CAPACITY OR TWO
IF(LC.NE.3
.AND. LC.NE.2) GO TO 285
---TWO STORAGE CAPACITIES
TF’=TOP(J,I,KT)
SYA=SC2(J,I,KT)
SCFA=SCl(J,I,K)
SoLD=SYA
IF(HOLD(J, I,K) .GT.TP) SOLD=SCFA
SNEW=SYA
IF(HSING.GT.TP) SNEW=SCFA
STRG=SCLD*(HOLD(J,I,KbTP1 + SNEW*TP- SNEWWSING
GO TO 288
STORAGE CAPACITY
285 SC=SCl(J,I,K)
STRG=SC*HOLD(JrI,K)- SC*HSING
&----ONE
-----STORE
CELL-BY-CELL FLOW IN BUFFER AND ADD TO ACCUMULATORS
288 IF(IBD.EQ.l)
BUFF(J,I,K)=STRG/DELT
l
IFtSTRG) 292,300,294
292 STCUT=STOUT-STRG
GO TO 300
294 STOIN=STOIN+STRG
C
300 CONTINUE
C
IBD FLAG IS SET RECORD THE CONTENTS OF THE BUFFER
f.2-----IF
IF(IBD.EQ.l) CALL UBUDSV(KSTP,KPER,TEXT,
IBCFCB,BUFF,NCCLrNRC%V,NLAY,IOUT)
1
C
c9 ------ADD
TOTAL RATES AND VOLUMES TO VBVL 8 PUT TITLES
305 VBVL(l,MSUM)=VBVL(l,MSUM)+STOIN
IN VBNM
VBVL(2rMSUM)=VBVL(2,MSUM)+STOUT
VBVL(3,MSUM)=STOIN/DELT
VBVL(4,MSUM)=STOUT/DELT
VBNM(lrMSUM)=TEXT(l)
VBNM(2,MSUM)=TEXT(2)
VBNM(3,MSUM)=TEXT(3)
VBNM(4rMSUM)=TEXT(4)
MSUM=MSUM+l
C
ClO----- CALCULATE FLOW FROM CONSTANT HEAD NODES
CALL SBCFlF (VBNM, VBVL, MSUM,HNEW,IBOUND, C&CC, CV, TOP, DELT,
NCOL, NROW,NLAY,KSTP,KPER, IBD, IBCFCB, ICBCFL,BUFF, IOUT)
1
C
Cl l--Cl l---
CALCULATE AND SAVE FLOW ACROSS CELL BOUNDARIES IF C-&C
FLc4J TERMS ARE REQUESTED.
IF(IBD.NE.0) CALL SBCFlB(HNEWrIBOUND,CRrCC,CV,TOP,NCDLrNROWrNLAY,
KSTP, KPER, IBCFCB,BUFF, IOUT)
1
C
C12----RETURN
RETURN
END
5-65
List
Variable
for
Global
cc
Global
CR
Global
cv
Global
DELT
HNEW
Global
Global
HOLD
Global
HSING
I
I BCFCB
Module
Module
Package
IBD
Package
I BOUND
Global
I CBCFL
Global
IOUT
ISS
Global
Package
J
K
Module
Module
Global
Module BCFlBD
Definition
Range
BUFF
KPER
of Variables
DIMENSION (NCOL,NROW,NLAY), Buffer
used to accumulate
information
before printing
or recording
it.
DIMENSION (NCOL,NROW,NLAY), Conductance in the column
CC(J,I,K) contains the conductance
direction.
between nodes (J,I,K)
and (J,I+l,K).
DIMENSION (NCOL,NROW,NLAY), Conductance in the row
direction.
CR(J,I,K) contains conductance
and (J+l,I,K).
between nodes (J,I,K)
DIMENSION (NCOL,NROW,NLAY-l), Conductance in the
CV(J,I,K) contains conductance
vertical
direction.
and (J,I,K+l).
between nodes (J,I,K)
Length of the current
time step.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate of
HNEWchanges at each iteration.
head in each cell.
DIMENSION (NCOL,NROW,NLAY), Head at the start of the
current
time step.
Temporary label for element of HNEW.
Index for rows.
Flag and a unit number.
> 0, unit number on which the cell-by-cell
flow terms
will
be recorded whenever I CBCFL is set.
= 0, cell-by-cell
flow terms will
not be printed
or
recorded.
< 0. flow from each constant-head
cell will
be orinted
whenever ICBCFL is set.
Flag.
= 0, cell-by-cell
flow terms for this
package
will
not be recorded.
f 0, cell-by-cell
flow terms for this package will
be recorded.
DIMENSION (NCOL,NROW,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
Flag.
= 0, cell-by-cell
flow terms will
not be recorded
or printed
for the current
time step.
f 0, cell-by-cell
flow terms (flow to constant
heads)
will
be either
printed
or recorded (depending on
IBCFCB) for the current time step.
IOUT = 6.
Primary unit number for all printed
output.
Flag.
= 0, simulation
is transient.
f 0, simulation
is steady
state.
Index for columns.
Index for layers.
Stress period counter.
5-66
B
List
Variable
l
Global
KT
Module
LAYCON
Package
LC
SC1
Module
Global
Global
Global
Global
Module
Module
Package
SC2
Package
SNEW*
SOLD*
STOUT
STRG
SYA
TEXT
TOP
Module
Module
Module
Module
Module
Module
Module
Package
TP
VBNM
Module
Global
VBVL
Global
STOIN
D
Range
KSTP
MSUM
NCOL
NLAY
NROW
SC
SCFA
*Note
than
of Variables
that the variables
in BCFlFM.
for
Module BCFlBD (continued)
Definition
Time step counter.
Reset at the start,of
each stress
period.
Index for top of layers (also used for secondary storage
terms).
DIMENSION (80) Layer type code:
0 - Layer strictly
confined.
- Layer strictly
unconfined.
: - Layer confined/unconfined
(transmissivity
is
constant).
3 - Layer confined/unconfined
(transmissivity
varies).
Temporary name for LAYCON(
Counter for budget entries
and labels
in VBVL and VBNM.
Number of columns in the grid.
Number of layers in the grid.
Number of rows in the grid.
Temporary name for the storage capacity.
Temporary name for the primary storage capacity.
DIMENSION (NCOL, NROW, NLAY), Primary storage capacity
of
each cell
(S*DELC*DELR).
DIMENSION (NCOL, NROW, NTOP), Secondary storage capacity
(NTOP is the number of
of each cell in the grid.
layers for which LAYCON = 2 or 3.)
Storage capacity
at the end of the time step.
Storage capacity
at the start
of the time step.
Sum of decreases in storage from individual
cells.
Sum of increases
in storage for individual
cells.
Volume of flow into or out of storage in a single cell.
Temporary name for the secondary storage capacity.
Labels recorded along with the cell-by-cell
flow terms.
DIMENSION (NCOL, NROW, NTOP), Elevation
of top of layers.
(NTOP is the number of layers for which LAYCON = 2
or 3.)
Temporary label for TOP(J,I,K).
DIMENSION(4,20), Labels for entries
in the volumetric
budget.
DIMENSION(4,20),
Entries
for the volumetric
budget. For
flow component N, the values in VBVL are:
(l,N),
Rate for the current
time step into the flow
field.
(2,N),
Rate for the current
time step out of the flow
field.
(3,N),
Volume into the flow field
during simulation.
(4,N),
Volume out of the flow field
during simulation.
SOLD and SNEWhave different
5-67
meanings
in this
subroutine
c
Narrative
for
Module SBCFlN
This module insures that the transmissive
properties
of each cell agree
with the codes specified
in the boundary array (IBOUND) and calculates
(1) horizontal-branch
conductance in layers where transmissivity
is constant,
(2) vertical-branch
conductance,
and (3) storage capacity.
The array IBOUND indicates
following
codes.
the status
of every
Code
Status
zero
positive
negative
inactive
variable
constant
cell
in the
grid
with
the
head
head
The values in the IBOUND array are read by the BASlRP module; transmissive
properties
are read by module BCFlRP. This module (SBCFlN) insures that
all transmissive
parameters are equal to zero for cells
designated
inactive
'inactive"
if all transmissive
by the IBOUND array and that cells
are designated
parameters
are equal to zero.
Module SBCFlN is called
by module BCFlRP and calls
submodule SBCFlC.
The SBCFlN module performs these functions
in the following
order:
inactive
(IBOUND = 0).
If
1. Check the cell to see if it is designated
it is inactive,
set the vertical
leakance (temporarily
stored in CV),
transmissivity
(temporarily
stored in CC), and hydraulic
conductivity
equal to
zero.
2. Check the cell that
least one nonzero transmissive
designate
missive
parameters,
(a)
transmissivity
the
(b)
hydraulic
is designated
active
to insure that there is at
If there are no such nonzero transparameter.
the cell inactive
and print
an error message.
If the transmissivity
or vertical-hydraulic
is constant
conductivity
(LAYCON = 0 or Z),
must be nonzero.
the
If the transmissivity
is a function
of head (LAYCON = 1 or 3),
conductivity
or vertical
conductance
must be nonzero.
the horizontal-branch
conductances
for layers where the
3. Calculate
transmissivity
is constant
(LAYCON = 0 or 2).
Submodule SBCFlC is invoked
to calculate
the branch conductance from the transmissivity
and cell dimensions.
the vertical
leakance between cells
(temporarily
4. Multiply
CV) by the cell dimensions to get the vertical
conductance.
7.
in
If
the simulation
is transient
multiply
the primary storage
by DELR and DELC to get the'primary
storage capacity
(SCl).
If
the layer is confined/unconfined,
multiply
the secondary storage
by DELR and DELC to get the secondary storage capacity
(SCZ).
coeff:&ent
coeff!iient
stored
RETURN.
5-68
Flow Chart
LAYER TYPES are designated
the LAYCON table.
Layer
types are:
for
Module SBCFlN
(xi-)
jn
FOR EACH CELL
O- confined
1 - unconfined
2 - constant/unconfined
but
transmissivity
is constant
3 - confined/unconfined
IF CELL IS
INACTIVE, SET
CONDUCTANCES
EQUAL TO ZERO
Primary storage capacity
is
taken as specific
yield
times
cell area for unconfined
layers,
and as confined
storage
coefficient
times cell area for
confined
or confined/unconfined
layers.
MAKE SURE
THERE IS A
NONZERO
TRANSMISSIVE
PARAMETER
Secondary storage capacity
is
defined for confined/unconfined
aquifers
and is always taken as
specific
yield
times cell area.
3
I
I
1
CALCULATE HORIZONTAL
BRANCHCONDUCTANCE
FOR LA)(;R;YPES
0
I
I
I
I
CALCULATE
CONDUCTANCE
CALCULATE
smm;;zY
CAPACITY
I
5-69
SUBROUTINE SBCFlN(HNEW,IBOUND,SCl,SCZ,CR,CC,CV,HY,TRPY,DELR,DELC,
ISS, NCOL, NROW,NLAY, IOUT)
1
C
C-----VERSION 1642 15MAY1987SBCFlN
C
C
C
C
C
C
C
C
******************************************************************
INITIALIZE AND CHECK BCF DATA
**+***************************************************************
SPECIFICATIONS:
-----------------------------------------------------------------DOUBLE PRECISION HNEWaHCNV
C
DIMENSIONHNEW(NCOL,NROW,NLAY)rIBOUND(NCOL,NROWINLAY)
1
~SC~(NCOL~NRC~‘J~NLAY)~CR(NCOL,NRCW~NLAY)
2
3
4
rCC(NCOL,NROW,NLAY)rCV(NCOLINROW,NLAY)
rHY(NCOL,NROW,NLAY)rTRPY~NLAY)rDELR(NCOL~
rSC2(NCOL,NROW,NLAY)
C
COMMON/FLWCOM/LAYCON(BO)
------------------------------------------------------------------
:
IF IBOUND=O, SET CV=O.r CC=O.r AND HY=O.
KB=O
DO 30 K=lrNLAY
IF(LAYCON(K1.EQ.3
.OR. LAYCON(K1.EQ.l)
KB=KB+l
DO 30 I=l,NROW
DO 30 J=lrNCOL
IF(IBOUND(J,IrK).NE.O1 GO TO 30
CV(J,I,K)=O.
IF(K.NE.NLAY)
Cl---
IF(K.NE.l) CV(J,I,K-l)=O.
CC(J,I,K)=O.
IFlLAYCONtK) .EQ.3 .OR. LAYCON .EQ.l)
C
a
HY(J,I,KB)=O.
30 CONTINUE
(-3--c2---
INSURE THAT EACH ACTIVE CELL HAS AT LEAST ONE NON-ZERO
TRANSMISSIVEPARAMETER. IF NOT, CONVERT CELL TO NOFLOW.
HCNV=888.88
KB=O
DO 60 K=lrNLAY
IFtLAYCONtK) .EQ.l .OR. LAYCON .EQ.3) GO TO 55
C2A--WHEN LAYER TYPE 0 OR 2, TRANSMISSIVITYOR CV MUST BE NONZERO
DO 54 I=l,NROW
DO 54 J=l,NCOL
IF(IBOUND(J,I,K).EQ.O) GOTO 54
IF(CC(J,I,K).NE.O.)
IF(K.EQ.NLAY)
GOTO 54
GO TO 51
IF(CV(J,I,K).NE.O.)
GOTO 54
51 IF(K.EQ.l) GOTO 53
IF(CV(J,I,K-11.NE.O.)
GOTO 54
53 IBOUND(J,I,K)=O
HNEW(J,I,K)=HCNV
WRITE(IOUT,52) K,I,J
52 FORMAT(lX,'NODE(LAYER,ROW,COL)',314,
1
’ ELIMINATED BECAUSEALL CONDUCTANCES
TO NODEARE 0’1
54 CONTINUE
GO TO 60
5-70
a
C
CZB----- WHEN LAYER TYPE IS 1 OR 3, HY OR CV MUST BE NONZERO
55 KB=KB+l
DO 59 I=lrNROW
DO 59 J=lrNCOL
IF(IBCUND(J,I,K).EQ.O) GOTO 59
IF(HY(J,I,KB).NE.O.) GOTO 59
IF(K.EQ.NLAY)
GO TO 56
IF(CV(J,I,K).NE.O.)
GOTO 59
56 IF(K.EQ.l) GOTO 57
IF(CV(J,I,K-11.NE.O.)
GOTO 59
57 IBOUND(J,I,K)=O
HNEW(J,I,K)=HCNV
CC(J,I,K)=O.
WRITE(IOUT,52) K,I,J
59 CONTINUE
60 CONTINUE
C
C3..-----
CALCULATE HOR. CONDUCTANCEtCRAND CC) FOR CONSTANT T LAYERS
DO 65 K=lrNLAY
KK=K
IF(LAYCON(K1.EQ.3
.OR. LAYCON(Kl.EQ.1) GO TO 65
CALL SBCFlC(CR,CC,TRPYrDELR,DELC,KK,NCQLrNROWrNLAY)
65 CONTINUE
C
VERTICAL LEAKANCE BY AREA TO MAKE CONDUCTANCE
c4 ------MULTIPLY
IF(NLAY.EQ.l)
GO TO 69
Kl=NLAY-1
DO 68 K=lrKl
DO 68 I=l,NROW
DO 68 J=lrNCOL
CV(J,I,K)=CV(J,I,K)*DELR(J)*DELC(I)
68 CONTINUE
C
C5-----C5------
IF TRANSIENTMULTIPLYPRIMARYSTORAGE COEFFICIENTBY DELR d
DELC TO GET PRIMARYSTORAGECAPACITYtSCl).
69 IF(ISS.NE.0) GOTO 100
KT=O
DO 80 K=lrNLAY
DO 70 I=lrNROW
DO 70 J=lrNCOL
SCl(J,I,K)=SCl(J,I,K)+DELR(J)*DELC(I)
70 CONTINUE
C
C6---C&---
IF LAYER IS CONF/UNCONF MULTIPLY SECONDARYSTORAGE COEFFICIENT
BY DELR AND DELC TO GET SECONDARYSTORAGE CAPACITY(SC2).
IF(LAYCON(Kl.NE.3
.AND. LAYCON(Kl.NE.2)
GO TO 80
KT=KT+l
DO 75 I=lrNROW
DO 75 J=lrNCOL
C
SCZ(J,I,KT)=SC2(J,I,KT)*DELR(J)*DELC(I)
75 CONTINUE
80 CONTINUE
C7------RETURN
100 RETURN
END
5-71
List
Variable
of Variables
for
Range
cc
Global
CR
Global
cv
Global
DELC
Global
DELR
Global
HCNV
HNEW
Module
Global
HY
Package
I
I BOUND
Module
Global
IOUT
ISS
Global
Package
Module SBCFlN
Definition
DIMENSION (NCOL,NROW,NLAY), Conductance in the column
direction.
CC(J,I,K) contains
conductance
between
nodes (J,I,K)
and (J,I+l,K).
This array is used to
temporarily
hold transmissivity.
DIMENSION (NCOL,NROW,NLAY), Conductance in the row
direction.
CR(J,I,K) contains
conductance
between
nodes (J,I,K)
AND (J+l,I,K).
DIMENSION(NCOL,NROW,NLAY-l), Conductance in the vertical
direction.
CV( J ,I,K)
contains
conductance
between
nodes (J,I,K)
and (J,I,K+l).
This array is used to
temporarily
hold Vcont.
DIMENSION (NROW), Cell dimension
in the column direction.
DELC(1) contains
the width of row I.
DIMENSION (NCOL), Cell dimension
in the row direction.
DELR(J) contains
the width of column J.
Indicator
in the HNEW array that the cell is inactive.
DIMENSION(NCOL,NROW,NLAY), Most recent estimate of
HNEW changes at each iteration.
head in each cell.
DIMENSION (NCOL,NR~W,NBOT), Hydraulic
conductivity
of
the cell.
(NBOT is the number of layers where
LAYCON = 1 or 3.)
Index for rows.
DIMENSION(NCOL,NROW,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
IOUT = 6.
Primary unit number for all printed
output.
Flag.
= 0, simulation
is transient.
* 0, simulation
is steady state.
Module
Index
KB
KK
Module
Module
Module
KT
Kl
LAYCON
Module
Module
Package
NCOL
NLAY
NROW
SC1
Global
Global
Global
Package
SC2
Package
TRPY
Package
Index for layers.
Index for bottom of layers.
Temporary variable
set equal to K. KK is used as an
actual argument in subroutine
calls to avoid using
the DO loop variable
K as an argument,
which causes
problems with some compilers.
Index for top of layers.
NLAY-1.
DIMENSION(80),
Layer type code:
0 - Layer strictly
confined.
1 - Layer strictly
unconfined.
(transmissivity
is
2 - Layer confined/unconfined
constant).
(transmissivity
3 - Layer confined/unconfined
varies).
Number of columns in the grid.
Number of layers
in the grid.
Number of rows in the grid.
DIMENSION (NCOL,NROW,NLAY), Primary storage capacity
of
each cell
(S*DELC*DELR).
DIMENSION(NCOL,NROW,NTOP), Secondary storage capacity
of each cell in the grid.
(NTOP is the number of
layers for which LAYCON = 2 or 3.)
DIMENSION (NLAY), Ratio of transmissivity
in the column
direction
to transmissivity
in the row direction.
;:
for
columns.
5-72
Narrative
for
Module SBCFlH
Module SBCFlH calculates
the horizontal-branch
conductances
(conductance
between nodes) for a layer in which the transmissivity
is a function
of head
(LAYCON = 1 or 3).
It calculates
the transmissivity
internally
and calls
It is called
by BCFlFM
submodule SBCFlC to calculate
the branch conductances.
for each type 1 or type 3 layer at each iteration.
Transmissivity
is the
product of hydraulic
conductivity
and saturated
thickness.
The saturated
thickness
of a completely
saturated
layer is computed as the elevation
of
the top (TOP) minus the elevation
of the bottom (BOT), the thickness
of
thickness
is computed
For a partially
saturated
layer , saturated
the layer.
as the head in the cell minus the elevation
of the bottom of the layer.
1.
For each cell,
calculate
If the cell is inactive,
2.
move on to the next cell.
the transmissivity.
DO STEPS 2-6.
set the transmissivity
equal
to zero and
Calculate
the thickness
of the saturation.
In a strictly
unconfined
In a
layer3*the
thickness
is the head (HNEW) minus the bottom (BOTTOM)
confiied/unconfined
layer,
the thickness
is the head (HNEW) minus'the
bottom or the top (TOP) minus the bottom, whichever is greater.
4.
Check to see if
the saturated
thickness
is greater
than
cell
is greater than
5. If the thickness
is the thickness
times the hydraulic
Print
zero,
If the saturated
thickness
is less than zero, the cell is dry.
6.
set all branch conductances
equal to
a message to that effect,
and set the boundary indicator
(IBOUND) equal to zero.
for
7. Call
the layer.
8.
submodule
SBCFlC to calculate
RETURN.
5-73
zero, the transmissivity
conductivity.
zero.
the
horizontal-branch
of the
conductances
Flow Chart
for
Module SBCFlH
SET TRANSMISSIVITY
EQUAL TO ZERO
CALCULATE
SATURATED
THICKNESS
6
I
PRINT
A
MESSAGE
SAYING CELL
WENT DRY
1
l
CALCULATE
HORIZONTAL
BRANCH
CONDUCTANCE
5-74
I
6A
SUBROUTINE SBCFlH(HNEWrIBDUND,CR,CC,CVrHY,TRPYrDELR,DELC
~~BOT,TCP,K,KB~KT,KITER,KSTP~KPERINCOL,NRCW~NLAY,IOUT)
C
1442 31DEC1986SBCFlH
C-----VERSION
C
******************************************************************
C
C
COMPUTE CONDUCTANCEFROM SATURATED THICKNESS AND HYDRAULIC
CONDUCTIVITY
C
******************************************************************
:
C
C
SPECIFICATIONS:
-----------------------------------------------------------------DOUBLE PRECISION
HNEW
C
DIMENSION
HNEW(NCOL,NROW,NLAY)rIBCUND(NCOL,NROW,NLAY)
1, CR(NCOLrNROW,NLAY)r CC(NCOL,NROW,NLAY)r CV(NCOLrNROW,NLAY)
ZrHY(NCOLrNROW,NLAY)r TRPYtNLAYlr DELRtNCOL),
3, BOT(NCOLrNROW,NLAY)rTOP(NCOL,NROW,NLAY)
DELCtNROW)
C
COMMON/FLWCOM/LAYCON(BO)
-----------------------------------------------------------------C
C
Cl--CALCULATE TRANSMISSIVIMAT EACH ACTIVE CELL.
Cl ------WILL
BE STORED TEMPORARILY IN THECC ARRAY.
DO 200 I=l,NRCM
DO 200 J=l,NCOL
C
C2---
IF CELL IS INACTIVETHEN SET T=O 6 MOVE ON TO NEXT CELL.
IF(IBOUND(J,I,K).NE.O) GOTO 10
CC(J,I,K)=O.
GO TO 200
C
C3------CALCULATE
SATURATED THICKNESS.
10 HD=HNEW(J,I,K)
IF(LAYCON(K1.EQ.l)
GO TO 50
IF(HD.GT.TOP(J,I,KT)) HD=TOP(J,I,KT)
50 THCK=HD-BOT(J,I,KB)
C
TO SEE IF SATURATED THICKNESS
c4 ------CHECK
IF(THCK.LE.0.)
GO TO 100
C
C5------
TRANSMISSIVITY
IS GREATER THAN ZERO.
IF SATURATED THICKNESS>0
THEN T=K*THICKNESS.
CC(JrI,K)=THCK*HY(J,I,KB)
GO TO 200
C
SATURATED THICKNESS
< 0, PRINT A MESSAGE AND SET
c6 ------WHEN
C6--TRANSMISSIVITY,
IBOUND,AND VERTICAL CONDUCTANCE=0
C
100 WRITE(IOUT,lSO)K,IrJrKITER,KSTP,.KPER
150 FORMAT(lHO,lO('*')r'NODE'r314,' (LAYER,ROWrCOL) WENT DRY’
1
,I AT ITERATION=',13,'
TIME STEP =‘,I3
2
,I
STRESS PERIOD=',I31
HNEW(JrI,K)=l.UO
CC(J,I,K)=O.
IBOUND(J,I,K)=O
IF(K.LT.NLAY)
CV(J,I,K)=O.
IF(K.GT.l) CV(J,I,K-l)=O.
GOTO 200
200 CONTINUE
HORIZONTAL BRANCH CONDUCTANCESFROM TRANSMISSIVITY
c7 ------COMPUTE
CALL SBCFlC(CR,CC,TRPY,DELR,DELC,K,NCOL,NROWrNLAY)
RETURN
END
5-75
List
Variable
Range
BOT
Package
cc
Global
CR
Global
cv
Global
DELC
Global
DELR
Global
HD
HNEW
Module
Global
HY
Package
I
I BOUND
Module
Global
IOUT
J
K
KB
KITER
KPER
KSTP
Global
Module
Module
Module
Global
Global
Global
KT
LAYCON
Module
Package
NCOL
NLAY
NROW
THCK
TOP
Global
Global
Global
Module
Package
TRPY
Package
of Variables
for
Module SBCFlH
Definition
DIMENSION (NCOL,NROW,NBOT), Elevation
of the bottom of
each layer.
(NBOT is the number of layers for which
LAYCON= 1 or 3.)
DIMENSION (NCOL,NROW,NLAY), Conductance in the column
direction.
CC(J, I ,K) contains conductance between
nodes (J,I,K)
and (J,I+l,K).
This array is used to
temporarily
hold transmissivity.
DIMENSION (NCOL,NROW,NLAY), Conductance in the row
direction.
CR(J,I,K)
contains conductance between
nodes (J,I,K)
and (J+l,I,K).
DIMENSION (NCOL,NROW,NLAY-l), Conductance in the vertical
direction.
CV(J,I,K)
contains conductance between
nodes (J,I,K)
and (J,I,K+~).
DIMENSION (NROW), Cell dimension in the column direction.
DELC(1) contains the width of row I.
DIMENSION (NCOL), Cell dimension in the row direction.
DELR(J) contains the width of column J.
Temporary label for an element in HNEW.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate of
head in each cell.
HNEWchanges at each iteration.
DIMENSION (NCOL,NROW,NBOT), Hydraulic
conductivity
of
the cell.
(NBOT is the number of layers where
LAYCON = 1 or 3.)
Index for rows.
DIMENSIoN(NC~L,NROW,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
Primary unit number for all printed output.
IOUT = 6.
Index lfor co1 umns.
Index for layers.
Index for bottom of layers.
Reset at the start of each time step.
Iteration
counter.
Stress period counter.
Reset at the start of each stress
Time step counter.
period.
Index for tops of layers.
DIMENSION(80), Layer type code:
confined.
0 - Layer strictly
unconfined.
1 - Layer strictly
is
(transm issivity
2- Layer confined/unconfined
constant)
(transm issivity
3- Layer confined/unconfined
varies).
Number of columns in the grid.
Number of layers in the grid.
Number of rows in the grid.
Saturated thickness.
DIMENsIoN(NC~L,NR~W,NT~P), Elevation 0f top 0f layers.
(NTOP is number of layers for which LAYCON= 2 or 3.)
DIMENSION (NLAY), Ratio of transmissivity
in the column
direction
to transmissivity
in the row direction.
5-76
Narrative
for
Module SBCFlC
The module SBCFlC calculates
horizontal-branch
conductances
for a layer
from transmissivity
and cell dimensions.
It is called by submodules SBCFlN
and SBCFlH. Recall that the branch conductances
between two nodes can be
expressed by
c=
However,
+
C&g(Cl
$9.
CI and C2 can be represented
by
Cl = TIW/(LI/2)
C2 = T2W/(L2/2).
Thus,
C = 2TIT2W/(TIL2
+ T2LI)+
This equation
is used to calculate
conductances
along rows and columns.
When calculating
conductance along rows, LI and L2 are DELR(J) and DELR(J+l),
When calculating
conductance
along columns,
respectively,
and W is DELC(I).
LI and L2 are DELC( I) and DELC( I+l),
respectively,
and W is DELR(J).
Conductance along columns is also multiplied
by TRPY(K), the ratio of
conductivity
in the column direction
to conductivity
in the row direction
in layer K.
1.
Process cells
one at a time calculating
branch
to the one on the right and the one in front.
that
cell
equal
If the transmissivity
is equal
2.
to zero and skip to the next cell.
cell
If the transmissivity
3.
to the right,
calculate
4.
in front,
5.
to zero,
conductances
set the branch
from
conductance
of the cell is not zero and if there is a
the branch conductance
(CR) along the row.
If the transmissivity
of the cell is not zero
calculate
the conductance along the column.
and there
is a cell
RETURN.
Note: Transmissivity,
which
when conductances
are calculated.
CR(J,I,K)
contains
was temporarily
the conductance
node J+l,I,K.
5-77
ai,j+l/z,k
stored
in
CC, will
be lost
between node J,I,K
and
Flow Chart
for
Module SBCFlC
FOR EACH CELL
1
CALCULATE
BRANCH
CONDUCTANCE
DOWN COLUMN
YES
I
5-78
SUBROUTINE SBCFlC(CR,CC,TRPY,DELR,DELC,K,NCOL,NROW,NLAY)
c
C
C-----VERSION 1334 22AUG1987 SBCFlC
**************~***************************************************
C
C
COMPUTEBRANCH CONDUCTANCEUSING HARMONIC MEAN OF BLOCK
C
CONDUCTANCES-- BLOCK TRANSMISSIVITY IS IN CC UPON ENTRY
***********************************~******************************
C
C
C
SPECIFICATIONS:
DIMENSION CR(NCOL,NROW,NLAY)r CC(NCOL,NROW,NLAY)
2
C
C
, TRPYtNLAY),
DELR(NCOL)r DELCtNROW)
-----------------------------------------------------------------YX=TRPY(K)*2.
C
Cl--Cl----
FOR EACH CELL CALCULATE BRANCH CONDUCTANCESFROM THAT CELL
TO THE ONE ON THE RIGHT AND THE ONE IN FRONT.
DO 40 I=l,NROW
DO 40 J=l,NCOL
Tl=CC(J,I,K)
C
c2----
IF T=O THEN SET CONDUCTANCEEQUAL TO 0. GO ON TO NEXT CELL.
IF(Tl.NE.0.)
GO TO 10
CR(J,I,K)=O.
GO TO 40
C
C3-----IF THIS IS NOT THE LAST COLUMNtRIGHTMOST)THEN CALCULATE
c3 ------BRANCH
CONDUCTANCEIN THE ROWDIRECTION (CR) TO THE RIGHT.
10 IF(J.EQ.NCOL) GO TO 30
T2=CC(J+lrIrK)
CR(J,I,K)=2.*T2*Tl*DELC(I)/(Tl*DELR(J+l~+T2*DELR~J~~
C
c4 ------IF
THIS IS NOT THE LAST ROWtFRONTMOST)THEN CALCULATE
c4 ------BRANCH
CONDUCTANCEIN THE COLUMNDIRECTION (CC) TO THE FRONT.
30 IF(I.EQ.NROW) GO TO 40
T2=CC(J,I+lrK)
CC(J,I,K)=YX*T2*Tl*DELR(J)/(Tl*DELC(I+l~+T2*DELC~I~~
40 CONTINUE
C
c5 ------RETURN
RETURN
END
5-79
List
Variable
cc
of Variables
Module SBCFlC
for
Definition
Range
Global
DIMENSION (NCOL,NROW,NLAY), Conductance in the column
CC(J,I,K) contains conductance between
direction.
nodes (J,I,K)
and (J,Itl,K).
This array is used to
temporarily
hold
transmissivity.
a3
Global
DIMENSION (NCOL,NROW,NLAY), Conductance in the row
CR(J,I,K) contains conductance between
direction.
nodes (J,I,K)
and (Jtl,I,K).
DELC
Global
DIMENSION (NROW), Cell dimension in the column
DELC( I) contains
the width of row I.
direction.
DELR
Global
DIMENSION (NCOL), Cell dimension in the row direction.
DELR( J) contains
the width of column J.
I
Module
Index
for
rows.
3
Module
Index
for
columns.
K
Module
Index for
NCOL
Global
Number of columns
NLAY
Global
Number of layers
NROW
Global
Number of rows in the grid.
TRPY
Package
DIMENSION (NLAY),
layers.
in the grid.
in the
column direction
direction.
grid.
Ratio of transmissivity
in the
to transmissivity
in the row
Tl
Module
Temporary
field
for
CC(J,I,K).
T2
Module
Temporary
field
for
CC(Jkl,I,K).
YX
Module
TRPY(K)*2.
5-80
Narrative
This
module calculates
BCFlBD when the user
its
tasks
1.
gathered
2.
the
right
face
4.
Clear
front
6.
Call
7.
Clear
gathered
8.
the lower
9.
10.
utility
the
calculate
buffer
Call
flow
is called
by module
It performs
terms.
flow
terms
are
and store
flow
it
in the
row direction
through
in the buffer.
(BUFF) in which
the contents
of the buffer.
cell-by-cell
flow
terms
in the
column direction
are
are calculated.
utility
calculate
the flow
and store
it
through
in the buffer.
module UBUDSV to write
the buffer
(BUFF) in which
the
contents
cell-by-cell
flow
of the buffer.
terms
are
are calculated.
For each cell,
face
the
module UBUDSV to write
of the cell
as they
cell -by-cell
It
are calculated.
For each cell,
face
faces.
(BUFF) in whi ch cell-by-cell
of the cell
as they
cell
order:
buffer
For each cell,
Call
5.
the
as they
3.
gathered
the
Module SBCFlB
across
has requested
in the following
Clear
flow
for
calculate
of the cell
utility
the flow
and store
it
5-81
vertical
direction
through
in the buffer.
module UBUDSV to write
RETURN.
in the
the contents
of the buffer.
Flow Chart
for
Module SBCFlB
BUFFER: the buffer
is an array
with one element for each
It is
cell in the grid.
used to store the results
of cell-by-cell
calculations
until
all cells
have been
The contents
processed.
of the buffer
are then
recorded as a unit.
THRU THE RIGHT
SIDE AND STORE IN
3
,
WRITE THE
CONTENTS
OF THE BUFFER
I
I
I
4
FOR EACH CELL
CALCULATE THE FLOW
THRU THE FRONT
SIDE AND STORE IN
THE BUFFER
4
OF THE BUFFER
FOR EACH CELL
CALCULATE THE FLOW
THRU THE BOTTOM
SIDE AND STORE IN
THE BUFFER
WRITE THE
CONTENTS
OF THE BUFFER
I
pETURN
5-82
SUBROUTINE SBCFlBtHNEW, IBOUND,CR,CC,CV,TOP,NCOL,NROW, NLAY,
KSTP, KPER, IBCFCB, BUFF, IOUT)
1
C
C-----VERSION 1548 12MAY1987
SBCFlB
C
C
C
C
C
C
C
*******+****t*****************************************************
COMPUTE
FLOWACROSS EACH CELL
WALL
*************************************~****************************
SPECIFICATIONS:
-_--------_------------------------------------------------------CHARACTER*4 TEXT
DOUBLE PRECISION
HNEW,HD
C
DIMENSION
HNEWtNCOLrNROWrNLAY), IBOUND(NCOL,NROW,NLAY)r
1
CR(NCOL,NROW,NLAY)r CC(NCOL,NROW,NLAY),
2
3
CV(NCOL,NRCM,NLAY)r TOP(NCOL,NR(TW,NLAY),
BUFF(NCOL,NROW,NLAY)
’ c
COMMON/FLWCOM/LAYCON(80)
C
DIMENSION
TEXT(12)
C
l
DATA TEXT(l),TEXT(Z)rTEXT(3),TEXT(4),TEXT(5),~~(6),~~(7),
1
TEXT(8)r'TEXT(9)rTEXT(lO),~~(ll),~~~l2~
2
/‘FLOW’,’
RIG','HT F’r’ACE ‘,
LOW’r’ER F’r’ACE
‘FLOW’,’ FRO’r’NT F’,‘ACE ‘,‘FLoW’,’
2
------------------------------------------------------------------
C
C
‘/
NCMl=NCOL-1
IF(NCMl.LT.1) GOTO 405
C
Cl-----CLEAR
THE BUFFER
DO 310 K=lrNLAY
DO 310 I=lrNROW
DO 310 J=lrNCOL
C
BUFF(J,I,K)=O.
310 CONTINUE
c2---
C
DO400 I=lrNRCW
DO 400 J=lrNCMl
IF((IBOUND(J,I,K).LE.O) .AND. (IBOUND(J+lrI,K).LE.0)) GOTO 400
HDIFF=HNEW(J,I,KbHNEW(J+l,I,K)
BUFF(J,I,K)=HDIFF*CR(J,I,K)
400 CONTINUE
C3-----
C
FOR EACH CELL CALCULATE FLOW THRU RIGHT’FACE & STORE IN BUFFER
DO 400 K=lrNLAY
RECORDCONTENTS OF BUFFER
CALL UBUDSV(KSTP, KPER,TEXT( 11, IBCFCB, BUFF, NCOL,NROW,NLAY, IOUT)
5-83
THE BUFFER
al -----CLEAR
405 NRMl=NROW-1
IF(NRMl.LT.1)
GO TO 505
DO 410 K=lrNLAY
DO 410 I=lrNROW
DO 410 J=l,NCOL
n
BUFF(J,I,K)=O.
410 CONTINUE
-----FOR
EACH CELL CALCULATE FLOW THRU FRONT FACE 8 STORE IN BUFFER
E5
DO 500 K=lrNLAY
DO 500 I=lrNRMl
DO 500 J=lrNCOL
C
IF((IBOUND(J,I,K).LE.O) .AND. (IBOLlND(J,I+lrK).LE.O)) GOTO500
HDIFF=HNEW(J,I,K)-HNEW(J,I+lrK)
BUFF(J,I,K)=HDIFF*CC(JIIIK)
500 CONTINUE
C&--
RECORDCONTENTS OF BUFFER.
CALL UBUDSV(KSTP,KPER,TEXT(5)rIBCFCB,BUFF,N~L,NR~,NLAY,IOUT)
505 NLMl=NLAY-1
C
C7-----
IF(NLMl.LT.1) GOTO 1000
CLEAR THE BUFFER
DO 510 K=lrNLAY
DO510 I=lrNROW
DO510 J=l,NCOL
BUFF(J,I,K)=O.
510 CONTINUE
a
c8-----FOR
EACH CELL CALCULATE FLOW THRU LOWERFACE 8 STORE IN BUFFER
KT=O
DO 600 K=l,NLMl
IF(LAYCON(K1.EQ.3
.OR. LAYCON(K1.EQ.Z) KT=KTtl
DO 600 I=lrNROW
DO 600 J=l, NCOL
IF((IBOUND(J,I,K).LE.O) .AND. (IBDUND(J,I,K+l).LE.O)) GOTO 600
HD=HNEW(J,I,K+l)
C
IF(LAYCON(K+l).NE.S
.AND. LAYCON(Kt11.NE.2)
GOTO580
TMF=HD
IF(TMP.LT.TOP(J,I,KTtT+1))
HD=TOP(J,IpKT+l)
580 HDIFF=HNEW(J,I,K)-HD
BUFF(J,I,K)=HDIFF*CV(J,I,K)
600 CONTINUE
c9 -----RECORD CONTENTS OF BUFFER.
CALL UBUDSV(KSTP,KPER,TEXT(9) ,IBCFCB,BUFF,NCOL,NROW,NLAY,
C
ClO----RETURN
1000 RETURN
END
5-84
IOUT)
List
Variable
BUFF
l
Global
obal
CR
obal
cv
obal
HD
HDIFF
HNEW
Module
Module
Global
&FCB
Module
Package
I BOUND
Global
IOUT
KPER
KSTP
Global
Module
Module
Global
Global
KT
LAYCON
Module
Package
NCMl
NCOL
NLAY
NLMl
NRMl
NROW
TEXT
Module
Global
Global
Module
Module
Global
Module
Module
Package
i
JMP
TOP
for
Range
cc
.m
of Variables
Module SBCFlB
Definition
DIMENSION (NC~L,NROW,NLAY), Buffer used to accumulate
information
before printing
or recording
it.
DIMENSION (NCOL,NROW,NLAY), Conductance in the column
direction.
CC(J,I,K)
contains
conductance
between
nodes (J,I,K)
and (J,I+l,K).
DIMENSION (NCOL,NROW,NLAY), Conductance in the row
direction.
Cft(J,I,K)
contains
conductance
between
nodes (J,I,K)
and (J+~,I,K).
DIMENSION (NCOL,NROW,NLAY-I), Conductance in the vertical
direction.
CV(J,I,K)
contains
conductance
between
nodes (J,I,K)
and (J,I,K+I).
Temporary field
for head.
Head difference
between two adjacent
nodes.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
of head
in each cell.
HNEWchanges at each iteration.
Index for rows.
Flag and a unit number.
> 0, unit number on which the cell-by-cell
flow terms
will
be recorded whenever ICBCFL is set.
= 0, cell-by-cell
flow terms will
be not be printed
or recorded
< 0, flow from each constant-head
cell will
be printed
whenever I CBCFL is set.
DIMENSION (NC~L,NROW,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
IOUT = 6.
Primary unit number for all printed
output.
Index for columns.
Index for layers.
Stress period counter.
Reset at the start
of each stress
Time step counter.
period.
Index for tops of layers.
DIMENSION( 80), Layer type code:
0 - Layer strictly
confined.
- Layer strictly
unconfined.
(transmissivity
is
: - Layer confined/unconfined
constant)
(transmissivity
varies).
3- Layer confined/unconfined
NCOL-1.
Number of columns in the grid.
Number of layers in the grid.
NLAY-1.
NROW-1.
Number of rows in the grid.
Label to be printed
or recorded with array data.
Temporary field
for head.
DIMENSION (NC~L,NR~W,NT~P), Elevation
of top of layers.
(NTOP is number of layers for which LAYCON = 2 or 3.)
5-85
Narrative
This
module calculates
accumulated
field
by sign
for
accumulated
utility
into
volumetric
flow
budget.
The flows
(CHOUT), the
The flows
are
flow
are also
from each constant-head
Module SBCFlF is called
basis.
cells.
(CHIN) and out of
to get the total
cell
on a
by module BCFlBD and calls
module UBUDSV.
Module SBCFlF performs
1.
flow
from constant-head
in the overall
by cell
cell-by-cell
flow
to get flow
inclusion
Module SBCFlF
for
Clear
field,
fields
they
flow
will
For each cell,
3.
will
cell-by-cell
(BUFF) in which
functions
in the
following
CHIN and CHOUT in which
respectively,
If
2.
the
its
flow
order:
into
and out of the
be accumulated.
terms
be stored
calculate
will
be recorded,
as they
the flow
clear
the buffer
are calculated.
to and from constant-head
cells.
DO STEPS 4-12.
If
4.
the
cell
and go on to the
Clear
5.
the flows
face
7.
to the
next
the
cell,
skip
further
processing
cell.
six
fields
corresponding
to the
six
the
flow
faces
through
which
be calculated.
For each face
6.
that
will
is not a constant-head
of the cell,
calculate
out of the cell
through
(STEPS 7-11).
If
there
next
face.
is
not a variable-head
5-86
cell
which
shares
the
face,
go on
8.
Calculate
9.
Test
adjacent
the
the sign
variable-head
of the adjacent
flow
through
of the flow
cell
the face
to see if
from the
variable-head
cell
into
it
the adjacent
is positive
(into
cell)
or negative
constant-head
into
cell.
the constant-head
the
cell).
(out
GO TO
EITHER STEP 10 OR 11.
10.
the flow
If
the flow
If
the
sign
is positive,
Add together
six
13.
the
14.
faces
negative,
If
the user
flows
If
15.
into
Put, labels
17.
flow
add the
flow
rate
to CHOUT (flow
add the
flow
rate
to CHIN (flow
If
specified
and store
x2,
out of
out of
x4,
number for
cell
into
are to be recorded,
them in the
terms
xs,
x5, xs)
corresponding
RATE.
a negative
terms
cell-by-cell
buffer
until
IBCFCB, and ICBCFL $ 0,
the aquifer.
add the
all
cells
are to be recorded,
call
six
flow
rates
are finished.
utility
module
them.
Put flow
for
(x1,
(RATE) from the constant-head
the
the
terms
in the field
the cell-by-cell
UBUDSV to record
16.
the
and leave
out of the cell
cells,
is
domain).
12.
print
sign
domain).
11.
to the
the
rates,
into
VBVL array
those
budget
for
and out of the flow
inclusion
terms
into
domain from constant-head
in the overall
VBNM.
RETURN.
5-87
volumetric
budget.
Flow Chart
for
Module SBCFlF
CHIN is a field
in which
flows,
into the flow
domain from constanthead cells,
will
be
accumulated.
CHOUT is a field
in which
flows,
out of the flow
domain to constanthead cells,
will
be
accumulated.
CLEAR THE
SUFFER (BUFF)
m EACH CELL
BUFF is a buffer
in which
cell-by-cell
flow terms
will
be stored as they
are calculated
prior to
recording
them on disk.
CLEAR FIELDS
IN WHICH SIX
FLOWS WILL SE
CALCULATED
FC,R EACH FACE
c
6
INTERNAL CELLS are those in
They
which head varies.
are in opposition
to
EXTERNAL CELLS (inactive
or constant
head) which
are on or outside
of a
boundary.
SUM
FLOWS THROUGH
SIX FACES
IF CELL-BY-CELL
FLOW TERMS ARE
NEEDED,
RECORD BUFF
5-88
B
SUBROUTINE SBCFlF (VBNM, VBVL, MSUM,HNEW,IBOUND, CR, CC, CV,
1
TOP, DELT,NCCL, NRCM,NLAY,KSTP,KPER, IBD, IBCFCB, ICBCFLr
BUFF, IOUT)
2
C-----VERSION
1549 12MAY1987 SBCFlF
C
*****************************************~************************
C
C
COMPUTE FLckl FROM CONSTANT HEAD NODES
******Ytt**tt****t***~******~~****~*********~*******~******~~**~~*
C
C
C
SPECIFICATIONS:
-----------------------------------------------------------------C
CHARACTER*4 VBNM,TEXT
DOUBLE PRECISION HNE’WIHD
C
DIMENSIONHNEW(NCOLrNRC%V,NLAY)r IBOUND(NCOL~NROWINLAY)~
1
CR(NCOLrNRUf,NLAY)r
CC(NCOLrNR(XJ,NLAY)r
CV(NCOLrNROW,NLAY)r VBNM(4r20)r
VBVL(4r20)r
TOP(NCOL,NRC&V,NLAY)rBUFF(NCOL,NR~,NLAY)
C
COMMON/FLWCOM/LAYCON(80)
C
DIMENSION TEXT(4)
C
C’,‘ONST’,‘ANT
‘,‘HEAD’/
DATA TEXT(l),TEXT(2)rTEXT(3)rTEXT(4)
/’
------_----------------------------------------------------------E
BUDGET ACCUMULATORS
Cl ------CLEAR
CHIN=O.
CHOUT=O.
C
c2---
CLEAR BUFFER IF CELL-BY-CELL
FLOW TERM FLAGiIBD)
IS SET
IF(IBD.EQ.0) GOTO 8
DO 5 K=lrNLAY
DO 5 I=l,NRW
DO5 J=lrNCOL
BUFF(J,I,K)=O.
5 CONTINUE
C
C3---- FOR EACH CELL
Q-----FACES.
8 KT=O
DO 200 K=lrNLAY
LC=LAYCON(K)
IF IT IS CONSTANT HEAD COMPUTE FLOW ACROSS 6
IF(LC.EQ.3 .OR. LC.EQ.2) KT=KT+l
DO200 I=l,NRCM
DO 200 J=lrNCOL
E4-----IF
CELL IS NOT CONSTANT HEAD SKIP IT 8 GO ON TO NEXT CELL.
IF (IBOUND(J,I,K).GE.O)GOTO 200
FIELDS FOR SIX FLOW RATES.
:5 -----CLEAR
x1=0.
x2=0.
x3=0.
x4=0.
x5=0.
X6=0.
EACH FACE OF THE CELL CALCULATE FLOW THROUGH THAT FACE
c6-----FOR
OF THE CONSTANT HEAD CELL AND INTO THE FLOW DOMAIN.
c6 -----OUT
COMMENTS 7-11 APPEAR ONLY IN THE SECTIONHEADED BY COMMENT 6A
c6 -----BUT
THEY APPLY IN A SIMILAR MANNER TO THE SECTIONS
HEADED
C(j--BY COMMENTS 6&6F.
C
(-3---
D
5-89
C6A----CALCULATE
FLOW THROUGH THE LEFT FACE
C
C7----- IF THERE IS NOT A VARIABLE HEAD CELL ON THE OTHER SIDE OF THIS
C7----- FACE THEN GO ON TO THE NEXT FACE.
IF(J.EQ.l) GOTO 30
IF(IBOUND(J-l,I,K).LE.O)GO
TO 30
HDIFF=HNEW(J,IrK)-HNEW(J-lrI,K)
C
C&---
CALCULATE FLOW THROUGH THIS
FACEINTO THE ADJACENT
CELL.
Xl=HDIFF"CR(J-lrIrK1
n
-----TEST
TO SEE IF FLOW IS POSITIVEOR NEGATIVE
E9
IF (Xl) 10,30,20
C
ClD---- IF NEGATIVE ADD TO CHOUTtFLOW OUT OF DOMAIN TO CONSTANT HEAD).
10 CHOUT=CHCUT-Xl
GO TO 30
C
Cll---- IF POSITIVEADD TO CHINtFLOWINTO DOMAINFROM CONSTANT HEAD).
20 CHIN=CHIN+Xl
n
b
C6&---
CALCULATE FLUV THROUGH THE RIGHT FACE
30 IF(J.EQ.NCOL) GOTO 60
IF(IBOUND(J+lrI,K) .LE.O) GO TO 60
HDIFF=HNEW(JrIrK)-HNEW(J+lrIrK)
X2=HDIFF*CR(J,I,K)
IF(X2140r60rSO
40 CHOLIT=CHOUT-X2
GO TO 60
50 CHIN=CHIN+X2
C
C6C----CALCULATE
60 IF(I.EQ.l)
FLU+’ THROUGH THE BACK FACE.
GOTO 90
IF (IBOUND(JrI-lrK1.LE.O)
HDIFF=HNEW(J,I,KbHNEW(JII-lrK)
G0 TO 90
X3=HDIFFi%C(J,I-1,K)
IF(X3) 70r90r80
70 CHOUT=CHOUT-X3
GO TO 90
80 CHIN=CHIN+X3
n
END----CALCULATE
FLOW THROUGH THE FRONT FACE.
90 IF(I.EQ.NRCW)
GO TO 120
IF(IBDUND(J,I+l,K).LE.O) GDTO 120
HDIFF=HNEW(J,IrKbHNEW(J,I+lrK)
X4=HDIFF%C(J,I,K)
IF (X4) 100.120r110
100 CHOUT=CHOUT-X4
GO TO 120
110 CHIN=CHIN+X4
C6E---120
CALCULATE FLOW THRWGH THE UPPER FACE
IF(K.EQ.l) GOTO 150
IF (IBOUNDtJrIrK-11.LE.O) GOTO 150
HD=HNEW(J,I,K)
IF(LC.NE.3
.AND. LC.NE.21
TMF= HD
GO TO 122
IF(TMP.LT.TOP(JrIrKT)) HD=TOP(JrI,KT)
122 HDIFF=HD-HNEWtJrIrK-1)
XS=HDIFFFV(J,IrK-1)
IF(X5)
130,150,140
130 CHOUT=CHOUT-X5
GO TO 150
140 CHIN=CHIN+X5
5-90
----CALCULATE
FLOW THROUGH THE LOWER FACE.
150 IF(K.EQ.NLAY)
GO TO 180
IF(IBOUND(J,I,K+1) .LE.O) GO TO 180
HD=HNEW(JrIrK+l)
IF(LAYCON(Kt11.NE.3
.AND. LAYCCN(K+l).NE.2)
TMP=HD
IF(TMP.LT.TOP(J,I,KT+l))
152 HDIFF=HNEW(JrI,K)-HD
X6=HDIFF+'CV(JrIrK)
IF(X6) 160,180,170
GD TO 152
HD=TOP(JrIrKT+l)
160 CHDUT=CHOUT-X6
GO TO 180
170 CHIN=CHIN+X6
C
c12--180
SUM UP FLOWS THROUGH SIX
RATE=Xl+X2+X3+X4+X5+X6
SIDES OF CONSTANT HEAD CELL.
C
Cl3-----PRINT
THE INDIVIDUALRATES IF REQUESTED(IBCFCB<O).
IF(IBCFCB.LT.O.AND.ICBCFL.NE.0)WRITE(IOUT,900) (TEXT(N),t+lr4),
1
KPER,KSTP,K,IrJrRATE
LAYER’, 13,
900 FOF&lAT(lHO,4A4,' PERIOD',I3,'
STEP'rI3,'
1'
ROW’rI4,’
RATE ‘rG15.7)
CDL’rI4,’
C
c14----
IF CELL-BY-CELL FLAG SET STORE SUM OF FLOWS FOR CELL
IF(IBD.EQ.l)
BUFF(J,I,K)=RATE
IN BUFFER
C
200 CONTINUE
C
c15---- IF CELL-BY-CELL FLAG SET THEN RECORD CONTENTS OF BUFFER
IF(IBD.EQ.l) CALL UBUDSV(KSTP,KPER,TEXT(l)r
1
IBCFCB,BUFF, NCDL, NRW, NLAY, IOUT)
C
C
C16---- SAVE TOTAL CONSTANT HEAD FLOWS AND VOLUMES IN VBVL TABLE
Cl6 ----FOR
INCLUSIONIN BUDGET. PUT LABELS IN VBNM TABLE.
VBVL(lrMSUM)=VBVL(lrMSUM)+CHIN*DELT
VBVL(2rMSUM)=VBVL(2rMSUM)+CHOUT*DELT
VBVL(3rMSUM)=CHIN
VBVL(4rMSUM)=CHOUT
C
C
---SETUP VDLUMETRIC BUM;ET NAMES
VBNM(lrMSUM)=TEXT(l)
VBNM(P,MSUM)=TEXT(2)
VBNM(3rMSUM)=TEXT(3)
VBNM(4rMSUM)=TEXT(4)
C
MSUM=MSUM+l
C
C
Cl7 ----RETURN
RETURN
END
5-91
List
Variable
Global
cc
Global
CHIN
Module
CHOUT
Module
CR
Global
cv
Global
DELT
HD
HNEW
Global
Module
Module
Global
I
I BCFCB
Module
Package
IBD
Package
I BOUND
Global
I CBCFL
Global
IOUT
Global
Module
Module
Global
Global
J
K
KPER
KSTP
for
Module SBCFlF
Definition
Range
BUFF
HDIFF
of Variables
DIMENSION (NCOL,NROW,NLAY), Buffer
used to accumulate
information
before printing
or recording
it.
DIMENSION (NCOL,NROW,NLAY), Conductance in the column
CC(J,I,K) contains conductance between
direction.
nodes (J,I,K)
and (J,I+l,K).
Accumulator
for flow into the model area from constant
heads.
Accumulator
for flow out of the model area to constant
heads.
DIMENSION (NCOL,NROW,NLAY), Conductance in the row
CR(J,I,K) contains conductance between
direction.
nodes (J,I,K)
and (J+l,I,K).
DIMENSION (NCOL,NROW,NLAY-l), Conductance in the vertical
CV(J, I ,K) contains
conductance
between
direction.
nodes (J,I,K)
and (J,I,K+~).
Length of the current
time step.
Temporary field
containing
a value from HNEW.
Head difference
between one node and the adjacent
node.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate of head
HNEWchanges at each iteration.
in each cell.
Index for rows.
Flag and a unit number.
> 0, unit number on which cell-by-cell
flow terms
will
be recorded whenever ICBCFL is set.
= 0, cell-by-cell
flow terms will
not be printed
or recorded.
< 0, flow from each constant-head
cell will
be
printed
whenever ICBCFL is set.
Flag.
= 0, cell-by-cell
flow terms for this package will
not be recorded.
f 0, cell-by-cell
flow terms for this package will
be recorded.
DIMENSION (NCOL,NROW,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
x 0, variable-head
cell
Flag.
= 0, cell-by-cell
flow terms will
not be recorded
or printed
for the current
time step.
f 0, cell-by-cell
flow terms (flow to constant
heads)
will
be either
printed
or recorded for the
current
time step.
Primary unit number for all printed
output.
IOUT = 6.
Index for columns.
Index for layers.
Stress period counter.
Reset at the start
of each stress
Time step counter.
period.
5-92
List
Variable
for
Module SBCFlF (Continued)
Range
KT
LAYCON
Module
Package
LC
MSUM
NCOL
NLAY
NROW
RATE
Module
Global
Global
Global
Global
Module
TEXT
TMP
TOP
Module
Module
Package
VBNM
Global
VBVL
Global
Xl
Module
Module
Module
Module
Module
Module
ii
x4
X5
X6
of Variables
Definition
Index for tops of layers.
DIMENSION(80), Layer type code:
0 - Layer strictly
confined.
1 - Layer strictly
unconfined.
(transmissivity
is
2 - Layer confined/unconfined
constant).
3 - Layer confined/unconfined
(transmissivity
varies).
Temporary label for an element of LAYCON.
Counter for budget entries
and labels
in VBVL and VBNM.
Number of columns in the grid.
Number of layers in the grid.
Number of rows in the grid.
Flow from the constant-head
cell into the aquifer.
(Reverse the sign to get the flow from the aquifer
into the constant-head
cell.)
Label to be printed
or recorded with array data.
Temporary field
for head.
DIMENSION (NCOL,NROW,NTOP), Elevation
of top of layers.
(NTOP is the number of layers for which LAYCON = 2
or 3.)
DIMENSION (4,20),
Labels for entries
in the volumetric
budget.
DIMENSION (4,20),
Entries
for the volumetric
budget.
For flow component N, the values in VBVL are:
(l,N),
Rate for the current
time step into the flow
field.
(Z,N), Rate for the current
time step out of the
flow field.
(3,N), Volume into the flow field
during simulation.
(4,N), Volume out of the flow field
during simulation.
Flow through the left
face.
Flow through the right
face.
Flow through the back face.
Flow through the front
face.
Flow through the upper face.
Flow through the lower face.
5-93
Chapter
6
RIVER PACKAGE
Conceptualization
Rivers
water
and streams
from
it
effects
regime.
of flow
To accomplish
features
contribute
depending
ground-water
on the
between
this,
Figure
contained
between each reach
water
of a stream
this
simple
system
conductance
of figure
33 is helpful
stream-aquifer
no discrete
techniques
of simulation
interpretation
Figure
of figure
which
33-b,
as it
surface
(26))
for
developed
to represent
on the
crosses
that
in which
layer
situations,
terms
an individual
open
of
the
simulation
that,
cell.
The
of figure
the
that
streambed
The length
of
in many
is present.
and parameters
as a
The system
occurs.
provided
idealized
of
represented
the conceptualization
view of the
6-1
is
must be recognized
these
the
system by a layer
flow
streambed
various
reach.
and describing
through
is
seepage is simulated
interconnection
it
each reach
33-b shows an idealization
one-dimensional
however,
34 shows an isolated
contains
Figure
low-permeability
is placed
the
systems.
(equation
so that
from the ground-water
in conceptualizing
be applied
reaches
33-a shows a situation
material.
interaction;
instances,
33 can still
that
the stream-aquifer
through
equation
Stream aquifer
cell.
of figure
in which
flow
into
and the model cell
streambed
and the
and ground-water
seepage to or from the
divided
is separated
low permeability
stream
or drain
seepage.
in a single
The cross-section
system
Package is to simulate
features
ground-water
32 shows a stream
completely
ground-water
between the
of the River
representing
by the
to the
head gradient
surface-water
terms
affected
water
The purpose
must be added to the
each cell
and Implementation
proper
are used.
conductance
of the
12
.
8
Figure 32.-Discretization
of a stream into reaches.
reaches are ignored.
6-2
Some small
Land
Low Permeability
a
.
.
Cell
Boundary
Impermeable
Walls
Head
in
Cell
,
.
.
.
.
.
.
*
.
.
, Low Permeability
-Yap-,
Material
.
.
,
*
,
.
.
.
.
.
.
~
.
a *-:
.
.
.
*
,
,
,
,
.
.
.
.
-
.
.
,
.
.
.
.
Cell
Boundary
Figure 33.-(a) Cross section of an aquifer containing a stream and
(b) Conceptual representation of stream-aquifer interconnection
in simulation.
6-3
.
of
Thickness
of Riverbed
M
\
/
v
W
Width of River
Streambed Conductance= KLW/M
Figure 34.~Idealization
of streambed conductance
individual cell.
6-4
in an
conductance
block
node; the width
taken
is taken
is taken
as the
as the thickness,
tivity
of the
that
measurable
to those
icant
head loss
width,
layer
underlying
layer;
and the
K.
stream
is,
saturated--that
tions,
and the ground-water
stream
streambed
is no signif-
and the
that
layer.
point
its
the
water
Under these
system
QRIV = K ML W (HRIV - h.
1 ,Lk
is made
assumed that
is,
of the
between the
layer
conduc-
are limited
there
It is further
does not drop below the bottom
flow
that
the
is
hydraulic
The assumption
of the streambed
fully
crosses
of flow
and the aquifer
itself--that
model node.
remains
L, as it
W; the distance
is designated
between the
streambed
model cell
of the stream,
streambed
between the bottom
by the
underlying
stream
material
head losses
the
length
M, of the
streambed
across
represented
as the
level
assump-
is given
by
)
(63-a)
or
QRIV = CRIV (HRIV - hi,j,k)
where QRIV is the
positive
if
it
flow
between the stream
is directed
CRIV is the hydraulic
stream;
interconnection
(KLW/M),
cell
the
underlying
If
across
into
the
a discrete
straightforward.
to situations
is
streambed
conductance
which
head losses
these
cases,
which
can be used in
the task
layer,
that
of the
as
stream-aquifer
head at the
all
node in the
significant
the application
streambed
restricted
to relate
a single
6-5
of equations
layer
to those
flow
head loss
equations
however,
is to formulate
(63-b)
taken
HRIV is the head in the
is the
satisfied
no discrete
are not
aquifer,
reach.
More frequently,
in which
and the
aquifer;
and hi,j,k
stream
assumption
the
(63-b)
across
(63)
is
(63) must be applied
can be identified,
such a layer.
conductance
between
occurs
the
term,
stream
or in
In
CRIV,
and the depth
represented
is
by node i,j,k
in general
single
a three-dimensional
conductance
field
wise,
they
of stream
guide
during
the
sectional
as the
value
choice
area of flow
product
assumed distance
the
streambed
this
series
in formulating
should
be recognized
account
exercise,
cases,
and that
interaction
however,
be visualized
the
layer
aquifer.
bottom
of flow
should
should
that
water
stream
levels
to the concept
bottom
described
35-b,
water
can be recognized
as conductances
term to
inherently
layer,
leaving
aquifer
of stream-
In most
point,
aquifer.
This
streambed
layer.
(63);
water
and flow
between the
it
required.
below a certain
layer,
an unsaturated
6-6
always
head values.
by equations
in
an empirical
approximation
of a discrete
in the
between
conductance
fall
of the streambed
level
interval
is almost
aquifer
the cell;
however,
range of aquifer
in the
to
In general,
an acceptable
to the head difference
of the streambed
is
calibration
provide
within
be treated
process
and
of magnitude
vertical
layers
of a single
during
a certain
length
conductance.
flow
situation
is above the
In figure
normally
Other-
the assumed cross-
ceases to depend on head in the
by returning
is proportional
distinct
formulation
normally
over
if
if
are
arbitrarily
be of the same order
reach
a
reliable
can be formulated
not exceed the
an equivalent
If
conductance.
For example,
flow
through
head difference
rules
and stream
and,
these
35-a shows the
aquifer
width
adjustment
(63)
seepage from the
Figure
normally
a three-dimensional
Equations
aquifer
should
interval,
for
of conductance.
and node i,j,k;
within
approximate.
an effective
Certain
This
representation
must be chosen more or less
of channel
the
and its
seepage and associated
model calibration.
initial
head difference.
be more than
may be used to calculate
a conductance
adjusted
process,
term can never
measurements
available,
to the corresponding
stream
has fallen
interval
can
level
in
through
that
and the
below the
beneath
that
Water
Table
I
Flow through
Streambed
I
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Head at the bottom
of the streambed
is equal to head
in the cell.
.
.
.
A
I
Flow through
Streambed
.
Water
Table
I ...
......
.........
....
.
Head at the bottom
of the streambed
is equal to elevation
of bottom of
streambed layer.
.
I
B
Figure 35.-Cross
sections showing the relation between head at
the bottom of the streambed layer and head in the cell.
Head in the cell is equal to the water-table elevation.
6-7
layer;
if
it
is assumed that
the head at its
elevation
base will
the streambed
simply
is designated
layer
itself
be the elevation
RBOT, the flow
through
remains
at that
saturated,
point.
the streambed
If
layer
this
is
given
QRI~ = CRIV (HRIv - RBOT)
where QRIV, CRIV, and HRIV are as defined
further
declines
streambed
tion
utilizes
in head below RBOT produce
layer;
(64),
the
as long
these
for
flow
simply
retains
as head remains
concepts
flow
between a stream
tion
set
equation
the
and a node i,j,k
a function
of the head,
zero when hi,j,k,
higher
values
lower
values
positive
is equal
of hi,j,k,
according
hi,j,k
flow
flow
increases
the
A relationship
generally
prevails
streambed
layer
linearly
flow
is present.
must become independent
that
and cell
equations
is,
is,
into
into
decreases,
interaction
equa-
i,j,k
65.
as
Flow is
HRIV.,
For
the stream;
the
until
(65)
for
aquifer.
hi,j,k
This
reaches
whether
seepage from the
even before
6-8
and figure
once a break
of head in the aquifer.
is established
to the
(65)
in the stream,
of equations
For example,
and the aquifer,
is,
constant.
to that
in stream-aquifer
using
that
as hi,j,k
remains
similar
between the stream
independence
is positive,
herein
5 RBOT
level
is negative,
by equa-
> RBOT
between the stream
to the water
given
the
interaction--that
is simulated
as calculated
flow
of hi,j,k,
RBOT; thereafter
this
hi,j,k,
value
through
The model described
QRIV = CRIV (HRIV - RBOT), hi,j,k
36 shows a graph of flow
Obviously,
in flow
constant
stream-aquifer
QRIV = CRIV (HRIV - hi,j,k),
Figure
(63-b).
no increase
below RBOT.
in simulating
(64)
or not a discrete
in saturation
stream
to the
In most cases,
a break
(36)
in saturation
occurs
aquifer
moreover,
occurs.
QRIV
Positive
QRIV
Indicates Flow
into
Aquifer
0
Negative
QRIV
Indicates Flow
into
Stream
I
I
HRIV
RBOT
Figure 36.-Plot of flow, QRIV, from a stream into a cell as
a function of head, h, in the cell where RBOT is the
elevation of the bottom of the streambed and HRIV is
the head in the stream.
6-9
Figure
37 shows a situation
in which
levels
enough below a stream
so that
only
between the streambed
and the
regional
37 will
show that
approximately
will
not increase
figure
and that
this
of head in the aquifer,
as the
limiting
condition
elevation
hl,
hydraulic
gradient
tions
mately
length
A value
beneath
be obtained
to hl.
stream
as it
stream
of limiting
by substituting
into
cell
conductance
cell
term,
the
i,j,k
the stream,
complex
In all
become
to decline.
will
reach tre
table
reaches
an
vertical
is given
and again
CRIV, consistent
selected
(64)
aF#proxi-
conductivity
and W is stream
QRIV in equation
an
one under the ccndi-
hydraulic
i,j,k,
seepage and with
KLW for
itself
stream.
Because the
vertical
column beneath
crosses
37 is
but will
is approximately
in
of further
must at some point
declines,
KLW, where K is the
in the saturated
the
37 when the water
equal
the stream
independent
involve
table
to that
seepage from a stream
elevation
in figure
water
similar
head continues
that
37, seepage from the
of the
value
table
be taken
of the stream-aquifer
estimated
CRIV.
water
as that
indicate
illustrated
by the product
of the material
the
local
RBOT should
of figure
beneath
seepage from the stream
conditions
is
may often
material
of figure
must be
regional
shown in figure
which
and unsaturated
independent
increase
of the
far
exists
connection
once a condition
conditions,
however,
hydrologic
Examination
lowering
Thus,
situations,
If
table.
saturated
The situation
of field
of saturated
connection
seepage from the stream
in the aquifer.
overimplification
patters
further
have fallen
saturated
water
in the
gradient.
37 is established,
head decline
a narrow
the head gradient
unity,
in the aquifer
value
L. is
width.
with
this
of RBOT can
and solving
f'or
This yields
CRIV =
KLW
HRIV-RBOT
6-10
(66)
-
---
Line of
Equal Head
Figure 37.-Limiting seepage from a stream at
unit hydraulic gradient
6-l 1
hi,j,k
In summary,
follow
if
the
limiting
the model of figure
elevation
at which
the transition
(65) should
the stream-aquifer
interaction.
this
within
the
that
the cell,
is
and constant
of flow
the
over
period--
for
banks,
or that
such events
Input
layer,
each
consists
of six
needed to calculate
conductance
of the
elevation,"
or level
attained
significantly
over
assumption
implies
during
the
does not go dry or overflow
its
duration
as to have no effect
are
entries
for
by the
containing
the
limiting
for
reach,
stress
specifying
the
and the three
or stage
(CRIV),
value
each
reach,
level
interconnection
the
user
each river
seepage--stream
stream-aquifer
at which
specified
(HRIV),
and the
of stream
.:he
"bot.:om
seepage is
(RBOT).
At the start
added to the flow
choice
river
row, and column of the cell
parameters
do not vary
are of such short
reach
is uniform
The latter
the stream
here assumes
of the stream
in the stream
to
interaction.
Data describing
period.
that
utilized
location
technique
approximation
period.
each stress
example,
interaction
of water
in the stream
stress
on stream-aquifer
level
seepage can be expected,
a reasonable
of the
to
table
The model simulation
(66).
provide
independent
and that
conditions
limiting
model of stream-aquifer
interaction
reach,
to this
then
seepage is expected
be chosen as the water
from equation
based on equations
The simplified
of stream
37, RBOT should
and CRIV may be calculated
that
condition
of which
of each iteration,
equation
river
is made by comparing
for
terms
each cell
seepage equation
the most recent
representing
containing
to use,
value
6-12
river
a river
equation
seepage 'are
reach.
The
63 or equation
of head at the
cell
to the
64,
,value
of RBOT for
iteration,
the
Since this
the most current
previous
iteration.
use lags
behind
is selected,
Thus,
value
process
the check for
If
-CRIV is
equation
is done at the start
of head (HNEW) is the
the seepage calculations
the term
is added to RHS.
is
reach.
which
river
64 is selected,
added to the term RHS.
6-13
from the
seepage equation
by one iteration.
added to the term
value
of each
If
equation
HCOF and the term
the term
to
63
-CRIV*HRIV
-CRIV (HRIV - RBOT)
River
Input
IUNIT(4).
to the
River
(RIV)
Package Input
Package is
read from the
unit
specifiecl
in
FOR EACH SIMULATION
RIVlAL
MXRIVR
110
1. Data:
Format:
IRIVCB
110
FOR EACH STRESS PERIOD
RIVlRP
2. Data:
Format:
ITMP
110
3. Data:
Format:
Layer
110
(Input
reach.
Row
110
Column
110
of Fields Used in
Instructions
MXRIVR--is
the maximum number of river
IRIVCB--is
a flag
Row--is
and a unit
reaches
active
at one time.
number.
If
IRIVCB > 0, it is the unit number on which cell-by-cell
flow
terms will
be recorded whenever ICBCFL (see Output
Control)
is set.
If
IRIVCB = 0, cell-by-cell
recorded.
If
IRIVCB < 0, river
leakage for
ICBCFL is set.
a flag
ITMP < 0, river
If
ITMP 10,
the
the
flow
terms
will
not be printed
each reach will
be printed
or
whenever
and a counter.
If
Layer--is
Rbot
FlO.0
item 3 normally
consists
of one record for each river
If ITMP is negative
or zero, item 3 is not read.)
Explanation
Input
ITMP--is
Cond
F10.0
Stage
F10.0
layer
data
from the
last
stress
period
ITMP will
be the number of reaches
current
stress period.
number of the cell
row number of the cell
containing
containing
6-14
the
the
river
will
active
river
be reused.
during
reach.
reach.
the
Column--is
Stage--is
the
column number of the cell
the head in the
Cond--is
the
riverbed
Rbot--is
the elevation
containing
river.
hydraulic
conductance.
of the bottom
of the
6-15
riverbed.
the
river
reach.
6-16
Module Documentation
The River
called
Package (RIVl)
consists
by the MAIN program.
RIVlAL
Allocates
contain
entry
cell
RIVlRP
are:
space for
a list
will
of the
riverbed.
the
the
riverbed,
reach,
all
(RIVR) which
of which
are
will
reach.
location
Each
of the
riverhead,
conductance
of the.bottom
reach,
the
reach,
riverhead,
and elevation
location
of the
conductance
of the bottom
of
riverbed.
Adds, for
each river
to the accumulators
RIVlBD
modules,
and the elevation
each river
containing
Package
each river
of the
the
riverbed,
of the
for
consist
containing
River
of four
an entry
Reads, for
the
The modules
of the
cell
RIVlFM
for
Calculates
the
leakage
into
rates
reach,
the appropriate
HCOF and RHS.
and accumulated
and out of the flow
6-17
terms
volume of river
system.
Narrative
This module allocates
for Module RIVlAL’
space in the X array
to store
the list
o,f river
reaches.
1.
of river
2.
Print
a message identifying
Read and print
indicating
list
4.
for
5.
saving
cell-by-cell
Set LCRIVR, which will
cell-by-cell
element
Calculate
point
to the first
element
pointing
in the r!ver
to the first
the amount of space needed for the river
riverhead,
column, layer,
and add it
the number of elements
riverbed
list
(six
conductance,
values
and
to ISUM.
in the X array
Package.
6.
flow terms or a flag
in the X array.
bottom elevation)
Print
reaches:) and
flow terms should be printed).
equal to ISUM, which is currently
each reach--row,
riverbed
MXRIVR (the maximum number of river
number for
whether
(RIVR),
unallocated
NRI'IIER (number
reaches).
IRIVCB (the unit
3.
the package and initialize
RETURN.
6-18
used by the Riv,er
B
Flow Chart
l
for
Module RIVlAL
NRIVER is the number of river
reaches
being simulated
at any given time.
pi--)
MXRIVR is the maximum number of river
reaches simulated.
IRIVCB is a flag
and a unit
number.
If IRIVCB > 0, it is the unit number
on which cell-by-cell
flow terms
will
be recorded whenever ICBCFL
(see RIVlBD module) is set.
If
IRIVCB = 0, cell -by-cell
terms
will
not be printed
flow
or recorded.
If IRIVCB < 0, river leakage for
each reach will
be printed
whenever
ICBCFL is set.
LCRIVR is the location
of the list
of river
PACKAGE AND
INITIALIZE
NUMBER OF
REACHES (NRIVER)
READ AND PRINT
MXRIVR AND
in the X array
data (RIVR).
l
CALCULATE
AMOUNT OF
SPACENEEDED
PRINT AMOUNT
OF SPACE USED
BY THE RIVER
6-19
SUBROUTINE
RIVlAL(ISUM,LENX,
LCRIVR, MXRIVR,NRIVER,IN,IOUT,
IRIVCB)
1
1554 lZMAY1987 RIVlAL
**C+*****+*****************************~*********************~~*****
ALLOCATE ARRAY STORAGE FOR RIVERS
*************************
3**********************************~~*****
SPECIFICATIONS:
----1---1-1-------------------------------------------------,-----------------------------------------------------------------,------
-----VERSION
C
C
C
C
C
C
C
C
Cl---
C
c2----
IDENTIFYPACKAGE AND INITIALIZE NRIVER.
WRITE(IOUT,l)IN
1, 9/l/87',
1 FORMAT(lHO,'RIVl-- RIVERPACKAGE, VERSION
1' INPUTREAD FROM UNIT',131
NRIVER=O
READ 8, PRINTMXRIVR 8 IRIVCB(UNITOR FLAG
READ(IN,2)MXRIVR,IRIVCB
2 FORMAT(2110)
WRITE(IOUT,3)MXRIVR
3 FORMATtlH , ‘MAXIMUM OF’, 15,' RIVERNODES’1
IF(IRIVCB.GT.0) WRITE(IOUT,9)IRIVCB
FOR C-B-C FLOWS)
FLOWS WILL BE RECORDEDON UNIT',131
IF(IRIVCB.LT.0) WRITE(IOUT,8)
8 FORMAT(lX,‘CELL-BY-CELL
FLOWS WILL BE PRINTED')
C
C3------ SET LCRIVREQUALTO ADDRESS OF FIRSTUNUSED SPACE IN X.
LCRIVR=ISUM
,
C
c4------CALCULATE AMOUNTOF SPACE USED BY RIVERLIST.
ISP=6*MXRIVR
IsuM=IsuMtIsP
9 FORMATtlX, ‘CELL-BY-CELL
:5 ------PRINT
AMOUNTOF SPACE USED BY RIVERPACKAGE.
WRITE(IOUT,4)ISP
4 FORMATtlX, 18,' ELEMENTS IN X ARRAY ARE USED FOR RIVERS'
1
ISUMl=ISUM-1
WRITE(IOUT,S)ISUMlrLENX
5 FORMAT(lX,I8,’
ELEMENTS OF X ARRAY USED OUT OF’,181
IF(ISUMl.GT.LENX)WRITE(IOUT,6)
***X ARRAY MUST BE DIMENSIONED
LARGER***‘)
6 FORMATtlX,’
C
c7-----mJ'URN
RETURN
END
8-20
List
Variable
of Variables
Module RIVlAL
for
Ranae
Definition
IN
Package
Primary
will
unit number from which
be read.
IOUT
Global
Primary
unit
IRIVCB
Package
flag
ISP
Module
Number of words
ISUM
Global
Index number of the lowest element in the X array which
has not yet been allocated.
When space is allocated
for an array, the size of the array is added to ISUM.
ISUMl
Module
ISUM-1.
LCRIVR
Package
Location
RIVR.
LENX
Global
Length of the X array in words.
This should always be
equal to the dimension of X specified
in the MAIN
program.
MXRIVR
Package
Maximum number of river
reaches
NRIVER
Package
Number of river
period.
active
number for
all
input
printed
for
this
output.
package
IOUT = 6.
and a unit number.
> 0, unit number on which cell-by-cell
flow terms
will
be recorded whenever ICBCFL (see RIVlBD
module) is set.
= 0, cell-by-cell
flow terms will
not be printed
or recorded.
< 0, river
leakage for each reach will
be printed
whenever ICBCFL is set.
in the
in the X array
reaches
6-21
X array
of the
allocated
first
active
during
by this
element
module.
of array
at any one time.
the
current
stress
Narrative
This
river
the
reaches
Test
2.
last
ITMP is
If
period
for
river
list.
the previous
ITMP is
will
the
the number of river
specified
ITMP.
stress
Module RIVlRP
reads data to build
Read ITMP.
1.
that
module
for
less
than
stress
zero,
Print
be reused.
reaches
or a flag
period
the
river
indicating
should
data
a message to that
be reused.
read for
effect
and RETURN.
3.
If
reaches
for
ITMP is
this
in the current
4.
period
If
stress
stress
Compare the
to the
NRIVER is
than
greater
or equal
period
equal
number of river
than
to zero,
Set the
period.
number specified
Print
5.
greater
it
is the
number of river
number of
reaches
(NRIVER)
to ITMP.
reaches
(NRIVER) in the current
as the maximum for
the
simulation
stress
(MXRIVR).
MXRIVR, STOP.
the number of river
reaches
in the
current
stress
period
' (NRIVER).
6.
in the
7.
See if
current
there
stress
Read and print
and the elevation
8.
are any river
period
the
reaches.
(NRIVER = 0),
layer,
of the bottom
row,
of the
If
bypass
column,
riverbed
RETURN.
6-22
there
are no river
further
riverhead,
for
river
processing.
riverbed
each reach.
reaches
conductance,
Flow Chart
for
Module RIVlRP
ITMP is both a flag
and a
counter.
If it is greater
than or equal to zero, it is
the number of reaches to be
simulated
during the current
stress
period.
If it is less
than zero, it indicates
that
the reaches simulated
in the
last stress period should be
simulated
in the current
stress period.
I
MXRIVR is the maximum number
of reaches to be simulated.
1 NO
I
OF REACHES
YES
READ ONE
DATA RECORD
FORREEEH
6-23
SUBROUTINE
RIVlRPtRIVR,NRIVER,
MXRIVR,
IN, IOUT)
c
C
C-----VERSION 1319 25AUG1982RIVlRP
*+**+*t*****+t*t****~~~*~***~**~~~~~~~***~*~**~***~*~****~~***~~~*
C
READ RIVERHEAD, CONDUCTANCE AND BOTTOM ELEVATION
C
C
*********************************************************~********
:
SPECIFICATIONS:
-------------------_----------------------_---------------------DIMENSION RIVR(6rMXRIVR)
------------------------------------------------------------------
C
C
C
C
Cl-.--
READ ITMPtNUMBER OF RIVER REACHES OR FLAG TO REUSE DATA)
READ(IN,8)ITMP
8 FORMATtIlO)
L
c2---
TEST ITMP.
IF(ITMP.GE.O)GOTO
50
n
:2 A-----IF
ITMP (0 THEN REUSE DATA FROM LAST STRESS PERIOD.
WRITE (IOUT, 7 1
7 FORMAT(lHO,‘REUSING
RIVER REACHES FROM LAST STRESS PERIOD’)
GO TO 260
:3
------IF ITMP=>ZERO
50 NRIVER=ITMP
THEN
IT
IS THE NUMBER OF RIVER REACHES
C
c4------IF
NRIVERBMXRIVR THEN STOP.
IF(NRIVER.LE.MXRIVR)GO
TO 100
WRITE(IOUT,99)NRIVER,MXRIVR
99 FORMAT(lHOr'NRIVER(',I4,') IS GREATER THANMXRIVR('rI4,')')
C
f-&+--
ABNORMAL STOP.
STOP
C
C5------
PRINT NUMBER OF RIVER REACHES
100 WRITE(IOUT,l)NRIVER
1 FORMAT(lHO,//lX,I5,' RIVER
IN THIS STRESS
PERIOD.
REACHES’)
------IF
THERE ARE NO RIVER REACHES THEN RETURN.
IF(NRIVER.EQ.0)
GO TO 260
C
C7------
READ AND PRINT DATA FOR EACH RIVER REACH.
WRITE(IOUT,3)
3 FORMATt lHO,15X,‘LAYER’ ,5X, ‘ROW’ ~5x1 ‘CQL
’
1, ’ STAGE
CONDUCTANCE BOTTOM ELEVATION
RIVER REACH’
2/1X,15X,80(‘-‘))
DO 250 II=lrNRIVER
C
READ(IN,4)K,I,JrRIVR(4rII),RIVR(5rII)rRIVR(6rII)
4 FORMAT(3110,3FlO.O)
WRITE~IOUT,5~K,I,J,RIVR~4,II~rRIVR~5rII~,RIVR~6,II~,II
5 F0RMAT(1X,15X,14r19,18,G13.4,G14.4,G19.4,110)
RIVR(lrII)=K
RIVR(Z,II)=I
RIVR(3,II)=J
250 CONTINUE
C8------RETURN
260 RETURN
END
6-24
List
Variable
of Variables
for
Module RIVlRP
Definition
Range
I
Module
Row number.
II
Module
Index
IN
Package
Primary
will
unit number from which
be read.
IOUT
Global
Primary
unit
ITMP
Module
Flag or number of rivers.
> 0, number of rivers
active
during the current
stress period.
< 0, same rivers
active
during the last stress
period will
be active
during the current
stress period.
3
Module
Column number.
K
Module
Layer
MXRIVR
Package
Maximum number of river
time.
reaches
NRIVER
Package
Number of river
reaches
stress period.
active
RIVR
Package
DIMENSION (6,MXRIVR), For each reach: layer,
column, river head, riverbed
conductance
elevation
of bottom of riverbed.
for
river
reach.
number for
all
input
printed
for
this
output.
package
IOUT = 6.
number.
6-25
active
during
at any one
the current
row,
and
Narrative
This
module adds terms
for
Module RIVlFM
representing
river
to the accumulators
leakage
HCOF and RHS.
If
1.
period,
NRIVER is
there
less
are no river
2.
For each reach
3.
Determine
4.
If
on this
of the
of the
7.
of the
If
8.
is
of the
the
row (IR),
and layer
(IL).
bypass
processing
reach.
and elevation
head in the
stress
DO STEPS 3-8.
get the
aquifer
river
of the
data
bottom
(riverhead
of the
riveriled).
(HNEW) to the elevation
of
the
(RBOT).
head in the aquifer
conductance;
If
next
internal,
riverbed
in the current
(IBOUND(IC, IR, IL) 5 0),
external
riverbed
RHS and the term
add the term
9.
cell
riverbed
the
bottom
accumulator
riverbed
the
Compare the
6.
(IC),
to zero,
RETURN.
in the RIVR list,
column
is
or equal
reaches.
and go on to the
Since
conductance
bottom
the cell
reach
5.
the
than
(HNEW) is
greater
(RBOT), add the term
-CRIV to the
accumulator
than
the elevation
-CRIV*HRIV
HCOF.
to the
(CRIV is the
HRIV is the riverhead.)
head in the aquifer
-CRIV*(HRIV
(HNEW) is
less
- RBOT) to the accumulator
RETURN.
6-26
than
RHS.
or equal
to :?BOT,
Flow Chart
for
Module RIVlFM
RHS is an accumulator
in
which the right
hand side
of the equation
is
formulated.
HCOF is an accumulator
which the coefficient
head in the cell is
formulated.
in
of
NO
2
FOR EACH REACH
DETERMINE
ROW, COLUMN,
AND LAYER
I
I
ADD TERMS
THocRoH~%D
THIS CELL
I
6-27
GET RIVER
HEAD. BOTTOM
ELEVATION AND
RIVERBED
CONDUCTANCE
ADD TERM
TO RHS
FOR THIS
CELL
I
1
SUBROUTINE RIVlFMt NRIVER,MXRIVR,RIVR, HNEW,HCOF,RHS,IBOUND,
NCOL,NROW,NLAY)
C
C-----VERSION
0915 27AUG1982 RIVlFM
*****t***********~******************************************~~*****
C
C
ADD RIVER TERMS TO RHS AND HCOF
************************************************************~~*****
C
C
C
SPECIFICATIONS:
------------------------------------------------------------~----C
C
DOUBLE PRECISION HNEW
DIMENSION RIVR(6rMXRIVR),HNEW(NCOL,NLAY)r
1
HCOF(NCOL,NROW,NLAY)rRHS(NCOL,NROW,NLAY),
2
IBOUNDt NCOL,NROW,NLAY1
------------------------------------------------------------~----C
C
C
Cl--IF NRIVER<=O THERE ARE NO RIVERS. RETURN.
IF(NRIVER.LE.O)RETURN
C
c2--PROCESS EACH CELL IN THE RIVER LIST.
DO 100 L=lr NRIVER
C
C3------ GET COLUMN, ROW, AND LAYER OF CELL CONTAINING REACH
IL=RIVR(lrL)
IR=RIVR(Zr L)
IC=RIVR(3,L)
C
c4 ------IF
THE CELL IS EXTERNAL SKIP IT.
IF(IBOUND(IC,IR,IL).LE.OYGO
TO 100
C
C5------ SINCE THE CELL IS INTERNAL GET THE RIVER DATA.
HRIV=RIVR(4, L)
CRIV=RIVR(5rL)
RBOT=RIVR(6rL)
HHNEW=HNEW
(IC, IR, IL 1
C
C6---COMPAREAAUIFER HEAD TO BOTTOM OF STREAM BED.
IF(HHNEW.LE.RBOT)GO TO 96
C
c7 ------SINCE
HEAD>BOTTOMADD TERMS TO RHS AND HCOF.
RHS(IC,IR,IL)=RHS(IC,IR,IL)-CRIV*HRIV
HCOF(IC,IR,IL)=HCOF(IC,IR,IL)-CRIV
GO TO 100
a
a
k3 ------SINCE
HEAD<BOTTOMADD TERM ONLY TO RHS.
96 RHS(IC,IR,IL)=RHS(IC,IR,IL)-CRIV+(HRIV-RBOT)
100 CONTINUE
-----~)-lJRN
RETURN
END
a
6-28
List
Variable
of Variables
for
Module RIVlFM
Ranae
Definition
CRIV
Module
Riverbed
HCOF
Global
DIMENSION (NCOL,NROW,NLAY), Coefficient
of head in
the cell
(J,I,K)
in the finite-difference
equation.
HHNEW
Module
HNEW (J,I,K),
HNEW
Global
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
of
head in each cell.
HNEW changes at each iteration.
HRIV
Module
Head in the
I BOUND
Global
DIMENSION (NCOL,NROW,NLAY), Status
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
IC
Module
Column number of the cell
IL
Module
Layer
IR
Module
Row number of the cell
L
Module
Index for
MXRIVR
Package
Maximum number of river
NCOL
Global
Number of columns
NLAY
Global
Number of layers
NRIVER
Package
Number of river
period.
NROW
Global
Number of rows in the grid.
RBOT
Module
Temporary
RHS
Global
DIMENSION (NCOL,NROW,NLAY), Right hand side of the
finite-difference
equation.
RHS is an accumulation
of terms from several different
packages.
RIVR
Package
DIMENSION (G,MXRIVR), For each reach: layer,
row,
column, riverhead,
riverbed
conductance
and
elevation
of bottom of riverbed.
conductance.
Single
precision.
river.
number of the cell
river
of each cell.
containing
the
containing
containing
the
the
river
river
river
reach.
reach.
reach.
reaches.
in the
in the
reaches
field:
6-29
elevation
reaches
active
at any one time.
grid.
grid.
active
j
during
of the
river
the current
stress
bottom.
Narrative
This
module calculates
for
rates
Module RIVlBD
and volumes
transferred
between the aquifer
and rivers.
Initialize
1.
accumulators
put zeros
3.
disk.
terms
If
there
the
Test
to see if
budget
terms
is not the
accumulated
for
flag
(IBD)
and the
skip
down to step
rate
proper
flow
terms
step
r ivers
will
terms
are to be saved on the
of the following
(ICBCFL = 0) or
during
this
be saved for
(IBD) and clear
flag
flow
either
time
17 and
rivers.
the cell-by-cell
are not to be saved for
flow-term
(NRIVER 2 0),
not be saved if
cell-by-cell
cell
flow-term
are no reaches
into
They will
(1) This
cell-by-cell
(RATIN and RATOUT).
If
2.
the
the
hold:
(2) ce 11-by-cell
simulation
this
buffer
conditions
(IRIVCB .L 0).
package,
in which
flow
set
they
will
the
cell-by-
be
(BUFF).
4.
For each reach,
5.
Determine
6.
If
do steps
5-15 accumulating
flows
from or into
the
river.
the
row,
column,
and layer
of the
cell
containinlg
the
reach.
of this
of the
the
cell
is external
(IBOUND( 1,J ,K) 5 0),
bypass
further-
processing
reach.
7.
Get the
8.
Check to see if
bottom
river
of the
parameters
from the
the head in the
riverbed.
6-30
river
cell
is
list.
greater
than the e*evation
9.
bottom
times
the
of the
the
10.
the
If
riverbed,
riverhead
If
of the
the
riverhead
set RATE equal
than
riverbed,
is
the elevation
to the conductance
less
minus the elevation
or equal
to the
conductance
of the bottom
of the
of the
of
riverbed
riverbed
- RBOT)).
the
cell-by-cell
flow
terms
are to be printed,
12.
If
the
cell-by-cell
flow
terms
are to be saved,
print
RATE.
add the RATE to
(BUFF).
13.
Check to see whether
the
14.
If
add it
to RATOUT.
15.
If RATE is positive,
add it
to RATIN.
16.
See if
RATE is
negative,
the cell-by-cell
If they are, call
flow
flow
module UBUDSV to
in VBVL for
to VBNM for
printing
is
into
terms
record
Move RATIN and RATOUT into
Add RATIN and RATOUT multiplied
accumulators
- HNEW)).
to the elevation
If
17.
riverbed
(RATE = CRIV*(HRIV
than
set RATE equal
of the
of the
11.
buffer
labels
greater
minus the head in the cell
(RATE = CRIV*(HRIV
the
is
the head in the cell
bottom
times
head in the cell
the
are to be saved
the
buffer
VBVL array
by the time-step
printing
or out of the aquifer.
by BASlOT.
(BUFF) onto
for
printing
length
to the
Move the
by BASlOT.
18.
Increment the budget-term counter (MSUM).
19.
RETURN.
6-31
(IBD =
river
1).
the disk.
by BASlOT.
volume
budget
term
Flow Chart
for
Module RIVlBD
c
IBD is a flag which, if set,
causes cell-by-cell
flow
terms for river leakage to
be recorded.
EXTERNAL: a cell is said to be
external
if it is either
no
flow or constant
head (i.e.,
an equation
is not formulated
for the cell).
RATE is the leakage rate into
the aquifer
from the river
in a cell.
‘R EACH REACH
BUFFER is an array in which
values are stored as they
are being gathered for
printing
or recording.
RATOUT is an accumulator
to
which all flows out of the
aquifer
are added.
RATIN is an accumulator
which all flows into
aquifer
are added.
IRIVCB is
number.
a flag
PARAMETERS
FROM RIVER
to
the
and a unit
If IRIVCB > 0, it is the unit
number on which cell-by-cell
flow terms for rivers
will
be recorded whenever ICBCFL
is set.
12
IF CELL-BY-CELL
FLOW TERMS ARE TO
BE RECORDED
ADD
RATE TO BUFFER
r-l
If IRIVCB = 0, cell-by-cell
flow terms for rivers
will
not be printed
or recorded.
If IRIVCB < 0, river leakage
for each reach will
be
printed
whenever ICBCFL is
set.
ICBCFL is
a flag.
If ICBCFL f 0, cell-by-cell
flow terms will
be printed
or recorded
(depending on
IRIVCB) for the current
time step.
6-32
SUBROUTINE RIVlBD(NRIVER,MXRIVR,RIVR,IBOUND,
HNEW,
NCOL,NROW,NLAY, DELT, VBVL, VBNM,MSUM,KSTP, KPER, IRIVCB,
2
ICBCFL,BUFF, IOUT)
1
C-----VERSION 1556 12MAY1987RIVlBD
***~**************************************************************
CALCULATE VOLUMETRIC
BUDGET FOR RIVERS
************************~*****************************************
SPECIFICATIONS:
--_-----------------------------------
----------------------------
CHARACTER*4 VBNM,TEXT
DOUBLE PRECISION HNEW
DIMENSION RIVR(6,MXRIVR),IBOUND(NCOL,NROW,NLAY),
HNEW(NCOL,NROW,NLAY),VBVL(4r20)rVBNM[4rZO~,
1
2
BUFF(NCOL,NROW,NLAY)
DIMENSION TEXT(4)
R’r’IVER’r’
DATA TEXT(l)rTEXT(Z),TEXT(3),TEXT(4)
/’
------------------------------------------------------------------
INITIALIZE CELL-BY-CELL FLOW TERM FLAG (IBD)
ACCUMULATORS(RATIN AND RATOUT).
Cl---
Cl---
LEA’r’KAGE’/
AND
IBD=O
RATIN=O.
RATOUT=O.
C
l
c2---
IF NO REACHES KEEP ZEROES
IF(NRIVER.EQ.O)GO TO 200
C
C3-----C
C3A-----
IN ACCUMULATORS.
TEST TO SEE IF CELL-BY-CELL FLOW TERMS ARE NEEDED.
.OR. IRIVCB. LE.0 1 GO TO 10
IF(ICBCFL.EQ.0
CELL-BY-CELL FLOW TERMS ARE NEEDED SET
IBD=l
DO 5 IL=lrNLAY
DO 5 IR=l,NROW
DO 5 IC=lrNCOL
IBD AND CLEAR BUFFER.
BUFFtIC, IR, IL)=O.
5 CONTINUE
C
c4 ------FOR
EACH RIVER REACH ACCUMULATERIVER FLOW (STEPS 5-15)
10 DO 100 L=lr NRIVER
C
C5------ GET LAYER, ROW& COLUMNOF CELL CONTAINING REACH.
C
(3j---
C
C7------
D
IL=RIVR(l,L)
IR=RIVR(Z,L)
IC=RIVR(3rL)
IF CELL IS EXTERNAL MOVE ON TO NEXT REACH.
IF(IBOUND(IC,IR,IL) .LE.O)GO TO 100
GET RIVER PARAMETERSFROM RIVER LIST.
HRIV=RIVR(4rL)
6-33
a
CRIV=RIVR(5,L)
RBOT=RIVR(6, L)
HHNEW=HNEW(IC,IR,IL)
C
C8------COMPARE
C
c9 ------AQUIFER
HEAD
IN AQUIFER TO BOTTOMOF RIVERBED.
HEAD > BOTTOM
THENRATE=CRIV*(HRIV-HNEW).
IF(HHNEW.GT.RBOT)RATE=CRIV*(HRIV-HHNEW)
C
cl+--
AQUIFER HEAD C BOTTOM
THENRATE=CRIV*(HRIV-RBOT)
IF(HHNEW.LE.RBOT)RATE=CRIV*tHRIV-RBOT)
C
Cl1 -----PRINT
THE INDIVIDUAL RATESIF REQUESTED(IRIVCE<O).
IF(IRIVCB.LT.O.AND.ICBCFL.NE.0) WRITE(IOUT,900) (TEXT(N)rN=lr4),
1
KPER, KSTP, L, IL, IR, IC, RATE
900 FORMAT(lHO,4A4,’
PERIOD’ ,13, ’
STEP’rI3,’
REACH',I4,
1'
LAYER',I3,'
ROW’,I4,’
COL’,I4,’
RATE’rG15.7)
C
c12---
IF C-B-C FLOW TERMS ARE TO BE SAVED THEN ADD RATE TO BUFFEI?.
IF(IBD.EQ.l) BUFF(IC,IR,IL)=BUFF(IC,IR,IL)+RATE
C
Cl3----- SEE IF FLOW IS INTO AQUIFER OR INTO RIVER.
IF(RATE)94,100,96
C
Cl4
-----AQUIFER IS DISCHARGING
TO RIVER SUBTRACT RATE FROM RATOUT.
94 RATOUT=RATOUT-RATE
GO TO 100
C
Cl5----- AQUIFERIS RECHARGEDFROM RIVER ADD RATE TO RATIN.
96 RATIN=RATIN+RATE
a
100 CONTINUE
El6 -----IF
C-B-C FLW TERMS WILL BE SAVED CALL UBUDSV TO RECORDTHEM.
IF( IBD. EQ. 1) CALL UBUDSVtKSTP, KPER, TEXT,IRIVCB, BUFF, NCOL, NROW.,
1
NLAY, IOUT)
C
Cl7 -----MOVE RATESsVOLUMES8, LABELS INTO ARRAYSFORPRINTING.
200 VBVL(3,MSUM)=RATIN
VBVL(I,MSUM)=RATOUT
VBVL(l,MSUM)=VBVL(lrMSUM)+RATIN*DELT
VBVL(2,MSUM)=VBVL(2,MSUM)+RATOUT*DELT
VBNM(lrMSUM)=TEXT(l)
VBNM(2,MSUM)=TEXT(2)
VBNM(3,MSUM)=TEXT(3)
VBNM(4rMSUM)=TEXT(4)
C
Cl+--
INCREMENT BUDGET TERM COUNTER
MSUM=MSUM+l
C
C19-----RETURN
RETURN
END
a
6-34
List
Variable
of Variables
Range
for
RIVlBD
Definition
BUFF
Global
DIMENSION (NCOL,NROW,NLAY), Buffer
used to accumulate
information
before printing
or recording
it.
CRIV
Module
Conductance
DELT
Global
Length
HHNEW
Module
HNEW (J,I,K),
HNEW
Global
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
of
HNEW changes at each iteration.
head in each cell.
HRIV
Module
Head in the
IBD
Module
Flag.
= 0, cell-by-cell
flow
not be recorded.
f 0, cell-by-cell
flow
be recorded.
of the bed of the
of the
current
Single
time
river
reach.
step.
precision.
river.
terms
for
this
package will
terms
for
this
package will
IBOUND
Global
DIMENSION (NCOL,NROW,NLAY), Status
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
IC
Module
Index for
ICBCFL
Global
Flag.
= 0, cell-by-cell
flow terms will
not be recorded
or printed
for the current
time step.
f 0, cell-by-cell
flow terms will
be either
printed
or recorded (depending on IRIVCB) for the
current
time step.
IL
Module
Index
I OUT
Global
Primary
IR
Module
Index for
IRIVCB
Package
Flag and a unit number.
> 0, unit number on which cell-by-cell
flow terms
will
be recorded whenever ICBCFL is set.
= 0, cell-by-cell
flow terms will
not be printed
or recorded.
< 0, river
leakage for each reach will
be printed
whenever ICBCFL is set.
KPER
Global
Stress
for
0f each cell.
columns.
layers.
unit
number for
all
printed
output.
IOUT = 6.
rows.
period
counter.
6-35
List
Variable
of Variables
for
Module RIVlBD
Range
(Continued)
Definition
KSTP
Global
Time step
period.
counter.
L
Module
Index
river
MSUM
Global
Counter
MXRIVR
Package
Maximum number of river
NCOL
Global
Number of columns
NLAY
Global
Number of layers
NRIVER
Package
Number of river
period.
NROW
Global
Number of rows in the
RATE
Module
Flow from the river
into
get the flow into the
RATIN
Module
Accumulator
rivers.
for
the total
flow
into
RATOUT
Module
Accumulator
rivers.
for
the total
flow
out of flow
RBOT
Module
Elevation
of the
bottom
RIVR
Package
DIMENSION (6,MXRIVR),
For each reach: layer,
row,
riverhead,
riverbed
conductance,
and elevation
bottom of the riverbed.
TEXT
Module
Label
VBNM
Global
DIMENSION (4,20),
VBVL
Global
DIMENSION (4,20),
Entries
for the volumetric
budget.
For flow component N, the values in VBVL are:
(l,N),
Rate for the current
time step into the flow
field.
(2,N),
Rate for the current
time step out of the flow
field.
(3,N), Volume into the flow field
during simulation.
(4,N),
Volume out of the flow field
during simulation.
for
for
Reset
at the
start
of each stress
reaches.
budget
entries
reaches
in the
in the
reaches
to be printed
6-36
and labels
in VBVL and VBNM.
active
at any one time.
grid.
grid.
active
during
the current
stress
grid.
the cell.
river.)
of the
or recorded
Labels for
budget.
(Reverse
the
the
field
flow
field
sign
to
from
into
riverbed.
with
entries
the array
column,
of the
data.
in the volumetric
CHAPTER 7
RECHARGEPACKAGE
Conc_e_etualization
The Recharge
(RCH) Package is designed
recharge
to the
a result
of precipitation
Recharge
applied
ground-water
that
(i,j)
recharge
flux
DELRj*DELCi,
within
allow
the
for
vertical
its
recharge
expressed
(in
units
vertical
occur
in model layer
system
may vary with
rises
of length
column of cells
per unit
natural
that
receives
occurs
for
the
to a single
ccl 1
j).
There
is no need to
at multiple
depths
in the same
the
ground-water
system
of the
ground-water
system will
vertical
position
and with
specifying
recharge
is the
to the map area,
app lied
is
enters
location
and Ii,j
applicable
at (i
the top
the
time;
cell
time
at
of the top of the
as the water-table
the cell
in each vertical
have been implemented
as described
below.
The RCH Package can potentially
be used to simulate
recharge
from
sources
other
example,
recharge.
If
ability
to apply
is
required,
specified
than
then
precipitation
recharge
the Well
at any model cell,
as
system.
to the model at horizontal
time)
located
situation,
options
ground-water
QRi,j,
recharge
1; however,
Three
and falls.
recharge
(67)
applied
simultaneously
horizontal
distributed
as
The recharge,
simplest
area1
volume per unit
column of cells
column because
In the
rate
as a fluid
to occur
areally
*DELRj*DELCi
flow
of the cell.
recharge
top.
to the
to the model is defined
is the
location
percolates
= Ii,j
to simulate
Most commonly,
system.
QRi,j
where QRi,j
and Implementation
--
-- for
to more than
Package,
one cell
which
can be used.
7-1
allows
artificial
in a vertical
recharge
the
column of cells
or discharge
to be
In the package described
herein,
a two dimensional
an option
is exercised
to use recharge
period).
These values
of recharge
flux
DELRjDELCi,
to obtain
horizontal
cell
maintained
in the
RECH array.
recharge
is applied
which
the
code,
NRCHOP, and optional
of the
cell
recharge
in the
dimensional
array
active
head cell
above it
to
receive
option,
cells
and there
the
if
there
it
units
used to
In the
location,
value
for
k, that
of RHSi,j,k
all
cells
independent
that
cell
application
is assumed that
in units
a given
is determind
(equation
receive
of aquifer
by the
application
recharge
there
to any
1 and 2, if
is
added.
no recharge
to the
a cell
designated
Under the
column of
is applied
would
that
in two
is no constant
in a vertical
the
cell
recharge
or (29)).
nothing
(1)
provided
equations,
recharge.
head,
option
to
be intercepted
are read into
with
the
by
the
length
and
model parameters.
horizontal
(26)
are
numbers contained
are consistent
other
recharge
recharge
values
by
column to
include:
any recharge
flux
that
all
then
stre:;s
which
of the
head cell
above,
of the matrix
with
by layer
(unless
multiplied
of the
no recharge
Recharge
previous
the
The options
are
period
each vertical
Under options
then
Ii,j,
of QRi,j,
through
column,
is a constant
represent
formation
associated
QRi,js
no-flow,
head source.
model must be expressed
time
vertical
is no active
column because
constant
in the
is
values
and (3) application
in the column.
recharge
third
this
cell
from the
within
IRCH.
1; (2)
flux,
are immediately
column as specified
IRCHi,j;
uppermost
fluxes
is specified
to model layer
vertical
RECHi,j,
The cell
array
of recharge
at each stress
read into
areas,
array,
values
This
recharge
location
option
is added to the
7-2
(i,j)
rate,
and ve-tical
is subtracted
from the
is done at each iteration
Because recharge
HCOFi,j,k.
flow
as defined
coefficient
is
of head,
Land
Surface
River
Estimated
Water
Table
River
Vertical Cross-Section Showing Field
Situation With Ftnite Difference Grid Superimposed
a
. .. .. . 1.1.. .*.*.a
Iti
cl Variable
Ei Constant
fgj Inactive
Head
Head
liiiiiiiiiiiiiiiiiivl
Status of Cells at End of Srmulation
b
II
11
Cells Whrch Receive Recharge
11 I”’
El
Cell Which Receives
Recharge
El
Cell Which Receives
Recharge
la
Inactive Cell Specified by
User to Receive Recharge
1
Under Optron 1
C
Cells Which Recerve Recharge
Heavy Line Encloses Cells
User Thought Would Receive Recharge
Based on Estrmated Water Table
Under Option 2
d
xxxxxxxxx
I
I
I
I
I
I I I I I I I I I
I
I
I
I
1-l
Cells Which Receive Recharge
El
Cell Whtch Receives
Recharge
Under Option 3
e
Figure 38.-Hypothetical
problem showing which cells receive
recharge under the three options available in the
Recharge Package.
7-3
Careful
consideration
to the other
the three
options
employed
recharge
For example,
should
options
figure
described
table
conditions,
of active,
option
the
horizontal
constant
simulated
head and no-flow
38-C illustrates
the
layer
vertical
columns
simulate
the
utilized,
simulation
slightly
cells
inactive
of the model.
beneath
given
those
(figure
38-a).
assuming
that
on the
basis
the
cells
cells
is
the
the water
shut
under water
column fall
final
distribution
38-b.
is permitted
table
layer,
only
shape has been
recharge
This
off.
during
to the model -if
recharge
in the top
seepage
Using the p*ovision
truncated
distribution
option
model
recharge,
formulation
yields
of
situation.
sectional
shown in figure
Thus once,
the
recharge
distribution
user
specifies
recharge
of an estimated
finally
the user
condition
recharge
which
in each vertical
process
stud:1 and
clearly
to the
fails
to
system.
38-d illustrates
from that
which
involving
cells
Under this
by the use of no flow
Figure
problem
cells
This
table.
1 above is utilized.
to the top
deciding
a cross
conductance
active
under
in a given
in which
a stream
uppermost
at the water
Figure
before
the model mesh has been progressively
so that
approximately
5 for
problem
above to utilize
a hypothetical
and seepage into
to the
simulation
38 shows a situation
in Chapter
simulation
in its
listed
has been used to simulate
from a stream,
be given
obtained
had designated
and thus
receive
water
in the
simulation
as recharge
no recharge.
7-4
table
cells
if
cells
option
prior
position,
process.
2 is
to the
which
differs
Four of the
have converted
to an
Figure
turns
this
38-e illustrates
the Simulation
out to be the one best
option,
column,
recharge
except
streams.
enters
suited
the
where constant
Thus,
a continuous
for
under the third
this
uppermost
head cells
particular
active
situation
of recharge
of recharge
to use.
determining
which
the program
automatically
determines
1, however,
can be useful
in situations
through
no-flow
in layer
the
designated
The model user
is the highest
no-flow
cells
should
cells
because they
not pass into
be used in this
situation
the
cells.
impermeable
least
effort
may be useful
to the
rater
the
table
is
layer.
option
3 uses slightly
for
specified
Other
active
cell
this
1.
factors
2.
layer
should
data.
memory than
than
options
options
1 and 2.
! specified
tha , will
y,
for
still
at
result
option
2
are IS and when
through
when choosing
may be
rat ! is zero
Similar
1 have outcrop
not penetrate
to consider
option
Option
not pass
3 could
option
recharge
the
of input
should
Any recharg
the
select
co umn because
some cell
Of course
that
should
time
3 is
the simu ation.
For example,
layer
2 uses more computer
more computer
throughout
are impermeable.
than
layers
option
in a vertical
where recharge
specification
other
from precipitation
does not have to be conce ned about
by specifying
The user
when layers
to the
to a lower
are that
in each vertical
have been used to t-e Iresent
distribution
the easiest
recharge
Under
.
For the typical
in the
which
situation.
cell
simulated.
those
option,
no-flow
th ! best
cells
option
1 an I 3, and option
Recharge
Package Input
Input to the Recharge (RCH) Package is read from the unit
in
specified
IUNIT(8).
FOR EACH SIMULATION
RCHlAL
1.
Data:
Format:
NRCHOP
110
IR CHCB
110
FOR EACH STRESS PERIOD
RCHlRP
2.
Data:
Format:
INRECH
110
INIRCH
110
3.
Data:
Module:
RECH(NCOL,NROW)
U2DREL
IF THE RECHARGEOPTION IS EQUAL TO 2
4.
IRCH(NCOL,NROW)
Data:
Module : UZDINT
Explanation
Input
of
Fields
Used in
Instructions
Recharge fluxes
are defined in a twoNRCHOP--is the recharge option code.
dimensional
array,
RECH, with one value for each vertical
column.
recharge is applied to one cell in each vertical
column,
Accordingly,
and the option code determines
which cell in the column is selected
for recharge.
l-
Recharge
2-
Vertical
distribution
array IR CH.
3-
Recharge
vertical
recharge
is only
to the top
grid
of ‘recharge
layer.
is
specified
in
is applied to the highest
active
cell in each
A constant-head
node intercepts
column.
and prevents deeper infiltration.
7-6
IRCHCB--is
a flag
and a unit
number.
If
IRCHCB > 0, it
If
IRCHCB 2 0, cell-by-cell
is the unit number on which cell-by-cell
flow
terms will
be recorded whenever ICBCFL (see Output
Control)
is set.
flow
terms
will
not be printed
or
recorded.
INRECH--is
the RECH read flag.
If
INRECH10,
If
INRECH < 0, recharge
used.
rates
the IRCH read flag.
When NRCHOPis two,
If
INIRCH 2 0, an array
of layer
If
INIRCH < 0, the array
INIRCH--is
an array
period
Note:
of recharge
is
(Lt-I).
RECH, is
from the preceding
read.
stress
numbers (IRCH) is
period
read.
(IRCH) used in the preceding
stress
reused.
When NRCHOPis one or three,
RECH--is the recharge flux
or equal to zero.
fluxes,
INIRCH is ignored.
Read only
if
INRECH is
greater
than
IRCH--is the layer number array that defines the layer in each vertical
Read only if NRCHOP is two and
column where recharge is applied.
if INIRCH is greater than or equal to zero.
7-7
are
m
*-I****
00000*
. . .
******
.
.
.
NNNOmC-7
. . . .
**.-I***
.
.
(YNNONc.3
. . . .
*****#-I
.
.
NCY****
-l*.-l***
Module Documentation
The Recharge
are called
for
Package (RCHl)
consists
by the MAIN program.
RCHlAL
Allocates
the
flux
recharge
modules,
all
of which
are:
recharge
flow
2 is specified,
(in
(if
flow
option
per unit
rate
the
layer-
area)
and
2 is specified).
recharge
flux
by cell
recharge
flow
rate
in which
Calculates
Package
(IRCH).
array
Multiplies
Subtract
option
array
indicator
RCHlBD
if
Reads recharge
lator
of four
space to contain
indicator
RCHlFM
Recharge
lhe modules
(RECH) and,
RCHlRP
the
area.
from the
accumu-
RHS is formulated.
the
rate
into
the
and accumulated
flow
7-9
system.
volume of
Narrative
This
areally
for
module allocates
distributed
Print
2.
Read and print
flow
See if
(not
1, 2, or 3),
If
NRCHOP is
5.
If
cell-by-cell
number where they
(ISUM) of the
the
array
7.
for
to
If
by the
9.
legal,
relating
first
first
(NRCHOP) and the unit
(NRCHOP) is
legal.
a message saying
print
flow
to
nunber
the
If
NRCHOPis
option
is illegal.
NRCHOP.
terms
are to be recorded,
print
the
unit
be recorded.
space for
element
the
recharge
array
(RECH).
of RECH (LCRECH) equal
unused element
in the X array
Space is
allocated
to the location
and adding
the
size
of
ISUM.
the
recharge
a layer-indicator
8.
data
STOP.
will
Allocate
indicator
option
print
storage.
the
to store
(IRCHCR).
recharge
4.
by setting
X array
the package.
the option
terms
the
Do not allocate
6.
space in,$the
a message identifying
cell-by-cell
illegal
Module RCHlAL
recharge.
1.
3.
for
Calculate
Recharge
option
array
and print
(NRCHOP) is
equal
to two,
allocate
space
(IRCH).
the
number of elements
Package.
RETURN.
7-10
in the X array
used
Flow Chart
NRCHOP is the
1 - Recharge
recharge
for
Module RCHlAL
option.
is to the top
layer.
2 - Recharge is to the layer
specified
by the user in
the indicator
array (IRCH).
3 - Recharge is to the uppermost active
cell.
IRCHCB is the unit number on
which cell-by-cell
flow
terms for recharge will
be
written.
RECH is an array which contains
a recharge rate for each
horizontal
cell location.
SHOWING
OPTION
IRCH is an array which contains
the layer number to which
recharge is applied for each
horizontal
location.
It is
used only if option 2 has
been specified.
ALLOCATE
SPACE
FORRECHARRAY
PRINT AMOUNT
OF SPACE USED
BY THE RCH
PACKAGE
f-l
7-11
0
1
SUBROUTINE RCHlAL(ISUM,LENX,LCIRCH,LCRECH,NRCHOP,
NCOLrNROW,INrIOUT,IRCHCB)
1559 12MAY1987 RCHlAL
: -----VERSION
******************************************************************
C
C
ALLOCATE ARRAY STORAGE FOR RECHARGE
**************************************~***************************
C
n
c”
SPECIFICATIONS:
E
Cl----
IDENTIFY
PACKAGE.
WRITE(IOUT,l)IN
1 FORMAT(lHOr’RCH1 -- RECHARGEPACKAGE, VERSION 1, 9/l/87',
1' INPUT READ FROM UNIT',131
~~------READ
NRCHOPAND IRCHCB.
READ(IN,Z)NRCHOP,IRCHCB
2 FORMAT(2110)
TO SEE THAT OPTION IS LEGAL.
c3 ------CHECK
IF(NRCHOP.GE.l.AND.NRCHOP.LE.3)GO
TO 200
C
C3A--w-m IF ILLEGAL PRINT A MESSAGE AND ABORT SIMULATION
WRITE(IOUT,8)
8 FORMAT(lX,‘ILLEGAL
STOP
OPTIONCODE. SIMULATION ABORTING’)
C
c4 ------IF
OPTION IS LEGAL PRINTOPTIONCODE.
200 IRK=ISUM
IF(NRCHOP.EQ.l)WRITE(IOUT,POl)
201 FORMATtlXr'OPTION
1 -- RECHARGETO TOP LAYER’)
IF(NRCHOP.EQ.2) WRITE(IOUT,202)
202 FORMAT(lX,'OPTION
2 --.RECHARGE TO ONE SPECIFIED NODE IN EACH’,
1
’ VERTICAL COLUMN’)
IF(NRCHOP.EQ.3) WRITE(IOUT,203)
203 FORMAT(lX,‘OPTION
3 -- RECHARGETO HIGHEST ACTIVE NODE IN EACH’,
1
’ VERTICAL COLUMN’)
:5
------IF CELL-BY-CELL FLOW TERMS TO BE SAVED THEN PRINT UNIT #
IF(IRCHCB.GT.0)WRITE(IOUT,204)IRCHCB
204 FORMAT(lX,‘CELL-BY-CELL
FLOW TERMS WILL BE RECORDEDON UNIT',131
& ------ALLOCATE
SPACE FOR THE RECHARGEARRAYtRECH).
LCRECH=ISUM
C
ISUM=ISUM+NCOL*NROW
C7------
IF OPTION2 THEN ALLOCATE SPACE FOR INDICATOR ARRAYtIRCH)
LCIRCH=ISUM
IF(NRCHOP.NE.2)GO
TO 300
ISUM=ISUM+NCOL*NROW
:8 ------CALCULATE
AND PRINT AMOUNT OF SPACE USED BY RECHARGE.
300 IRK=ISUM-IRK
WRITE(IOUT,4)IRK
4 FORMAT(lX,IBr' ELEMENTS OF X ARRAY USED FOR RECHARGE’)
ISUMl=ISUM-1
WRITE(IOUT,S)ISUMl,LENX
5 FORMAT(lX,IB,' ELEMENTS OF X ARRAY USED OUT OF’,181
IF(ISUMl.GT.LENX)WRITE(IOUT,6)
6 FORMAT(1X,'
***X ARRAY MUST BE MADE LARGER***‘)
C
c9 -----~J-(JRN
RETURN
END
7-12
List
Variable
of Variables
for
Definition
Range
IN
Package
IOUT
I RCHCB
Global
Package
IRK
Module
ISUM
Global
ISUMl
LCIRCH
Module
Package
Module RCHlAL
Primary unit number from which input for this package
will be read.
Primary unit number for all printed
output.
IOUT = 6.
Flag.
IRCHCB -< 0, cell-by-cell
flow terms will
not be
printed
or recorded.
IRCHCB > 0 and ICBCFL f 0, cell-by-cell
flow terms
for the RCHl Package will
be recorded
on UNIT = IRCHCB.
Before this module allocates
space, IRK is set equal
to ISUM. After allocation,
IRK is subtracted
from
ISUM to get the amount of space in the X array
allocated
by this module.
Index number of the lowest element in the X array which
has not yet been allocated.
When space is allocated
for an array,
the size of the array is added to ISUM.
ISUM-1.
Location
in the X array
of the
first
element
of array
of the
first
element
of array
IRCH.
LCRECH
Package
Location
in the X array
RECH.
LENX
Global
Length of the X array
NCOL
NRCHOP
Global
Package
NROW
Global
in words.
This should always be
equal to the dimension of X specified
in the MAIN
program.
Number of columns in the grid.
Recharge option:
= 1, recharge is to the top grid layer.
= 2, recharge is to the grid layer specified
in
array IRCH.
= 3, recharge is to the highest
variable-head
cell
which is not below a constant-head
cell.
Number of rows in the grid.
7-13
Narrative
This module
areally
distributed
1.
2.
INRECH is
period
will
effect.
4.
stress
zero,
If
represent
indicate
the
last
whether
stress
the data
period
#2re
period.
the
in this
INRECH is greater
rate
recharge
flux
(RECH) is coming
recharge
rate
used in the
stress
period.
Print
last
from.
stress
a message to that
array
Multiply
the specified
If the recharge
If
stress
to that
7.
period
recharge
option
CALL UZDREL to read the
flux
rates
by the cell
will
(NRCHOP) is not equal
than
zero,
the data
be used in this
areas
to get
to two,
a layer-indicator
stress
in
IRCH left
period.
Print
over
from the
a message
GO TO STEP 8.
INIRCH is greater
than
or equal
IRCH array.
8.
to zero,
GO TO STEP 8.
INIRCH is less
effect.
If
or equal
rate.
is not needed.
6.
than
(RECH).
volumetric-recharge
5.
the
which
GO TO STEP 5.
recharge
last
than
be used again
3.
the
current
INRECH to see where the
less
the terms
RECH and IRCH used during
the
Test
used to calculate
INRECH and INIRCH which
values
in arrays
to be used for
Module RCHlRP
recharge.
Read the
contained
If
reads data
for
RETURN.
7-14
to zero,
CALL UZDINT to read
Flow Chart
for
Module RCHlRP
INRECH is a flag which, when set,
indicates
that recharge rates
it
(RECH) should be read for If the
current
stress period.
is clear (< 0), recharge rates
from the last stress period
should be reused.
INIRCH is a flag similar
to
INRECH used for the layer
indicator
array IRCH.
2A
RECH is an array containing
recharge rate for every
horizontal
cell location.
a
PRINT A
MESSAGE.
“REUSE
RECH”
-
IRCH is an array containing
a
recharge indicator
for each
horizontal
cell location.
For each horizontal
cell
location,
it indicates
the
layer number of the cell at
that location
which gets
recharge.
It is used only if
the recharge option (NRCHOP)
is equal to two.
3
CALL MODULE
UPDREL TO
READ RECH
4
MULTIPLY
RR’;‘;;“;~’
CELL AREA
I
7-15
CALL MODULE
U2DINT to
READ IRCH
I
SUBROUTINE RCHlRPt NRCHOP,IRCH,RECH,DELR, DELC, NROW,NCOL,
IN,IOUT)
1
C
C-----VERSION
1634 24JlJL1987 RCHlRP
****************+**********~*******~***********~************~~*****
READ RECHARGERATES
************************************************************~~*****
C
C
C
a
SPECIFICATIONS:
--------------------____l__l____________-----
:
C
CHARACTER*4 ANAK
DIMENSION
IRCH(NCOL,NROW),RECH(NCOL,NROW),
ANAME(6rZ)rDELR(NCOL)rDELC(NROW)
1
C
DATA ANAME~1,1~,ANAME~2,1~,ANAME~3,1~,ANAME~4,1~,ANAME~5,1~,
‘,‘RECH’r’ARGE’r’
LAY’r’ER I'r'NDEX'/
1 ANAME(6rl)/'
DATA ANAME(l,Z)rANAME(2,2),ANA~(3,2),ANAME(4r2)rANAME(5,2)r
‘,‘RECH’r’ARGE’/
1,'
1,'
','
------------------------------------------------------------,------
1 ANAME(6,2)/'
C
C
Cl----
READ FLAGS SHOWINGWHETHERDATA
READ(IN,4)INRECH,INIRCH
IS
TO BE REUSED.
4 FORMAT(2110)
C
TEST INRECH
TO SEE WHERE RECH IS COMING
FROM.
IF(INRECH.GE.O)GO
TO 32
c2---
INRECHKO
THEN REUSE RECHARGEARRAY FROM LAST STRESS PERIOD
WRITE(IOUT,3)
FORMAT(lHD,‘REUSING RECH FROM LAST STRESS
PERIOD')
GOTO55
:2A -----IF
3
a
C
c3------IF
INRECH=>O THEN CALL U2DREL TO READ RECHARGERATE.
U2DREL(RECH,ANAME(1,2)rNROW,NCOL,O,IN,IOUT~
C
c4------MULTIPLY RECHARGERATE BY CELL AREA TO GET VOLUMETRIC
RATE..
DO 50 IR=l,NROW
DO50 IC=l,NCOL
RECH(IC,IR)=RECH(IC,IR)*DELR(IC)+DELC(IR~
50 CONTINUE
32 CALL
:5 ------IF
55 IF
NRCHOI-2 THEN A LAYER INDICATOR ARRAY IS NEEDED.
(NRCHOP.NE.2)GO TO 60
C
C&---
IF INIRCHCO THEN REUSE LAYER INDICATOR ARRAY.
IF(INIRCH.GE.O)GO
TO.58
WRITE(IOUT,2)
2 FORMAT(lHO,‘REUSING IRCH FROM LAST STRESS PERIOD’)
GO TO 60
C
C7-----IF
58 CALL
INIRCH=>O
CALL U2DINT TO READ LAYER IND ARRAYtIRCH)
U2DINT(IRCH,ANAME(lrl)rNROW,NCOL,O,IN,IOUT~
C
c8---EJ-URN
60 RETURN
END
7-16
c
List
B
Variable
of Variables
for
Module RCHlRP
Definition
Range
ANAME
Module
Label
DELC
Global
DIMENSION (NROW), Cell dimension in the
DELC(1) contains
the width of row I.
DELR
Global
DIMENSION (NCOL), Cell dimension in the row direction.
DELR(J) contains
the width of column J.
IC
Module
Index for
IN
Package
Primary
will
INIRCH
Module
Flag.
-> 0, IRCH array
for
< 0,
INRECH
Module
l
printout
of the
input
array.
column direction.
columns.
unit number from which
be read.
will
will
number for
this
package
in memory from the last
be used.
be read.
< 0, RECH array already
stress period will
unit
for
be read.
IRCH array already
stress period will
Flag.
-> 0, RECH array
input
all
in memory from the
be used.
printed
output.
last
IOUT
Global
Primary
IOUT = 6.
IR
Module
Index for
IRCH
Package
DIMENSION (NCOL,NROW), Layer number for each horizontal
cell location
to which recharge will
be applied
if
the recharge option (NRCHOP) is equal to 2.
NCOL
Global
Number of columns
NRCHOP
Package
Recharge option:
= 1, recharge is
= 2, recharge is
array IRCH.
= 3, recharge is
which is not
rows.
in the grid.
to the top grid layer.
to the grid layer specified
to the highest
variable-head
below a constant-head
cell.
NROW
Global
Number of rows in the
RECH
Package
DIMENSION (NCOL,NROW), Recharge flow rate.
flux is read into RECH and than multiplied
area to obtain recharge flow rate.
7-17
in
cell
grid.
Recharge
by cell
Narrative
This module adds terms
accumulators
1.
If
the top
in which
the
for
representing
the terms
recharge
(a)
If
areally
distributed
option
(NRCHOP) is equal
location,
to one,
recharge
DO STEPS (a)
is externa 1 (IB~~ND(~,~,K)
the cell
recharge
to the
HCOF and RHS are formulated.
For each horizontal
layer.
Module RCHlFM
is to
AND (b).
5 0),
ignore
it.
SKIP STEP (b).
(b)
If
2.
in the
the
recharge
(a)
Get the
(b)
If
(c)
Subtract
If
the
the
option
array
cell
the
recharge
cell
cell
on to the
(b)
If the
(c)
Subtract
next
horizontal
flow
is three,
RHS accumulator.
is only
to the
cells
specified
is
rate
it.
recharge
array
(IRCH).
SKIP STEP (c).
from the
head, there
cell
no flow,
recharge
cell
layer-indicator
is
RHS accumulator.
in the
uppermost
internal
location:
horizontal
the
from the
recharge
ignore
is constant
cell
rate
from the
is external,
For each horizontal
the
is two,
index
option
If
flow
(IRCH).
layer
Move on to the next
4.
recharge
recharge
(a)
it.
the
layer-indicator
3.
cell.
Subtract
will
location.
RETURN
7-18
below
and go back to
(a).
location.
move down a cell
flow
be no recharge
rate
from the
RHS accumulator.
Move
Flow Chart for Module RCHlFM
RHS is the right
hand side
of the finite-difference
It includes
all
equation.
terms that are independent
of head at the end of the
time step.
(2
ENTER
RCHIFM
IRCH is an array which contains the layer number to
which recharge is applied
for each horizontal
location.
It is used only if option 2
has been specified.
NRCHOPis
the
1 - Recharge
layer.
recharge
option.
is to the top
r
2A
2 - Recharge is to the
layer specified
by the
user in the indicator
array
GET
LAYER
FROM
THE
INDEX
IRCH
L3
&
(IRCH).
3 - Recharge is to the
uppermost active
cell.
R EACH LAYER
7-19
SUBROUTINE RCHlFM(NRCHOP,IRCHrRECH,RHS,IBOUND,NCOLr
NRW,NLAY)
1
C
RCHlFM
C-----VERSION 1404 12MAY1987
C
**********t***********************~*******************~~~**~~*****
C
SUBTRACT RECHARGEFROM RFS
******************+*******************~***************************
C
C
C
SPECIFICATIONS:
”
DIMENSION
IRCH(NCOLrNRW),RECH(NCDL,NRW)r
RHS(NCOLrNRW,NLAY)rIBOUND(NCOL,NRW,NLAY)
1
E
Cl----
IF NRCHOP IS 1 RECHARGEIS IN TOP LAYER. LAYER INDEX IS 1.
IF(NRCHOP.NE.l)GOTO 15
C
DO 10 IR=lrNRCM
DO 10 IC=l,NCOL
C
Cl&----
IF CELL IS EXTERNAL THERE IS NO RECHARGEINTO IT.
IF(IBWND(IC,IR,l).LE.O)GO TO 10
C
ClB----- SUBTRACT RECHARGE RATE FROM RIGHT-HAND-SIDE.
RH.S(IC,IR,1)=RHS(IC,IR,1)-RECH(IC,IR)
10 CONTINUE
GO TO 100
C
c2---IF OPTION IS 2 THEN RECHARGEIS INTO LAYER IN INDICATOR
ARRAY
C
15 IF(NRCHOP.NE.P)GO TO 25
DO 20 IR=l,NRW
DO 20 IC=lrNCOL
i-3’+----
LAYER INDEXIS IN INDICATOR
ARRAY.
IL=IRCH(IC,IR)
C
C2&---- IF THE CELL IS EXTERNAL THERE IS NO RECHARGEINTO IT.
IF(IBOUND(IC,IR,IL).LE.O)GOTO 20
C
QC----
SUBTRACT RECHARGEFROM RIGHT-HAND-SIDE.
RHS(IC,IR,IL)=RHS(IC,IR,IL)-RECH(IC,IR)
20 CONTINUE
GO TO 100
C
C3------ IF OPTIONIS 3 RECHARGEIS INTOHIGHESTINTERNAL
CELL.
25 IF(NRCHOP.NE.3)GO
TO 100
CANNOT PASS TliRCUGH CONSTANT HEAD NODE
C
DO 30 IR=lrNRW
DO 30 IC=lrNCOL
DO 28 IL=lrNLAY
C
C3A----- IF CELL IS CONSTANT HEAD MOVE ON TO NEXT HORIZONTAL LOCATION.
IF(IBWND(IC,IR,IL) .LT.O) GO TO 30
C
c35---- IF CELL IS INACTIVEMOVE DOWNA LAYER.
IF (IBOUND(IC~IR,IL).EQ,O)GO
TO 28
C
C3C----- SUBTRACT RECHARGE FROM RIGHT-HAND-SIDE.
RHS(IC,IR,IL)=RHS(IC,IR,IL)-RECH(IC,IR)
GO TO 30
28 CONTINUE
30 CONTINUE
100 CONTINUE
C
c4------RETURN
RETURN
END
7-20
List
D
Variable
of Variables
for
Module RCHlFM
Definition
Range
I BOUND
Global
DIMENSION (NCOL,NROW,NLAY), Status
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
IC
Module
Index
for
columns.
IL
Module
Index
for
layers.
IOUT
Global
Primary
IR
Module
Index for
IRCH
Package
DIMENSION (NCOL,NROW), Layer number for each horizontal
cell location
to which recharge will
be applied
if
the recharge option (NRCHOP) is equal to 2.
NCOL
Global
Number of columns
NLAY
Global
Number of layers
NRCHOP
Package
Recharge option:
= 1, recharge
= 2, recharge
IR CH.
= 3, recharge
which is
unit
number for
all
of each cell.
printed
output.
IOUT = 6.
rows.
in the
grid.
in the grid.
is to the top grid layer.
is to the grid layer specified
is to the highest
variable-head
not below a constant-head
cell.
in array
cell
NROW
Global
Number of rows in the
RECH
Package
DIMENSION (NCOL,NROW), Recharge
RHS
Global
DIMENSION (NCOL,NROW,NLAY), Right hand side of the
finite-difference
equation.
RHS is an accumulation
of terms from several different
packages.
7-21
grid.
flow
rate.
Narrative
This
areally
module calculates
distributed
1.
Clear
2.
If
in which
If
3.
Process
the
the
rates
Module RCHlBD
and volumes
added to the
aquifer
by
recharge.
the
rate
accumulators
cell-by-cell
they
for
will
the
flow
RATIN and RATOUT.
terms
will
be saved,
clear
the buffer
(BUFF)
be accumulated.
recharge
horizontal
option
is
locations
cell
one, the
recharge
goes into
the top
layer.
one at a time.
(a)
If
the
is external,
(b)
If
cell-by-cell
flow
(c)
If
the
is
do not calculate
terms
will
be saved,
budget.
add recharge
to
buffer.
recharge
positive,
add it
to RATIN; otherwise,
add it
to RATOUT.
4.
If
in indicator
the
the
array
recharge
(IRCH).
cell
option
is two,
Process
(a)
Get the
(b)
If
the
(c)
If
cell-by-cell
flow
(d)
If
the
is
cell
layer
the
recharge
goes into
horizontal
locations
from indicator
is external,
array
do not calculate
terms
will
be saved,
the
layer
specified
one at a time.
(IRCH).
budget.
add the
recharge
to
buffer.
recharge
positive,
to RATOUT.
7-22
add it
to RATIN; otherwise,
add it
If
5.
the
variable-head
Process
recharge
cell
option
provided
the horizontal
is three,
there
the
recharge
goes into
is not a constant-head
locations
one at a time.
Start
cell
with
the top
above it.
the top cell
and work down.
(a)
If
move down to the
(b)
horizontal
the cell
next
If
is
there
is
no recharge
into
that
is constant,
there
is
no recharge
at this
cell;
one.
the cell
location;
inactive,
move on to the next
horizontal
(c)
If
cell-by-cell
flow
terms
(d)
If
the
recharge
is positive,
cell-by-cell
flow
location.
are to be saved,
add the
recharge
to
the buffer.
add it
to RATIN; otherwise,
add it
to RATOUT.
6.
write
If
the buffer
terms
be saved,
call
module UBUDSV to
the VBVL array
for
printing
length
to the
(BUFF) onto disk.
7.
Move RATIN and RATOUT into
8.
Add RATOUT multiplied
accumulators
will
in VBVL for
9.
Move the
10.
Increment
11.
RETURN.
printing
recharge
the
by the time-step
volume
by BASIOT.
budget-term
budget-term
by BASlOT.
labels
counter
7-23
to VBNM for
(MSUM).
printing
by BASlOT.
Flow Chart
RATIN is an accumulator
which all flows into
aquifer
are added.
for
Module RCHlBD
to
the
ENTER
RCHIED
182
52
RATOUT is an accumulator
to which all flows out
of the aquifer
are
added.
BUFFER is an array in
which values are stored
as they are being
gathered for printing
or recording.
NRCHOP is the
option.
1 - Recharge
CLEAR RATIN
AN;WTFUT
NEEDED,
SUFFER
FOR EACH HORIZONTAL
CELL LOCATION
3E:.3C
,1
ADD RECHARGE 10
RATIN OR RATOUT
STORE RECHAROE
IN BUFFER
recharge
is to the
top layer.
FOR EACH HORIZONTAL
4C ,4D
2 - Recharge
is to the
layer specified
by
the user in the
indicator
array
(IRCH).
3 - Recharge
uppermost
cell.
is to the
active
FOR EACH HORIZONTAL
CELL LOCATION
FOR EACH LAYER
I
IRCH is an array containing a recharge indicator
for each horizontal
It is used only
cell.
if the recharge option
(NRCHOP) is equal to two.
RATlN OR RATOU’I
STORE RECHARGE
VBVL is a table of budget
entries
calculated
by
component-of-flow
packages
for use in calculating
the volumetric
budget.
VBNM is a table of labels
for budget terms.
MOVE RATIN
AND RATOUT
TO “BVL AND
LABELS TO “BNM
EXTERNAL: a cell is external
if it is either
no flow
(inactive)
or constant
head.
7-24
I
SUBROUTINE RCH~BD(NRCHOPIIRCH,RECH,IBOUNDINROWINCOL~NLAYI
DELT,VBVL~VBNM,MSUM,KSTPIKPERIIRCHCBIICBCFL,BUFFIIOUT)
1
-----VERSION 1602 12MAY1987
RCHlBD
******************************************************************
:
CALCULATE VOLUM3RIC
BUDGET FOR RECHARGE
:
C
******************************************************************
:
SPECIFICATIONS:
----_-------------------------------------------------------------
C
C
C
Cl---
CHARACTER*4 VBNM,TEXT
DIMENSION
IRCH(NCOLrNROW)rRECH(NCOLrNROW)r
1
IBOL~ND(NCOL,NROW,NLAY)~BUFF(NCOLINROWINLAY)~
2
VBVL(4rZO)rVBNM(4,20)
DIMENSION TEXT(4)
‘,‘RECH’r’ARGE’/
DATA TEXT(l),TEXT(Z)rrr~CT(3)rTEXT(4)
/’
‘,’
-----_-“_--__-------____________________--------------------------CLEAR THE RATE ACCUMULATORS.
RATIN=O.
RATOUT=O.
C
c2---
IF CELL-BY-CELL FLOW TERMS WILL BE SAVED THEN CLEAR THE BUFFER.
IBD=O
IF(ICBCFL.EQ.0 .OR. IRCHCB.LE.0)GOTO 5
IBD=l
DO2 IL=l,NLAY
DO 2 IR=lrNRW
DO2 Ic=l,NcOL
BUFF(IC,IR,IL)=O.
2 CONTINUE
:3 ------IF
NRCHOP=l RECH GOES INTO LAYER 1. PROCESS EACH HORIZONTAL
c3 ------CELL
LOCATION.
5 IF(NRCHOP.NE.l)
GO TO 15
C
---RECHARGE IS APPLIED TO TOP LAYER
C
DO 10 IR=lrNRW
DO10 Ic=lrNcOL
CELL IS EXTERNAL THEN DO NOT DO BUDGET FOR IT.
IF(IBOUND(IC,IR,l).LE.O)GO TO 10
Q=RECH(IC,IR)
:3A -----IF
:3E+
----IF CELL-BY-CELL FLOW TERMS WILL BE SAVED THEN ADD RECH TO BUFF
IF(IBD.EQ.l) BUFF(IC,IR,l)=Q
C
(-J3C-----
IF RECH POSITIVEADD IT TO RATIN ELSE ADD IT TO RATOUT.
IF(Q) 8r10,7
7 RATIN=RATIN+Q
GO TO 10
8 RATOUT=RATOUT-Q
10 CONTINUE
GO TO 100
C
c4------IF NRCHOP=Z RECH IS IN LAYER SHOWNIN INDICATOR ARRAYtIRCH).
c4------PROCESS HORIZONTAL CELL LOCATIONS ONE AT A TIRE.
15 IF(NRCHOP.NE.P)GO
TO 25
DO 20 IR=l,NRW
DO 20 IC=l,NCOL
C
()$A--- GETLAYER INDEXFROM INDICATOR
ARRAYtIRCH).
IL=IRCH(IC,IR)
C
cJ&--- IF CELL IS EXTERNAL DO NOT CALCULATE BUDGET FOR IT.
IF(IBOUND(IC,IR,IL) .LE.O)GO TO 20
7-25
Q=RECH(ICI IR)
C
(-JjC----
IF C-8-C FLOW TERM WILL BE SAVED THEN ADD RECHARGETO BUFFER.
BUFF(IC,IR,IL)=Q
IF(IBD.EQ.l)
ti4D-----IF RECHARGEIS POSITIVEADD TO RATINELSE ADD IT TO RATOUT.
IF(Q) 18rZOr17
17 RATIN=RATIN+Q
GOTO 20
18 RATOUT=RATOUT-Q
20 CONTINUE
GO TO 100
C
C5------ IF OPTION=3
RECHARGEIS INTO HIGHEST INTERNAL CELL. IT WILL NOT
C5------ PASS THROUGHA CONSTANT HEAD CELL. PROCESS HORIZONTAL CELL
ONE AT A TIRE.
c5 ------LOCATIONS
25 IF(NRCHOP.NE.3)GO TO 100
DO 30 IR=lrNRCW
DO 30 IC=l,NCOL
DO
&A
28 IL=l,NLAY
-----IF CELL IS CONSTANT HEAD MOVE ON TO NEXT HORIZONTAL LOCATION.
IF(IBOUND(IC,IR,IL).LT.O) GOTO 30
----IF
CELL IS INACTIVEMOVE DOWNTO NEXT CELL.
(IBOLIND(IC,IR,IL).EQ.O)GO TO 28
Q=RECH(IC,IR)
IF
-----IF C-&C FLOW TEFU.6 TO BE SAVED THEN ADD RECHARGETO BUFFER.
IF(IBD.EQ.l) BUFF(IC,IR,IL)=Q
h
&D -----IF RECH IS POSITIVE ADD IT TO RATIN ELSE ADD IT TO RATOUT.
IF(Q) 27r30r26
26 RATIN=RATIN+Q
GO TO 30
27 RATOUT=RATOUT-Q
GO TO 30
28 CONTINUE
30 CONTINUE
C
100 CONTINUE
C
C-B-C
c6 ------IF
C
FLOW TERMS TO BE SAVED CALL UBUDSV TO WRITE THEM.
IF(IBD.EQ.l) CALL UBUDSV(KSTP,KPER,TEXT,IRCHCB,BUFFrNCOL,NRCWr
1
NLAY, IOUT)
C7------
MOVE TOTAL RECHARGERATE
VBVL(4rMSUM)=RATOUT
VBVL(3rMSUM)=RATIN
INTO VBVL FOR PRINTINGBY BASlOT.
RECHARGEFOR TIRE STEP TO RECHARGEACCUMULATORIN VBVL.
ii3 ------ADD
VBVL(P,MSUM)=VBVL(2rMSUM)+RATOUT*DELT
VBVL(lrMSUM)=VBVL(l,MSUM)+RATIN*DELT
C
BUDGET TERM LABELS TO VBNM FOR PRINT BY MODULE BAS-OT.
c9 ------MOVE
VBNM(l,MSUM)=TEXT(l)
VBNM(P,MSUM)=TEXT(Z)
VBNM(3rMSUM)=TEXT(3)
VBNM(4rMSUM)=TEXT(4)
C
Cl&---
INCREMENT BUDGET TERM COUNTER.
MSUM=MSUM+l
El1 -----RETURN
RETURN
END
7-26
List
Variable
of Variables
for
Module RCHlBD
Definition
Range
BUFF
Global
DIMENSION (NCOL,NROW,NLAY), Buffer
used to accumulate
information
before printing
or recording
it.
DELT
Global
Length
IBD
Module
Flag.
= 0, cell-by-cell
flow
not be recorded.
f 0, cell-by-cell
flow
be recorded.
IBOUND
Global
of the current
time
terms
for
this
package will
terms
for
this
package will
DIMENSION (NC~L,NROW,NLAY), Status
< 0, constant-head
= 0, inactive
cell
> 0, variable-head
l
step.
IC
Module
Index
for
I CBCFL
Global
Flag.
= 0, cell-by-cell
or printed
z 0, cell-by-cell
the current
of each cell.
cell
cell
columns.
flow terms will
not be recorded
the current
time step.
flow terms will
be recorded for
time step.
for
IL
Module
Index
IOUT
Global
Primary
IR
Module
Index
IRCH
Package
DIMENSION (NCOL,NROW), Layer number for each horizontal
cell location
to which recharge will
be applied
if
the recharge option
(NRCHOP) is equal to 2.
IRCHCB
Package
Flag.
IRCHCB 5 0, cell-by-cell
flow terms
recorded or printed.
for
layers.
unit
for
number for
all
printed
output.
rows.
IRCHCB > 0 and ICBCFL f 0, cell-by-cell
for the RCHl Package will
on UNIT = IRCHCB.
B
IOUT = 6.
KPER
Global
Stress
period
KSTP
Global
Time step
period.
MSUM
Global
Counter
NCOL
Global
Number of columns
for
will
not be
flow terms
be recorded
counter.
counter.
budget
7-27
Reset
entries
in the
at the start
and labels
grid.
of each stress
in VBVL and VBNM.
List
of Variables
for
Module RCHlBD (Continued)
Variable
Range
Definition
NLAY
Global
Number of layers
NRCHOP
Package
Recharge option:
= 1, recharge is
= 2, recharge is
array IRCH.
= 3, recharge is
which is not
in the grid.
to the top grid layer.
to the grid layer specified
to the highest
variable-helad
below a constant-head
cell.
NROW
Global
Number of rows in the
Q
Module
Flow from recharge into a cell.
get flow out of the cell.)
RATIN
Module
Accumulator
recharge.
for
the total
flow
into
RATOUT
Module
Accumulator
for
to recharge.
the total
flow
out of the
RECH
Package
DIMENSION (NCOL,NROW), Recharge
flow
rate.
TEXT
Module
Label
with
the
VBNM
Global
DIMENSION(4,20),
to be printed
in
cell
grid.
(Reverse
or recorded
Labels
for
entries
the
the flow
sign
field
flow
field
array
data.
in the
to
from
volumetric
budget.
VBVL
Global
DIMENSION
(4,20),
Entries
for the volumetric
budget.
For flow component N, the values in VBVL are:
(l,N),
Rate for the current
time step into the flow
field.
(2,N),
Rate for the current
time step out 07 the
flow field.
(3,N),
Volume into the flow field
during simulation.
(4,N),
Volume out of the flow field
during simulation.
7-28
CHAPTER8
WELL PACKAGE
Conceptualization
The Well
Package is designed
which withdraw
rate
the
during
cell
wells,
water
from the
a given
stress
area and the
developed
on the
either
from
it,
for
well
beginning
stress
formulated,
well
in the
rate
to it)
is
at a specified
independent
The discussion
in this
to be simulated
of both
section
is
are actually
Well Package by specifying
adds water
period
to the aquifer
of the simulation.
discharge,
while
of each stress
each well--the
that
one well
where the
the features
well
each stress
the we11 is located,
(equation
(or add water
such as wells
the
or removes water
Negative
positive
rate,
values
values
of Q
of Q indicate
a
well.
At the
during
features
or recharging.
is handled
are used to indicate
values
that
each individual
recharging
aquifer
head in the cell.
discharging
during
to simulate
period,
assumption
Well discharge
Q, at which
and Implementation
period.
falls
within
as the RHS term
for
a single
for
the discharge
associated
summed within
the program
or recharge
each well
the cell
cell,
that
the calculation
cell
is assembled.
with
each individual
the total
well,
four
in which
Q, of the well
as the matrix
containing
8-1
rate,
is subtracted
that
to obtain
WELlRP module'reads
number of the cell
At each iteration,
of Q for
or (29))
the
row, column and layer
and the d ischarge
the value
(26)
period,
equations
are
from the RHS value
well.
is
Where more than
repeated
Thus the user
and these
discharge
for
each
specifies
are in effect
from the
cell.
The Well
wells
which
well
of this
Package,
as it
are open to more than
type
an individual
approach
is
used,
or apportioned
model program.
discharge
layers
stress
period,
transmissivity
of all
equation
(68),
be implemented
well,
and for
This
of single
between
penetrated
or some other
by the
user
each stress
externally
to the
cular
in that
well
stress
the
Again,
i .e.
in a given
period,
Tl is the
sum of the transmissivities
it's
important
the
to the program
for
to note that
discharge,
must
each multi-layer
period.
a multi-layer
wells,
fails
various
layers
provided
to take
into
by the well
well
account
well
effects
8-2
is
represented
the
itself,
A package which
problem.
of multi-layer
externally
(68)
method of apportioning
in which
of the
ties
1 to a parti
by the well.
If this
must be divided
layers,
transmissivi
QI
TI
-- = -Qw XT
1 and ET represents
and each
is to div ide the well
this
discharge
layer
approximation
individual
a
wells,
period.
well
layer
from layer
Qw is the well
approach,
representation
of the multi-layer
to the
However,
well,
each stress
A common method of doing
of layer
layers
for
in some way among the
where Ql is the discharge
of the model.
by the multi-layer
Q term specified
in proportion
does not accommodate
as a group of single-layer
tapped
the discharge
formulated,
one layer
can be represented
each open to one of the
having
is presently
as a gr,oup
interconnection
and is thus
will
provide
is under development.
an inclomplete
an improved
Well
Input
IUNIT(2).
for
the Well
Packaae Inout
(WEL) Package is
read from the
unit
specified
in
FOR EACH SIMULATION
WELlAL
1. Data:
Format:
MXWELL IWELCB
110
110
FOR EACH STRESS PERIOD
WELlRP
2. Data:
Format:
ITMP
110
3. Data:
Format:
Layer
Row
Column
Q
110
110
110
F1O.O
(Input item 3 normally
consists
of one record for
If ITMP is negative
or zero, item 3 is not read.)
Explanation
Input
of Fields Used in
Instructions
MXWELL--is
the maximum number of wells
IWELCB--is
a flag
ITMP--is
used at any time.
number.
If
IWELCB > 0, it is the unit number on which cell-by-cell
flow
terms will
be recorded whenever ICBCFL (see Output
Control)
is set.
If
IWELCB = 0, cell-by-cell
If
IWELCB < 0, well
a flag
flow
recharge
will
terms
will
Column--is
the
from the
last
period
ITMP -> 0, ITMP will
be the number of wells
current
stress period.
layer
data
stress
If
Row--is
whenever
or recorded.
ICBCFL is set.
and a counter.
ITMP < 0, well
the
not be printed
be printed
If
Layer--is
--is
and a unit
each well.
number of the model cell
row number of the model cell
that
the column number of the model cell
A positive
the volumetric
recharge rate.
and a negative
value indicates
discharge.
8-3
that
will
active
contains
contains
that
value
be reused.
during
the
the well.
the well.
contains
indicates
the well.
recharge
.
i
8-4
Module Documentation
The Well
Package (WELl)
by the MAIN program.
consists
The modules
WELlAL
Allocates
WELlRP
Reads location
rate)
the
Package
modules,
all
of which
are called
are:
the list
and Q value
all
of wells
(WELL).
(discharge
or recharge
wells.
Q is entered
discharge
Well
of four
space for
for
Note:
for
as a negative
and as a positive
number for
number for
well
well
recharge.
WELlFM
WELlBD
Subtracts
Q values
from the term
containing
pumping wells.
Calculates
the
recharge
rates
and accumulated
to or discharge
by pumping wells.
8-5
RHS for
from the flow
each cell
volume of
system
Narrative
This
module allocates
The X array
tables,
lists,
1.
cell-by-cell
list
flow
unallocated
4.
equal
should
in the
the
each cell--row,
Print
5.
the
list
of wells.
space is allocated
the
package
and initialize
for
NWELLS (a
maximum number of wells)
flow
terms
or a flag
and IWELBD
indicating
that
be printed).
will
point
to ISUM, which
Calculate
the
MXWELL (the
cell-by-cell
terms
element
for
to store
number of wells).
Set LCWELL, which
(WELL),
values
the
number for
3.
X array
of memory space from which
Read and print
unit
space in the
a message identifying
containing
2.
Module WELlAL
and arrays.
Print
counter
(the
is a pool
for
to the
first
is currently
element
pointing
in the well
to the
first
X array.
amount of space needed for
column,
layer,
number of elements
the well
and rate)
in the
list
and add it
X array
(four
to
ISUM.
used by the Well
Package.
If
6.
(ISUM) is
warning
the
greater
that
7.
pointer
the
than
X array
to the
lowest
the length
will
unallocated
of the
X array
have to be enlarged.
RETURN.
8-8
element
(LENX),
in the X array
print
a message
Flow Chart
for
Module WELlAL
MXWELL is the maximum number
of wells that will
be active
at any one time during the
simulation.
IWELCB is a flag
number.
and a unit
If IWELCB > 0, it is the unit
number on which cell-by-cell
flow terms will
be recorded
whenever ICBCFL is set.
IDENTIFYING
If IWELCB = 0, cell-by-cell
flow terms will
not be
printed
or recorded.
2
READ MXWELL
AND IWELCB
If IWELCB < 0, well recharge
will
be printed
whenever
ICBCFL is set.
LCWELL is a location
pointer
the first
storage location
occupied by the well list.
to
SET LCWELL
EOUAL TO ISUM
ISUM is the location
of the
lowest unallocated
storage
location
in the X array.
ADD THE AMOUNT
OF SPACE NEEDED
FOR WELLS TO ISUM
X array is the pool of memory
space allocated
for storing
specific
tables,
arrays,
and
lists.
LENX is
the size
of the X array.
PRINT MESSAGES
SHOWING HOW MUCH
OF THE X ARRAY HAS
BEEN ALLOCATED
IF ISUM IS LARGER
THAN LENX, PRINT A
WARNING MESSAGE
8-7
SUBROUTINE WELlAL (ISUM,LENX, LCWELL,MXWELL,NWELLS,IN,
IWELCB)
1
IOUT,
C
C-----VERSION 1538 12MAY1987 WELlAL
C
C
C
********************~*****************************~**********~~****
ALLOCATE ARRAY STORAGE FOR WELL PACKAGE
*******~******************************************~*****~****~~~***
:
C
C
C
Cl----
SPECIFICATIONS:
--------------------------------------------------------------,-----------------------------------------------------------------,----
IDENTIFY PACKAGE AND. INITIALIZE NWELLS
WRITE(IOUT,l)IN
1 FORMAT(lHO,‘WELl -- WELL PACKAGE, VERSION1, 9/l/87',
1' INPUT READ FROM',131
NWELLS=O
C
c2--(32---
READ MAX NUlvBER OF WELLS AND
UNIT OR FLAG FOR CELL-BY-CELL FLOW TERMS.
READtIN,
MXWELL,IWELCB
2 FORMAT(2110)
WRITE(IOUT,31 MXWELL
3 FORMAT(lH r ‘MAXIMUM OF’ rI5,’
WELLS’ 1
IF(IWELCB.GT.0)
WRITE(IOUT,9) IWELCB
9 FORMATtlX, ‘CELL-BY-CELL FLOWS WILL BE RECORDEDON UNIT' ,131
IF(IWELCB.LT.0) WRITE(IOUTt8)
8 FORMAT(lX,‘CELL-BY-CELL
:3 ------SET
FLOWS WILL BE PRINTED WHEN ICBCFL NOT 0’)
LCWELL EQUAL TO LOCATION OF WELL
LIST IN X ARRAY.
LCWELL=ISUM
C
c4
------ADD
AMOUNTOF SPACE USED BY WELL
LIST TO ISUM.
ISP=4*MXWELL
IsuM=IsuM+IsP
:5 ------PRINT
NUM3ER OF SPACES IN X ARRAY USED BY WELL PACKAGE.
WRITE(IOUT,4) ISP
4 FORMATtlX, 18,' ELEMENTS IN X ARRAY ARE USED FOR WELLS’ 1
ISUMl=ISUM-1
WRITE(IOUT,S) ISUMl,LENX
5 FORMAT(lX,I8,' ELEMENTS OF X ARRAY USED OUT OF’,181
C
(3-w--
IF THERE ISN’T ENOUGHSPACE IN THE X ARRAY THEN PRINT
WARNING
MESSAGE.
c6 ------A
IF(ISUMl.GT.LENX)
WRITE(IOUT,6)
***X ARRAY MUST BE DIMENSIONED
LARGER***‘)
6 FORMATt1X, ’
C7------RETURN
RETURN
END
8-8
List
Variable
of Variables
for
Module WELlAL
Definition
Range
IN
Package
Primary
will
unit number from which
be read.
I OUT
Global
Primary
unit
ISP
Module
Number of words in the
I SUM
Global
Index number of the lowest
ISUMl
Module
ISUM-1.
I WELCB
Package
Flag and a unit number.
> 0, unit number on which cell-by-cell
flow terms
will
be recorded whenever ICBCFL is set.
= 0, cell-by-cell
flow terms will
not be printed
or recorded.
< 0, well recharge will
be printed
whenever ICBCFL
is set.
LCWELL
Package
Location
in the
WELL.
LENX
Global
Length of the X array in words.
This should alwaysbe
equal to the dimension of X specified
in the MAIN
program.
MXWELL
Package
Maximum number of wells
NWELLS
Package
Number of wells
number for
all
input
printed
X array
for
this
IOUT = 6.
output.
allocated
package
by this
module.
element in the X array which
has not yet been allocated.
When space is allocated
for an array,
the size of the array is added to ISUM.
X array
active
8-9
of the first
active
during
element
of array
at any one time.
the current
stress
period.
Narrative
This
1.
If
the
than
the
less
than
be reused.
If
number of wells
If
ITMP is
will
(b)
greater
the WELL list.
Read ITMP.
period
2.
Module WELlRP
module reads data to build
(a)
stress
for
ITMP is
zero,
Print
greater
the well
a message to that
than
or equal
read for
effect
to zero,
(NWELLS) in the
current
number of wells
(NWELLS) in the
number specified
data
stress
it
the
last
and RETURN.
is equal
to the
period.
current
as the maximum for
the
stress
period
simulation
is
(MXWELL),
STOP.
3.
Print
4.
If
bypass
5.
recharge
6.
the
there
further
well
number of wells
are no wells
in the
in the
current
current
stress
stress
period
period
(NWELLS).
(NWELLS),
processing.
For each well,
read and print
the
rate.
RETURN.
8-10
layer,
row, column,
and well
Flow Chart
for
Module WELlRP
ITMP is a flag and/or the
number of wells.
If it is
less than zero, it is a flag
which indicates
that the well
data from the last stress
period will
be reused.
If
it is greater than or equal
to zero, it is the number
of wells active
during the
current
stress period.
NWELLS is the number of wells
active
during the current
stress period.
MXWELL is the maximum number
of wells which will
be active
at any one time during the
simulation.
FOR EACH WELL
5
I
8-l 1
a
SUBROUTINE WELlRP(WELL,NWELLS,MXWELL,IN,IOUT)
C
C
C-----VERSION 1544 22DEC1982WELlRF’
*************************~************************************~~***
C
READ NEW WELL LOCATIONS AND STRESS RATES
C
**********************~***************************************~~***
C
C
SPECIFICATIONS:
C
”
DIMENSIONWELL(4,MXWELL)
--------------------------------------------------------------.----
C
C
Cl---
READ ITMPfNUMBER OF WELLS OR FLAG SAYING REUSE WELL DATA)
READ(IN,11 ITMP
1 FORMATtIlO)
IF(ITMP.GE.0) GO TO 50
C
ClA---
IF ITMP LESS THAN ZERO REUSE DATA. PRINT MESSAGE AND RETURN.
WRITE(IOUT,6)
6 FORMAT(lHO,'REUSING
WELLS FROM LAST STRESS PERIOD’)
RETURN
n
Zilb ----ITMP=>O. SET NWELLS EQUAL TO ITMP.
50 NWELLS=ITMP
IF(NWELLS.LE.MXWELL)
GO TO 100
C
c2---
NWELLS>MXWELL. PRINT MESSAGE. STOP.
WRITE(IOLJT,991NWELLSIMXWELL
99 FORMAT(lHO,'NWELLS('rI4,'1 IS GREATER THAN MXWELL(‘rI4,‘)‘)
STOP
C
NUMBER OF WELLS IN CURRENT STRESS PERIOD.
c3 ------PRINT
NWELLS
100 WRITE (IOUT,
2 FORMAT(lHO,lOX,I4,' WELLS’)
C
c4 ------IF
THERE ARE NO ACTIVE WELLS IN THIS STRESS PERIOD THEN RETURN
IF(NWELLS.EQ.0)
GO TO 260
C
C5-----READ AND PRINT LAYER,ROW,COLUMN AND RECHARGE RATE.
a
WRITE(IOUT,3)
3 FORMATf1H ,47X, ‘LAYER
1,48X,45(‘-‘))
DO 250 II=lrNWELLS
READ (IN,41 K,I,J,Q
ROW
COL
STRESS RATE
WELL NO. ‘I’
4 FORMAT(3110,FlO.O)
WRITE (IOUT,
K,I,J,Q,II
5 FORMAT(48X,I3,18,17,G16.5,18)
WELL(lrII)=K
WELL(2,111=1
WELL(3rII)=J
WELL(4rII)=Q
250 CONTINUE
C
c6 ------RETURN
260 RETURN
END
a
8-12
List
Variable
of Variables
for
Module WELlRP
Definition
Range
I
Module
Row number of cell
II .
Module
Index
IN
Package
Primary
will
unit number from which
be read.
I OUT
Global
Primary
unit
ITMP
Module
Flag or number of wells.
> 0, number of wells active during the current
stress period.
< 0, same wells active
during the last stress
will
be active during the current
stress
for
containing
well.
wells.
number for
all
input
printed
this
output.
package
IOUT = 6.
3
Module
Column number of cell
K
Module
Layer
MXWELL
Package
Maximum number of wells
NWELLS
Package
Number of wells
the
current
stress
9
Module
Rate at which the well adds water
(negative
for discharging
well).
to the
aquifer
WELL
Package
DIMENSION (4,MXWELL), For each well:
and recharge rate of the well.
number of cell
active
8-13
containing
for
containing
active
during
period
period.
well.
well.
at any one time.
layer,
period.
row, column,
Narrative
This
in which
1.
period,
module adds terms
If
NWELLS is
less
are no wells.
For each well
(a)
5 0),
representing
well
recharge
to the accumulator
If
(b)
If
the cell
the cell
of 0 from the accumulator
than
or equal
to zero
in the current
stress
RETURN.
in the WELL list:
bypass processing
3.
Module WELlFM
the term RHS is formulated.
there
2.
for
containing
on this
the well
well
containing
RHS for
and go on to the
the well
that
RETURN.
8-14
is external
cell.
is
active,
(IBOUND (IC,IR,IL)
next well.
subtract
the
value
B
1
SUBROUTINE WELlFMt NWELLS,MXWELL,RHS, WELL, IBOUND,
NCOL,NRw,NLAY)
C
C-----VERSION
:
C
C
C
1233 12MAY1987 WELlFM
***********************************************************~******
SUBTRACT Q FROM RHS
******************************************************************
SPECIFICATIONS:
-----------------------------------------------------------------DIMENSION FtiS(NCOL,NROW,NLAY)rWELL(4,MXWELL),
1
IBCXJND(NCOL,NROW,NLAY)
El ------IF
NUlrlBER OF WELLS <= 0 THEN RETURN.
IF(MJELLS.LE.0)
RETURN
l
:2 ------PROCESS
EACH WELL IN THE WELL LIST.
DO 100 L=lrNWELLS
IR=WELL(2rL)
IC=WELL(3rL)
IL=WELL(l,L)
G=WELL(4rL)
C
C2A---IF THE CELL IS INACTIVE THEN BYPASS PROCESSING.
IF(IBOUND(IC, IR,IL) .LE.O) GO TO 100
:2E+ ----IF
THE CELL IS VARIABLE HEAD THEN SUBTRACTQ FROM
C
THE RHS ACCUMULATOR.
RHStIC, IR, IL)=f?HS(IC, IR, IL14
100 CONTINUE
C
C3------RETURN
RETURN
END
8-15
List
Variable
of Variables
for
Module WELlFM
Definition
Range
IB OUND
Global
DIMENSION (Nc~L,NROW,NLAY),
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
IC
Module
Index
for
columns.
IL
Module
Index
for
layers.
IOUT
Global
Primary
IR
Module
Index for
rows.
L
Module
Index
wells.
MXWELL
Package
Maximum number of wells
NCOL
Global
Number of columns
NLAY
Global
Number of layers
NROW
Global
Number of rows in the
NWELLS
Package
Number of wells
current
stress
Q
Module
Rate at which the well adds water to the
(negative
for discharging
wells).
aquifer
RHS
Global
DIMENSION (NCOL,NROW,NLAY), Right hand side of the
finite-difference
equation.
RHS is an accumulation
of terms from several
different
packages.
WELL
Package
DIMENSION (4,MXWELL), For each well:
and recharge rate of the well.
unit
for
number for
all
in the
8-18
of
printed
active
in the
active
Status
each
cell,
output.
IOlJT = 6.
at any one time.
grid.
grid.
grid.
during
the
layer,
row,
period.
column,
Narrative
This module calculates
aquifer
and wells.
which
1. Clear
indicates
2.
If
for
rates
Module WELlBD
and volumes
transferred
between the
the rate accumulators
RATIN and RATOUT and the flag (IBD)
that cell-by-cell
flow terms should be recorded on a disk.
there
are no wells,
skip
down to step
7.
flow terms for wells will
be written
3. Determine if the cell-by-cell
on a disk.
They will
be if (1) this is the proper time step (ICBCFL is not
equal to zero),
(2) if the channel for well-budget
terms (IWELCB) is greater
than zero, and (3) if the number of wells (NWELLS) is greater than zero.
the
on a disk,
4. If budget terms are to be written
buffer
(BUFF) in which they will
be accumulated.
5.
not equal
set
If the number of wells in the current
stress period
to zero, then for each cell in the well list:
(a)
bypass further
If the cell
processing
containing
the well
of the cell.
is external
(b)
If the user has requested that cell-by-cell
(IWELCB < 0 and ICBCFL + 0), print the rate (0).
rate
(c)
If the budget terms
(Q) to the buffer
(BUFF).
If
Q is positive,
add it
to RATIN.
(e)
If
Q is negative,
add it
to RATOUT.
rates
Move RATIN and RATOUT into
the VBVL array
for
Move the well
budget
10.
Increment
budget-term
11.
RETURN.
the
term labels
counter
8-17
to VBNM for
printing
(MSUM).
length
printing
2 0),
be printed
add the flow
flow terms are to be recorded,
call
of buffer
(BUFF) onto the disk.
8. Add RATIN and RATOUT multiplied
by the time-step
accumulators
in the VBVL array for printing
by BASlOT.
9.
(NWELLS) is
(IBOUND(I,J,K)
are to be saved on a disk,
(d)
If the cell-by-cell
6.
UBUDSV to write the contents
7.
IBD = 1 and clear
module
by BASlOT.
to the
volume
by BASlOT.
Flow Chart for Module WELl BD
RATIN is an accumulator to which all flows
into the aquifer are added.
RATOUT is an accumulator to which all flows
out of the aquifer are added.
IBD is a flag which, if set, causes cell-by-cell
flow terms for well flow to be recorded.
BUFFER is an array in which values are stored
as they are being gathered for printing or
recording.
EXTERNAL: a cell is said to be external if it is
either no flow or constant head (i.e., an
equation is not formulated for the cell).
Q is the rate at which the well recharges the
aquifer. A discharging well is represented by
a negative rate.
IWELCB is a flag and a unit number.
If IWELCB > 0, it is the unit number on which
cell-by-cell flow terms will be recorded
whenever ICBCFL is set.
= 0, cell-by-cell
be printed or recorded.
If IWELCB
flow terms will not
If IWELCB < 0, well recharge rate will be
printed whenever ICBCFL is set.
ICBCFL is a flag.
If ICBCFL # 0, cell-by-cell flow terms will be
either printed or recorded (depending on
IWELCB) for the current time step.
MOVE LABELS
FOR BUDGET
8-18
1
SUBROUTINE WELlBD( NWELLS,MXWELL,VBNM,VBVL, MSUM,WELL, IBOUND, DELT,
NCOL,NROW,NLAY,KSTP, KPER, IWELCB,
ICBCFL,BUFF, IOUT)
C
C-----VERSION 1509
12MAY1987 WELlBD
******************************************~*************~*********
CALCULATE VOLUMETRIC
BUDGET FOR WELLS
~******~***~**********~*~*******~**~*~~*~********~*****~****~*****
C
C
C
C
C
SPECIFICATIONS:
----------_-------------------------------------------------------
C
CHARACTER*4 VBNM,TEXT
DIMENSION
VBNM(4,MSUM),VBVL(4,MSUM),WELL(4,MXWELL),
1
IBOUND(NCOL,NROW,NLAY)rBUFF(NCOL,NROW,NLAY~
DIMENSION
TEXT(4)
C
DATA TEXT(l)rTEXT(2)rTE>CT(3)rTE>CT(4)
/’
-----------------------------------------------------------------C
C
Cl ------CLEAR
RATIN AND RATOUT ACCUMULATORS.
‘,’
‘,’
W’r’ELLS’/
RATIN=O.
RATOUT=O.
C
IBD=O
c2----
l
IF THERE ARE NO WELLS DO NOT ACCUMULATEFLOW
IF(NWELLS.EQ.0) GO TO 200
C
c3------TEST
TO SEE IF CELL-BY-CELL FLOW TERMS WILL BE
IF(ICBCFL.EQ.0.OR. IWELCB.LE.0)GOTO 60
C
c4 ------IF
CELL-BY-CELL FLOWS WILL BE SAVED THEN CLEAR THE BUFFER.
IBD=l
DO50 IL=l,NLAY
DO50 IR=l,NROW
DO 50 IC=l,NCOL
BUFF(IC,IR,IL)=O.
50 CONTINUE
:5 ------PROCESS
WELLS ONE AT A TIME.
60 DO 100 L=l,NWELLS
IR=WELL(2,L)
IC=WELL(3rL)
IL=WELL(lrL)
Q=WELL(4rL)
C
C5A-m-wIF
RECORDED.
THE CELL
IS
EXTERNAL IGNORE
IT.
8-19
IF(IBOUND(IC,IR,IL).LE.O)GOTO
100
C
c5B----- PRINTTHE INDIVIDUALRATES IF REQUESTED(IWELCB<O).
IF(IWELCB.LT.O.AND.ICBCFL.NE.0)
WRITE(IOUT,900)(TEXT(N),N=1:~4),
1
KPER, KSTF’, L, IL I IR, ICI Q
WELL’ rI4r
PERIOD'rI3,' STEP',I3,'
900 FORMAT(lHOs4A4,’
RATE',G15.7)
CQL’rI4,’
1'
LAYER'rI3,' ROW ‘rI4r’
:5c -----IF
CELL-BY-CELL FLOWS ARE TO BE SAVED THEN ADD THEM TO BUFFER.
IF(IBD.EQ.l)
BUFF(IC,IR,IL)=BUFF(IC,IR,IL)+Q
IF(Q) 90,100,80
C
C5D-w-w-WMPINGRATE IS POSITIVEtRECHARGE).
ADD IT
80 RATIN=RATIN+Q
TO RATIN.
GO TO 100
C
C5E----- PUMPING
RATEIS NEGATIVEtDISCHARGE).
ADDIT TO RATOUT.
90 RATOUT=RATOUT-Q
100 CONTINUE
E6------IF CELL-BY-CELL FLOWS WILL BE SAVED CALL UBUDSV TO RECORD THEM
IF(IBD.EQ.l) CALL UBUDSV(KSTP,KPER,TEXT,IWELCB,BUFF,NCQL,NROW~
1
NLAY,IOUT)
C
C7------ MOVE RATES INTOVBVL FOR PRINTINGBY MODULEBASlOT.
200 VBVL(3,MSUM)=RATIN
VBVL(4rMSUM)=RATOUT
C
c8 ------MOVE
RATES TIMESTIME STEPLENGTH INTO VBVL ACCUMULATORS.
VBVL(l,MSUM)=VBVL(lrMSUM)+RATIN*DELT
VBVL(2rMSUM)=VBVL(2rMSUM)+RATOUT*DELT
C
c9 ------MOVE
BUDGET TERM LABELS INTO VBNM FOR PRINTING.
VBNM(lrMSUM)=TEXT(l)
VBNM(2rMSUM)=TEXT(2)
VBNM(3,MSUM)=TEXT(3)
VBNM(4,MSUM)=TEXT(4)
C
Cl()---
INCREMENT BUDGET TERM COUNTERtMSUM).
MSUM=MSUMtl
C
Cll-----RETURN
RETURN
END
8-20
List
D
D
Variable
of Variables
Module WELlBD
for
Definition
Range
BUFF
Global
DIMENSION (NCOL,NROW,NLAY), Buffer
used to accumulate
information
before printing
or recording
it.
DELT
Global
Length
IBD
Module
Flag.
= 0, cell-by-cell
flow
not be recorded.
z 0, cell-by-cell
flow
be recorded.
of the current
time
step.
terms
for
this
package will
terms
for
this
package will
IBOUND
Global
DIMENSION (NCOL,NROW,NLAY), Status
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
IC
Module
Index
ICBCFL
Global
Flag.
= 0, cell-by-cell
flow terms will
not be recorded
or printed
for the current
time step.
f 0, cell-by-cell
flow terms wil-1 be either
printed
or recorded (depending on IWELCB) for the
current
time step .
IL
Module
Index
IOUT
Global
Primary
IR
Module
Index
I WELCB
Package
Flag and a unit number.
> 0, unit number on which cell-by-cell
flow terms
will
be recorded whenever ICBCFL is set.
= 0, cell-by-cell
flow terms will
not be printed
or recorded.
< 0, well recharge rate will
be printed
whenever
ICBCFL is set.
KPER
Global
Stress
KSTP
Global
Time step
period.
counter.
L
Module
Index
wells.
MSUM
Global
Counter
MXWELL
Package
Maximum number of wells
for
columns.
for
layers.
unit
for
number for
a 11 printed
output.
IOUT = 6.
rows.
period
for
of each cell.
for
counter.
budget
8-21
Reset
entries
at the
start
and labels
active
of each stress
in VBVL and VBNM.
at any one time.
List
Variable
of Variables
for
Module WELlBD (Continued)
Definition
Range
NCOL
Global
Number of columns
NLAY
Global
Number of layers
NROW
Global
Number of rows in the grid.
NWELLS
Package
Number of wells
current
stress
Q
Module
Rate at which the well adds water to the
(negative
for discharging
wells).
aquifer
RATIN
Module
Accumulator
wells.
for
the total
flow
into
RATOUT
Module
Accumulator
wells.
for
the total
flow
out
TEXT
Module
Label
VBNM
Global
DIMENSION (4,20),
budget.
VBVL
Global
DIMENSION (4,20),
Entries
for the volumetric
budget.
For flow component N, the values in VBVL are:
(l,N)
,"&,for
the current
time step into the flow
WELL
Package
in the grid.
in the
active
to be printed
grid.
during
the
or recorded
Labels
for
the current
with
entries
time
the
flow
of the
the
field
flow
field
array
data.
in the
from
into
volumetric
(2,N)
l?;-t;dtor
.
(3,N)
(4,N)
Voluml into the flow field
during simulation.
Volume out of the flow field
during simulation.
DIMENSION (4,MXWELL), For each well:
and recharge rate of the well.
8-22
step
period.
out of the
layer,
flow
row, column,
CHAPTER9
DRAIN PACKAGE
Conceptualization
The Drain
Package is designed
as agricultural
portional
drains,
head or elevation,
this
are actually
the
run only
partially
normally
drain
full,
so that
(h i,j,k)
di,j,k
characterize
the
Prevails
head hi,j,k
vertical
plane,
as the drain
pattern
forms
component
that
pro-
and some fixed
elevation,
The discussion
the features
in
to be simulated
there
exists
one part
a radial
conductivity
used for
i,j,k--because
in that
of the
for
within
region
differs
presence
9-l
The
does not
area in which
flow
pattern
steeper
flow
An additional
vicinity
of the drain
from the
average
of foreign
in the
head gradients
converging
hi,j,k-di,j,k.
immediate
and is
itself.
and the
this
by the model
the cell,
the drain--it
or semiradial
of the head difference
the hydraulic
is approximately
by progressively
in the
concepts
is assumed to
from the drain
within
The head loss
may occur
value
Between the drain
characterized
is approached.
The drain
the drain
an average
locally,
illustrating
The head computed
at some distance
only
a cell,
di,j,k.
as a whole.
normally
through
head within
is actually
of head loss
cell
at a rate
is above that
level.
in the model.
elevation,
prevails
cell
section
of drains
assumed to prevail
head,
below that
such
drains.
simulation
i,j,k
of features
from the aquifer
on the assumption
to the median drain
cell
the effects
head in the aquifer
head falls
39 shows a cross
underlying
remove water
as the
if
agricultural
Figure
for
so long
is phrased
to simulate
between the head in the aquifer
have no effect
section
equal
which
to the difference
but which
and Implementation
material
value
around
if
Drain
Pipe
- - - - -’ \ \ --4 0 0
Line of
Equal Head
-----
Figure 39.-Cross section through cell i,j,k illustrating
head loss in convergent flow into drain.
9-2
di,j,k
the drain
pipe,
or channel-bed
Finally,
40).
upon the
which
head losses
number and size
those
openings
material
occur
of the
in the case of an open drain
through
the wall
openings
may be blocked
in the
by chemical
of a drain
pipe,
pipe,
(figure
depending
and the degree
precipitates,
to
plant
roots,
etc.
The three
flow
through
drain,
material
and flow
which
that
processes
discussed
of different
through
conductivity
the wall
the discharge
losses,occur
as proportional
i,j,k
the total
to QD.
head loss
in the Drain
Package.
function
is described
by the equation
'
ai,j4k(h'i,j,k
conductance
of cell
describing
i,j,k
in which
That is,
it
as well
the
system--
Because these
may also
has been assumed that
head
be taken
CDi,j,k
of equation
(69)
all
of the head loss
the
head hi,j,k
drain
for
hi,j,k
> di,j,k
(64)
for
hi,j,k
5 di,j,k
(70)
is a lumped (or equivalent)
between the drain
and the
can be the assumed to prevail.
of the convergent
as on the character
the
pair
- di,j,k)
depends on the characteristics
drain,
head losses
QD, through
hi,j,k-di,j,k
QDi,j,k = 0
The coefficient
around the
generate
the drain.
the drain,
This has been done in the method of simulation
embodied
QDi,j,k
into
toward
immediately
to the discharge,
from cell
in series,
flow
of the drain--each
may be assumed proportional
is,
above--convergent
flow
pattern
of the dra in itself
istics
toward
and its
region
it
the
immediate
environment.
One could
equations
for
the equivalent
attempt
to calculate
conductance
series
for
values
the three
conductance.
flow
for
CD by developing
processes,
The conductance
9-3
for
and then
approximate
calculate
each process
would
be
(4
/
Drain Pipe
Open
Drain
(W
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Figure 40.-Factors
affecting head loss immediately
around a drain: (a) buried drain pipe in
backfilled ditch and (b) open drain.
9-4
based on the
vary
formulation
significantly
so no general
depending
formulation
most situations
that
the
material,
of the drain
hydraulic
pipe
h-d is
calibration
(69)
and the
not accurately
known,
the
(figure
excluded,
and positive
values
flow
the drain.
Package could
in fact
and the
it
as defined
to that
for
that
flow
flow
of QD have been taken
With proper
selection
be utilized
to perform
adjusted
is more
equation
during
model
of QD to model calculated
hi,j,k
36) except
of
number and size
In practice,
CD is usually
is similar
distribution
of QD and h-d using
to match measured values
function
around
materials,
materials.
in
information
material,
the amount of clogging
CD from measured values
Also,
head distribution
of fill
of the clogging
simulated,
here.
detailed
conductivity
aquifer
into
require
hydraulic
41 shows a graph of QD vs.
and (70);
stream
would
such as detailed
openings,
being
CD is presented
formulation
The formulations
system
near the drain,
in order
Figure
drain
conductivity
common to calculate
If
equation.
hydraulic
conductivity
(6%.
flow
specific
calculating
available,
aquifer
fill
on the
for
a specific
is not usually
the drain,
of a one-dimensional
into
by equations
between
the
a surface
aquifer
is
as corresponding
of coefficients,
the
values.
functions
to
the River
of the Drain
Package.
Because QDi,j,k
i,j,k,
it
cell
affected
must be subtracted
elevation.
whether
to
in equation
by a drain,
This
HCOFi,j,k
as the matrix
provided
drain
(equation
equations
has been taken
from the
is accomplished
head exceeds
(69)
(26))
left
side
of equation
the head hi,j,k
in the Drain
elevation,
and if
and adding
are assembled.
9-5
as a flow
(24)
for
each
is above the drain
Package by testing
so, by adding
the term
out of cell
-CDi,j,kdi,j,k
to determine
the term
-ai,j,k
to RHSi,j,k,
d
Figure 41.-Plot of flow, QD, into a drain as a function
of head, h, in a cell where the elevation of the drain is
d and the conductance is CD.
9-6
Drain
Input
IUNIT(3).
to the
Drain
Package Input
(DRN) Package is
read from the unit
specified
in
FOR EACH SIMULATION
DRNlAL
MXDRN
110
Data:
Format:
1.
IDRNCB
I10
FOR EACH STRESS PERIOD
DRNlRP
2.
Data:
Format:
ITMP
110
3.
Data:
Format:
Layer
110
co1
110
Row
110
Cond
F10.0
Elevation
F10.0
(Input item 3 normally
consists
of one record for each drain.
If ITMP is negative
or zero, item 3 will
not be read.)
Explanation
Input
MXDRN--is
the maximum number of drain
IDRNCB--is
ITMP--is
of Fields Used in
Instructions
a flag
and a unit
cells
active
at one time.
number.
If
IDRNCB > 0, it is the unit number on which cell-by-cell
flow
terms will
be recorded whenever ICBCFL (see Output
Control)
is set.
If
IDRNCB = 0, cell-by-cell
recorded.
If
IDRNCB < 0, drain leakage for
ICBCFL is set.
a flag
flow
terms
will
each cell
not be printed
will
be printed
or
whenever
and a counter.
If
ITMP c 0, drain
If
ITMP 10,
data
from the
ITMP will
be the
stress period.
last
stress
number of drains
9-7
period
active
will
be reused.
during
the current
Layer--is
Row--is
the
the
Column--is
Elevation--is
layer
number of the cell
row number of the cell
the
containing
column number of the cell
elevation
Condo-is the hydraulic
and the drain.
containing
the
drain.
the drain.
containing
the drain.
of the drain.
conductance
of the interface
9-8
between the aquifer
9-9
Module Documentation
The Drain
called
Package (DRNl)
by the MAIN program.
DRNlAL
DRNlRP
consists
drain
list
Package
modules,
all
of which
are:
an array
that
contains
(DRAI).
Reads location,
Adds the terms
Drain
of four
space for
conductance
DRNlFM
the
The modules
Allocates
the
for
drain
elevation,
of each cell
-CDi,j,k
the accumulators
and drain
containing
a drain.
and -CDi,j,kdi,j,k
HCOFi,j,k
to
and RHSi,j,k,
respectively.
DRNlBD
Calculates
drainage
the
rates
from the
9-10
and accumulated
flow
system.
volume of
are
Narrative
This
module allocates
Print
1.
for
Module DRNlAL
space in the
a message identifying
the
X array
to store
package
the
list
and initialize
of drains.
NDRAIN
(number of drains).
Read and print
2.
(the
file
that
cell-by-cell
saving
flow
equal
to ISUM (which
maximum number of drains)
cell-by-cell
terms
Set LCDRAI (which
3.
list)
number for
MXDRAN (the
should
will
terms
or a flag
indicating
be printed).
point
points
flow
and IDRNCB
to the
first
to the first
element
unallocated
in the drain
element
in the
X array.
4.
values
Calculate
for
the
amount of space needed for
each drain--row,
column,
layer,
drain
the drain
elevation,
list
(five
and drain
conductance).
5.
Print
the
number of elements
in the X array
Package.
6.
RETURN.
9-11
used by the Drain
Flow Chart
for
Module DRNlAL
(TiiC)
-L
NDRAIN is the number of drains
being simulated
at any given
time.
MXDRN is
drains
IDRNCB is
the maximum number of
simulated.
a flag
and a unit
number.
1
If IDRNCB > 0, it is the unit
number on which cell-by-cell
flow terms will
be recorded
whenever ICBCFL is set.
If IDRNCB = 0, cell-by-cell
terms will
not be printed
recorded.
1
IDENTIFY
PACKAGE ANC i
INITIALIZE
NUMBER OF
DRAINS (NDRAIN)
I
flow
or
If IDRNCB < 0, drain leakage for
each drain will
be printed
whenever
ICBCFL is set.
LCDRAI is the location,
in the X
array,
of the list
of drain data
(DRAI).
FIRST ELEMENIOF DRAIN LIST
9-12
SUBROUTINE DRNl AL (ISUM,LENX, LCDRAI, NDRAIN, MXDRN,IN,
1
IDRNCB)
IOUT,
C
C-----VERSION 1604 12MAY1987 DRNlAL
c”
C
C
C
C
C
C
Cl-----
**********************************************~*******************
ALLOCATE ARRAY STORAGE FOR DRAINPACKAGE
*****************************~************************************
SPECIFICATIONS:
---------------------~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-----------~---------~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
IDENTIFY PACKAGE AND INITIALIZE NDRAIN.
WRITE(IOUT,l)IN
1 FORMAT(lHO,‘DRNl -- DRAIN PACKAGE, VERSION1, 9/l/87',
1' INPUT READ FROM UNIT',131
NDRAIN=O
C
c2---
READ 8, PRINT MXDRN 8 IDRNCBtUNIT8 FLAG FOR CELL-BY-CELL FLOW)
READtIN, MXDRN,IDRNCB
2 FORMAT(2110)
WRITE(IOUT,3) MXDRN
3 FORMATtlH r'MAXIMUMOF'rI5,'
DRAINS')
IF(IDRNCB.GT.0) WRITE(IOUT,9) IDRNCB
9 FORMAT(lX,‘CELL-BY-CELL
FLOWSWILL BE RECORDEDON UNIT',131
IF(IDRNCB.LT.0) WRITE(IOUT,8)
8 FORMAT(lX,‘CELL-BY-CELL
FLOWS WILL BE PRINTEDWHEN ICBCFL NOT 0’)
C
C3------ SET LCDRAIEQUAL TO ADDRESS OF FIRST UNUSED SPACE IN X.
LCDRAI= ISUM
C
c4------CALCULATE AMOUNTOF SPACE USED BY THE DRAIN PACKAGE.
ISP=5*MXDRN
IsuM=IsuMtIsP
:5 ------PRINT AMOUNTOF SPACE USED BY DRAIN PACKAGE.
WRITE(IOUT,4) ISP
4 FORMAT(lXII8,’
ELEMENTS IN X ARRAY ARE USED FOR DRAINS')
ISUMl=ISUM-1
WRITE(IOUT,5) ISUM1,LENX
5 FORMATt1X, 18,' ELEMENTS OF X ARRAY USED OUT OF’, 18)
IF(ISUMl.GT.LENX) WRITE(IOUT,6)
***X ARRAY MUST BE DIMiNSIONEDLARGER***‘)
6 FORMATt1X, ’
C
C6------RETURN
RETURN
END
9-13
List
Variable
IDRNCB
of Variables
for
Module DRNlAL
Definition
Range
Package
Flag
and a unit
number.
> 0, unit number on which cell-by-cell
flow terms
will
be recorded whenever ICBCFL is set.
= 0, cell-by-cell
flow terms will
be neither
printed
nor recorded.
< 0, leakage for each drain will
be printed.
IN
Package
Primary
will
unit number from which
be read.
IOUT
Global
Primary
unit
ISP
Module
Number of words
module.
ISUM
Global
Index number of the lowest element in the X array
number for
all
input
printed
in the X array
for
this
output.
allocated
package
IOUT = 6.
by this
which has not yet been allocated.
When space
is allocated
for an array,
the size of the
array is added to ISUM.
1.
ISUMl
Module
ISUM -
LCDRAI
Package
Location
in the
DRAI.
LENX
Global
Length
X array
of the X array
of the
first
element
of arra.y
in words.
This should always
of X specified
in the
be equal to the dimension
MAIN Program.
MXDRN
Package
Maximum number of drains
NDRAIN
Package
Number of drains
period.
9-14
active
active
during
at any one ti'me.
the
current
stress
Narrative
for Module DRNlRP
This module reads data to build
Read ITMP.
1.
that
drain
2.
the last
stress
list.
ITMP is the number of drains
data from the previous
Test ITMP.
the drain
If
period
stress
period
be reused.
Print
indicating
should be reused.
ITMP is less than zero,
will
or a flag
the drain
data read for
a message to that
effect
and RETURN.
3.
If
ITMP is greater
drains
for this
current
stress
4.
stress
period
NDRAIN is greater
5.
Print
6.
See if
period
7.
period.
is the number of
(NDRAIN) in the
equal to ITMP.
(NDRAIN) in the current
as the maximum for the simulation
stress
period
(MXDRN). If
than MXDRN, STOP.
the number of drains
there
in the current
are any drains.
If there
(NDRAIN = 0), bypass further
Read and print
the layer,
drain
stress
RETURN.
9-15
period
are no drains
(NDRAIN).
in the current
processing.
row, column, elevation,
each drain.
8.
it
Set the number of drains
Compare the number of drains
to the number specified
stress
than or equal to zero,
and conductance
for
Flow Chart
for
Module DRNlRP
ITMP is both a flag and a
counter.
If it is greater
than or equal to zero, it is
the number of drains to be
simulated
during the current
stress
period.
If it is less
than zero, it indicates
that
the drains simulated
in the
last stress period should be
simulated
in the current
stress
period.
MXDRN is the maximum number of
drains to be simulated.
STOP
DATA RECORD
9-16
SUBROUTINE DRN1RP(DRAI,NDRAIN,MXDRN,IN,IOUT)
C
C
C-----VERSION
1603 25APR1983 DRNlRF’
******************************************************************
READ DRAIN LOCATIONS,ELEVATIONS, AND CONDUCTANCES
******************************************************************
C
C
E
C
SPECIFICATIONS:
”
DIMENSION DRAI(5,MXDRN)
------------------------------------------------------------------
C
ITMPtNUMBER OF DRAIN CELLS OR FLAG TO REUSE DATA)
El ------READ
READtIN,
ITMP
8 FORMATtIlO)
ITMP
IF(ITMP.GE.0) GOTO 50
:2------TEST
C
(32/J----
IF ITMP<OTHEN REUSE DATA FROM LAST STRESS PERIOD.
WRITE(IOUT,7)
7 FORMAT(lHO,‘REUSING DRAINS FROM LAST STRESS PERIOD')
RETURN
C
C3------
IF ITMF=>O THEN IT IS THE NUMBEROF DRAINS.
50 NDRAIN=ITMP
IF(NDRAIN.LE.MXDRN) GO TO 100
C
NDRAIN>MXDRNTHEN STOP
c4 ------IF
WRITE(IOUT,99) NDRAIN,MXDRN
99 FORMAT(lHOr’NDRAIN(‘rI4,‘)
IS GREATER THAN MXDRN(‘rI4,‘)‘)
STOP
C
c5 ------PRINT
NUMBEROF DRAINSIN THIS STRESS PERIOD.
100 WRITE(IOUT,l) NDRAIN
1 FORMAT(lHO,//lX,I5,' DRAINS')
E6------IF
THERE ARE NO DRAINS THEN RETURN.
IF(NDRAIN.EQ.0)
GO TO 260
AND PRINT DATA FOR EACH DRAIN,
:7 ------READ
WRITE(IOUT,S)
3 FORMATtlHD,15X, ‘LAYER’ ,5X, ‘ROW’ ,5X
1,‘COL
ELEVATION
CONDUCTANCE DRAIN NO. ‘/1X,15X,60(
DO 250 II=lrNDRAIN
READ (IN,41 K,I,J,DRAI(4,II)rDRAI(5rII)
4 FORMAT(3110,2FlO.O)
WRITE (IOUT,
K,I,J,DRAI(4rII)rDRAI(5rII)rII
5 F0RMAT(1X,15X,14,19,18,G13.4,G14.4,18)
DRAI(l,II)=K
DRAI(2,11)=1
DRAI(3,II)=J
250 CONTINUE
C
c8------RETURN
260 RETURN
C
END
9-17
I-‘)
1
List
of Variables
for
Module DRNlRP
Definition
Variable
Range
DRAI
Package
DIMENSION (S,MXDRN), For each drain:
layer,
row,
head in drain,
and conductance
into drain.
I
Module
Index
II
Module
Index for
IN
Package
Primary
will
unit number from which
be read.
IOUT
Global
Primary
unit
I TMP
Module
Flag
for
colulmn,
rows.
drains.
number for
all
input
printed
for
output.
this,package
IOUT = 6.
or number of drains.
during the current
-> 0, number of drains active
stress period.
< 0, same drains active
during the last stress
period will
be active
during the current
stresis
period.
J
Module
Index
K
Module
Index for
MXDRN
Package
Maximum number of drains
NDRAIN
Package
Number of drains
for
columns.
layers.
9-18
active
active
during
at any one time.
the
current
str'lass
period.
Narrative
This
module adds terms
for
represent
Module DRNlFM
ing dra in leakage
to the
accumulators
HCOF and RHS.
If
1.
there
'For
Determine
4.
If
the
drain
than
in the drain
the column
cell
or equal
(IC),
is external
If
the
cell
6.
If
the
head in the aquifer
7.
drain
accumulator
8.
there
is
is
internal,
no drain
(IBOUND(IC,
(EL),
in the current
stress
period,
add the term
RHS and the term
DO STEPS 3-7.
and layer
IR,
(IL).
IL) 5 0),
bypass
processing
drain.
get the drain
leakage.
If the head in the aquifer
list,
row (IR),
and go on to the next
5.
drain,
to zero
RETURN.
each drain
3.
on this
the
less
are no drains.
2.
the
NDRAIN is
(HHNEW) is
data
(elevation
and conductance).
greater
than
the elevation
of
greater
than
the elevation
of
RETURN.
(HHNEW) is
-C*EL (C is the drain
conductance)
-C to the accumulator
HCOF.
RETURN.
9-19
to the
Flow Chart
RHS is an accumulator
in
which the right
hand side
of the equation
is
formulated.
HCOF is an accumulator
which the coefficient
head in the cell is
forrmlated.
for
Module DRNlFM
pi--)
in
of
YES
FOR EACH DRAIN
GET DRAIN
ELEVATION
AND
CONDUCTANCE
YES
ADD TERMS
TO RHS AND
HCOF FOR THIS
SUBROUTINE DRNlFMt NDRAIN, MXDRN,DRAI,HNEW,HCOF,RHS,
IBOUND,
NCOL,NROW,NLAY)
1
C
1030 lOAPR1985
DRNlFM
C-----VERSION
C
**************************,****************************************
C
ADD DRAINFLOW TO SOURCETERM
C
******************************************************************
C
C
C
SPECIFICATIONS:
-----_----_------------------------------------------------------DOUBLE FRECI
SIONHNEW
C
C
DIMENSION
DRAI(5rMXDRN)rHNEW(NCOL,NRW,NLAY)r
1
RHS(NCOL,NROW,NLAY)rIBOUND(NCOLINROWINLAY),
1
HCOF(NCOL,NROW,NLAY)
C
C
Cl----
C
C2----
------------------------------------------------------------------
IF NDRAIN<=O THERE ARE NO DRAINS.
IF(NDRAIN.LE.0)RETURN
RETURN
PROCESS
EACHCELLIN THEDRAINLIST
DO 100 L=l,NDRAIN
:3 ------GET COLUMN, ROWAND LAYER OF CELL CONTAINING
DRAIN.
IL=DRAI(lrL)
IR=DRAI(ZrL)
IC=DRAI(3rL)
C
c4-------IF THE CELL IS EXTERNAL SKIP IT.
IF(IBOUND(IC,IR,IL).LE.O) GO TO 100
:5 -------IF
THECELLIS INTERNAL
GETTHEDRAINDATA.
EL=DRAI(4rL)
C
C6---
HHNEW=HNEW(IC,IR,IL)
IF HEAD IS LOWERTHANDRAINTHEN
IF(HHNEW.LE.EL) GO TO 100
SKIP THIS CELL.
IS HIGHERTHANDRAIN.ADD TERMS TO
C=DRAI(5rL)
HCOF(IC,IR,IL)=HCOF(IC,IR,IL)-C
RHS(IC,IR,IL)=RHS(IC,IR,ILbC*EL
100 CONTINUE
&----+JJ~
:7 ------HEAD
RETURN
END
9-21
RHS AND HCOF.
List
Variable
of Variables
for
Module DRNlFM
Definition
Range
C
Module
Conductance
into
the drain.
DRAI
Package
DIMENSION (S,MXDRN), For each drain:
head in the drain
layer,
row, column,
into the drain.
and conductance
EL
Module
Elevation
of the drain
HCOF
Global
DIMENSION (NCOL,NROW,NLAY), Coefficient
cell
(J,I,K)
in the finite-difference
HHNEW
Module
Head in the
HNEW
Global
DIMENSION (NCOL,NROW,NLAY), Most recent estima,te
HNEW changes at each iteration.
in each cell.
IBOUND
Global
DIbiENsION (NC~L,NR~W,NLAY),
cell
(head in the
containing
c 0, constant-head
= 0, inactive
cell
> 0, variable-head
the
drain).
of head in the
equation.
drain.
Status
of head
0f each cell.
cell
cell
IC
Module
Index for
columns.
IL
Module
Index for
layers.
IOUT
Global
Primary
IR
Module
Index for
MXDRN
Package
Maximum number of drains
active
NCOL
Global
Number of columns
grid.
NDRAIN
Package
Number of drains
active
during
NLAY
Global
Number of layers
in the
grid.
NROW
Global
Number of rows in the
RHS
Global
DIMENSION (NCOL,NROW,NLAY), Right hand side of the
finite-difference
equation.
RHS is an accumulation
of terms from several
different
packages.
unit
number for
all
printed
output.
IOUT = 6.
rows.
9-22
in the
at any one time'.
the
current
stress
period.
grid.
Narrative
This module calculates
for
Module DRNlBD
rates
and volumes
cell-by-cell
flow-term
transferred
between the
aquifer
and drains.
Initialize
1.
accumulator
zeros
are no drains
the budget
Test
They will
is
there
into
3.
to see if
proper
time
are not needed for
terms
(IBD)
terms
will
and clear
for
(IBD)
and the
rate
step
drains
4.
For each drain,
5.
Determine
6.
If
the
flow
down to step
12 and put
are to be saved on disk.
of the following
this
do steps
conditions
simulation
they
will
and layer
flow
(IDRNCB 2 0).
(1) this
terms
If
cell-by-cell
flow-term
be accumulated
3-11 accumulating
column,
hold:
(2) cell-by-cell
set the cell-by-cell
drains,
in which
row,
terms
(ICBCFL = 0) or
during
buffer
skip
drains.
either
be saved for
the
(NDRAIN 5 0),
cell-by-cell
not be saved if
not the
flow
flag
(RATOUT).
If
2.
the
flows
of the cell
flag
(BUFF).
into
drains.
containing
the
drain.
processing
the
cell
of this
is external
Get the drain
a.
If
further
,K),
2 0),
bypass
further
drain.
7.
bypass
(IBOUND(I,J
parameters
the head in the cell
processing
of this
from the
is
less
drain.
9-23
drain
than
list.
the elevation
of the drain,
If
9.
drain,
the head in the cell
set
"Q" equal
elevation
is
greater
to the conductance
(EL) minus the head in the
Add Q to the
accumulator
than
the elevation
of the drain
cell
of the
(C) times
(HHNEW) (Q = C*(EL
RATOUT to get the total
flow
the drain
- HHNEW!).
from the
aquifer
into
drains.
10.
If
the
ICBCFL # 0),
11.
If
print
the
to the buffer
12.
they
are,
13.
cell-by-cell
print
printing
terms
are to be printed
flow
terms
for
(IDRNCB < 0 and
Q.
cell-by-cell
drains
are to be saved,
add Q
(BUFF).
See if
call
the cell-by-cell
module UBUDSV to
Move RATOUT into
RATOUT multiplied
for
flow
terms
record
the
the VBVL array
by the time-step
by BASlOT.
flow
Move the drain
buffer
for
length
are to be saved
(BUFF) onto
printing
to the
(IBD = 1).
disk.
by BASlOT.
volume accumulator
budget-term
labels
Add
in VBVL
to VBNM fol*
by BASlOT.
14.
the Basic
15.
Increment
the
Package for
budget-term
a detailed
counter
explanation
RETURN.
9-24
(MSUM).
See the
If
section
in
of VBVL, VBNM, and MSUM.
flow
Chart
for
Module DRNlBD
IBD is a flag
which, if set,
causes cell-by-cell
flow
terms for drains to be
recorded.
ACCUMULATORS
EXTERNAL: a cell is said to be
external
if it is either
no
flow or constant
head (i.e.,
an equation
is not formulated
for the cell).
BUFFER is an array in which
values are stored as they
are being gathered for
printing
or recording.
RATOUT is an accumulator
to
which all flows out of the
aquifer
are added.
Q is the negative
to a drain.
EL is the elevation
drain.
IDRNCB is a flag
number.
of discharge
GET DRAIN
PARAMETERS
FROM DRAIN
LIST
of the
and a unit
c,=C (EL-HHNEW,
If
IDRNCB > 0, it is the unit
number on which cell-by-cell
flow terms will
be recorded
whenever ICBCFL is set.
11
IF CELL-BY-CELL
FLOW
TERMS ARE TO BE
RECOR;;FF;;D
0 TO
If IDRNCB = 0, cell-by-cell
flow terms will
not be printed
or recorded.
r-
If IDRNCB < 0, drain leakage
for each drain will
be printed
whenever ICBCFL is set.
ICBCFL is a flag.
If I CBCFL f 0, ccl l-by-cell
flow terms will
be either
printed
or recorde d for the
current
time step.
9-25
1
SUBROUTINE DRNlBD(NDRAIN,MXDRN,VBNM,VBVL,MSUM,DRAI,DELT,HNEW,
NCOL,NROW,NLAY,IBOUND,KSTP,KPER,IDRNCB,ICBCFL,BUFF,IOUT~
1338 22AUG1987 DRNlBD
: -----VERSION
C
******************************************************************
C
CALCULATE VOLUMETRIC BUDGET FOR DRAINS
C
**t***************************************************************
C
C
C
SPECIFICATIONS:
----------------------------------------------------------------,-C
CHARACTER*4 VBNM,TEXT
DOUBLE PRECISIONHNEW
C
DIMENSION VBNM(4rMSUM),VBVL(4,MSUM)rDRAI(5,MXDRN),
1
HNEW(NCOL,NROW,NLAY)rIBOUND(NCOL,NROW,NLAY~,
2
BUFF(NCOL,NROW,NLAY)
DIMENSIONTEXT(4)
C
C
C
Cl---Cl----
DATA TEXT(l)rTEXT(Z),TEXT(3)rTEXT(4)
/’
----------------------------------------------------------------,-INITIALIZE
CELL-BY-CELL FLOW TERM FLAG
ACCUMULATORS(RATIN AND RATOUT).
RATOUT=O.
1,’
‘,’
DR’r’AINS’/
(IBD) AND
IBD=O
C
Q----
IF THERE ARE NO DRAINS THEN DO NOT ACCUMULATEDRAIN FLOW
IF(NDRAIN.LE.0) GOTO 200
C
C3-----C
c3 B-----
TEST TO SEE IF CELL-BY-CELL FLOW TERMS ARE NEEDED.
IF(ICBCFL.EQ.0 .OR. IDRNCB.LE.0) GO TO 60
CELL-BY-CELL FLOW TERMS ARE NEEDED SET
IBD=l
DO 50 IL=lrNLAY
IBD AND CLEAR BUFFER.
DO 50 IR=lrNROW
DO 50 IC=lrNCOL
BUFF(IC,IR,IL)=O.
50 CONTINUE
C
c%------FOR
EACH DRAIN ACCUMULATEDRAIN FLOW
60 DO 100 L=lrNDRAIN
C
C5------ GET LAYER, ROW& COLUMN OF CELL CONTAININGREACH.
IL=DRAI(l,L)
IR=DRAI(Z,L)
9-26
IC=DRAI(3,L)
C
(-3j-em--
IF CELL IS EXTERNAL IGNORE IT.
IF(IBOUND(IC,IR,IL).LE.O)
GO TO
C
100
c7 ------GET
DRAIN PARAMETERSFROM DRAINLIST.
EL=DRAI(4,L)
C=DRAI(5rL)
HHNEW=HNEW(IC,IR,IL)
C
C&-----
IF HEAD LOWERTHAN DRAIN THEN FORGET THIS CELL.
IF(HHNEW.LE.EL) GO TO 100
C
c9 ------HEAD
HIGHER THAN DRAIN. CALCULATE Q=C*(EL-HHNEW).
c9 ------SUBTRACT
Q FROM RATOUT.
Q=C*(EL-HHNEW1
RATOUT=RATOUT-Q
C
Cl&---PRINT THE INDIVIDUAL RATES IF REQUESTED(IDRNCB<O).
IF(IDRNCB.LT.O.AND.ICBCFL.NE.0)
WRITE(IOUT,900)
(TEXT(N)rN=lr4),
1
KPER,KSTP,L,IL,IR,IC,Q
900 FORMAT(lH0,4A4, ’
STEP’rI3,’
PERIOD'rI3,'
DRAIN'rI4,
1
'
LAYER'rI3,'
RATE’,G15.7)
ROW’,I4,’
COL’rI4,’
C
Cll---IF C-EC FLOW TERMS ARE TO BE SAVED THEN ADD Q TO BUFFER.
l
IF(IBD.EQ.l)
100 CONTINUE
BUFF(IC,IR,IL)=BUFF(IC,IR,IL)+Q
C
c12----
IF C-EC
IF(IBD.EQ.l)
FLOW TERMS WILL BE SAVED CALL UBUDSV TO RECORDTHEM.
CALL UBUDSV(KSTP,KPER,TEXT,IDRNCB,BUFF,NCOL,NROW,
NLAY, IOUT)
1
C
Cl3----MOVE RATESsVOLUMES8, LABELS INTO ARRAYS FOR PRINTING.
200 VBVL(3rMSUM)=O.
VBVL(4rMSUM)=RATOUT
VBVL(2rMSUM)=VBVL(2,MSUM)+RATOUT*DELT
VBNM(lrMSUM)=TEXT(l)
VBNM(2rMSUM)=TEXT(2)
VBNM(3,MSUM)=TEXT(3)
VBNM(4,MSUM)=TEXT(4)
C
Cl4----INCREMENT BUDGET TERM COUNTER
MSUM=MSUMtl
C
Cl5 -----RETURN
RETURN
END
l
9-27
List
Variable
of Variables
for
Module DRNlBD
Definition
Range
BUFF
Global
DIMENSION (NCOL,NROW,NLAY), Buffer used to accumulate
information
before printing
or recording
4t.
C
Module
Conductance
DELT
Global
Length
DRAI
Package
DIMENSION (5,MXDRN),
head in the drain
EL
Module
Elevation
HHNEW
Module
Head in the cell
HNEW
Global
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
HNEW changes at each iteration.
in each cell.
IBD
Package
Flag.
= 0, cell-by-cell
flow
not be recorded.
# 0, cell-by-cell
flow
be recorded.
into
drains.
of the current
time
step.
For each drain:
and conductance
of the drain
(head in the
containing
the
for
this
package will
terms
for
this
package will
DIMENSION (NCOL,NROW,NLAY), Status
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
IC
Module
Index
I CBCFL
Global
Flag.
= 0, cell-by-cell
or printed
f 0, cell-by-cell
the current
Package
of head
terms
Global
IDRNCB
drain).
drain.
IBOUND
for
layer,
row, column,
into the drain.
of each cell.
columns.
flow terms will
not be recorded
the current
time step.
flow terms will
be recorded for
time step.
for
Flag.
> 0 and if ICBCFL f 0, cell-by-cell
flow
for the DRNl Package will
be recorded
UNIT = IDRNCB.
IL
Module
Index
IOUT
Global
Primary
IR
Module
Index
KPER
Global
Stress
for
layers.
unit
for
terms
on
number for
rows.
period
counter.
Q-28
all
printed
output.
IOUT = 6.
List
Variable
of Variables
for
Module DRNlBD (Continued)
Definition
Range
Reset
at the
start
of each stress
KSTP
Global
Time step
period.
counter.
L
Module
Index
drains.
MSUM
Global
Counter
MXDRN
Package
Maximum number of drains
NCOL
Global
Number of columns
NDRAIN
Package
Number of drains
period.
active
during
NLAY
Global
Number of layers
in the
grid.
NROW
Global
Number of rows in the
Q
Module
Flow from a drain into a cell.
get the flow into the drain.)
RATOUT
Module
Accumulator
for the total
into the drains.
TEXT
Module
Label
VBNM
Global
DIMENSION (4,20),
budget.
VBVL
Global
DIMENSION (4,20),
Entries
for the volumetric
budget.
For flow component N, the values in VBVL are:
(l,N) Rate for the current
time step into the flow
field.
(2,N) Rate for the current
time step out of the flow
field.
(3,N) Volume into the flow field
during simulation.
(4,N) Volume out of the flow field
during simulation.
for
for
budget
entries
active
in VBVL and VBNM.
at any one time.
in the grid.
to be printed
9-29
and labels
the current
stress
grid.
flow
out of the
or recorded
Labels
for
(Reverse
with
entries
the
the
sign
flow
array
in the
to
field
data.
volumetric
CHAPTER 10
EVAPOTRANSPIRATION PACKAGE
Conceptualization
The Evapotranspiration
transpiration
"ET surface"
evaporation
The approach
regime.
(1) when the water
occurs
(ET) Package simulates
and direct
ground water
table
in this
table
termed
the
piration
specified
depth"
from the water
transpiration
table
from the water
This
water
can be expressed
elevation
or "cutoff
ceases;
table
of plant
from the
is based on the following
depth"
varies
in equation
termed
from the water
a specified
in this
linearly
with
of the
interval,
report,
between these
the
table
(2) when the depth
exceeds
and (3)
saturated
assumptions:
elevation,
loss
by the user;
ET surface
"extinction
in removing
evapotranspiration
report,
below the
the effects
is at or above a specified
at a maximum rate
water
and Implementation
evapotrans-
limits,
water
evapo-
table
elevation.
form as
RETi,j
= RETMi,j
hi,j,k
> hsi,j
(71)
RETi,j
= 0
hi,j,k
< hsi,j'di,j
(72)
RETi,j
= RETMi ,
j{
hi,j,k
- (hsi,j
-----------------------)
di,j
- di,j)
(h si,j-di,j)
_< hi,j,k
2
(73)
hsi,j
where RETi,j
is the
rate
the map area DELRjDELCi;
the cell
from which
possible
value
of RETi,j;
elevation
at which
occurs;
and di,j
per unit
in volume of water
evapotranspiration,
table
of loss
hi,j,k
per unit
is the head,
the evapotranspiration
hsi,j
this
is the cutoff
surface
is the
area of water
area per unit
or water
occurs;
ET surface
maximum value
or extinction
10-l
table
time,
due to
within
elevation
in
REmi,j
is the maximum
elevation,
or the water
of evapotranspiration
depth,
table
such that
loss
when the
distance
between
hsi,j
In implementing
and hi,j,k
the
finite
exceeds
difference
evapotranspiration
loss
from a given
the
product
of the
loss
rate
DELRjDELCi,
of the
cell
from which
QETi,j
through
the
is designated
of volumetric
rate
is given
and the horizontal
surface
required.
occurs,
loss
volumetric
This
is
area,
the
ceases.
of
as
area,
i.e.
= RETi,j*DELRj*DELCi
in volume of water
equations
QEmi,j,
discharge
(74)
If the maximum Value
the area DELRjDELCi.
to REMi,j)
terms
per unit
evapotranspiration
approach
cell
is the evapotranspiration,
where QETi,j
di,j
of
per unit
(corresponding
QETi,j
(71)-(73)
time,
can be expressed
in
as
QETi,j
= QElM,j
hi,j,k
> hsi,j
(75)
QETi,j
= D
hi,j,k
< hsi,j-di,j
(75)
QETi,j
=
hi,j,k
QE~i,j{---------,7-~----------}
- (hsi,j
- di,j)
(hsi,j-di,j)
2 hi,j,l(
5
(77)
,
hsi,j
Figure
in cell
with
42 shows a graph of evapotranspiration
i,j,k
the
river
similar,
except
based on equations
or drain
that
functions
the linear
both ends by constant
values,
Evapotranspiration
beneath
layer,
portion
rather
k) using
drawn from the
specifies
evapotranspiration
the
than
only
cell,
within
the
is to
be taken.
at the
layer
of the model;
vertical
In either
IO-2
first
vs head
ET funlction
are mathematically
lower
in the
designates
Under the
of the
ET function
one cell
the user
uppermost
the three
of the
is drawn from only
one of two options.
QETi,j,
Comparison
shows that
the map area DELRj*DELCi;
is always
user
(75)-(77).
loss,
the
option,
is bounded at
end.
vertical
cell
(i.e.
the
evapotranspiration
under the
column at i,j,
column
second, the
from whici
case the computed
the
evapotrans-
QET
Maximum
evapotranspiration
-
h
Figure 42.-Plot of volumetric evapotranspiration, QET, as a
function of head, h, in a cell where d is the cutoff depth
and h, is the ET surface elevation.
10-B
piration
has no influence
a no-flow
cell
or a constant
For each cell
stress
period
reads
per unit
time)
multiplied
rate
(i,
an option
values
an array
then
to the
EVTR array
area,
in the
values
consists
the model,
maximum volumetric
of RETMi,j
Values
of hsi,j,
evapotranspiration
array
SURF by the
depth
are read into
must be subtracted
expressions
package
1)
ET surface
ET package;
has been defined
left
side
HCOF and RHS of equation
rates
per un!t
calculation
carried
(or water
appear
input
as
depth
EXDP.
of equation
this
table
elevation
at
the two dimension31
or extincti
Because the term QETi,j
as an outflow
(26),
Thus, the
Lst-l.
of the cutoff
array
area
maximum volumetric
EVTR array
are read into
the two-dimensonal
from the
in the
elevation
values
ET
per unit
EVTR array.
In the
dimensions
is maximum),
(75)-(77)
in the
the entries
having
the
which
of equations
however,
the
the maximum volumetric
QETM; these
Lt-'.
values)
each
are immediately
of maximum evapotranspiration
rates,
is either
and for
loss
These rates
to obtain
from each cell,
the
cell
plane,
to use prior
EVTR.
and as such must have dimensions
out within
horizontal
is exercised
DELRj*DELCi,
areas,
replace
j),
labelled
of evapotranspiration
rates
the designated
of REm (maximum evapotranspiration
into
by cell
if
head cell.
location,
(unless
package
on the simulation
(24).
from the
aquifer
In terms
is accomplished
it
of the
in tha
ET
as follows:
if
hi,j,k
or RHS for
2)
if
hi,j,k
3)
if
(hsi,j,k
HCOFi ,j ,k
< (hsi,j,k
cell
no changes
are made in the terms
HCOF
i,j,k;
> hsi,j,
- di,j)
and
- di,j)
‘QETMi
QEMi,j
5 hi,j,k
,j
is added to RHSi,j;
5 hsi,j,ks
h.
.-d..
{ -Z~Z!----I~~}
di,j
10-4
and
-QEmi,j/di,j
is added to
is added to RHS i,j,k.
The value
piration
of hs,i,j,
the water
is maximum, should
elevation
table
normally
be taken
in the map area DELRjDELCi;
is then
frequently
surface
(although
considerable
the cutoff
the
presence
distance
from land surface
variation
of deep-rooted
at which
as the
assumed to be on the order
factors,
care must be exercised
in choosing
various
parameters
average
of six
table
land surface
feet
the
(70),
below
land
Where the
extensively
in implementing
di,j,
by climatic
or so on).
varies
of equation
depth,
to eight
can be introduced
to the water
evapotrans-
or extinction
phreatophytes,
area of a cell,
the
elevation
within
the
ET package and
or misleading
results
may be obtained.
The options
provide
also
for
selection
some flexibility
require
similar
in adapting
some care
to that
of the
discussed
for
the
using
the
provision
table
conditions
inactive
for
(Chapter
and figure
(no flow)
Under option
uppermost
cells
model,
layer
in this
Figure
use of option
5).
cells
43-c),
of the model;
deletes
43-d shows the situation
2, assuming
distribution
that
the
but
a cross
the water
formulation
table,
under water
situation
of variable
head and
in the simulation.
evapotranspiration
from the
to represent
which could
simulation
10-5
is drawn only
shown, the presence
evapotranspiration
fails
in which
43-a shows the hydrologic
in the problem
the simulation
situations,
to follow
conductance
Figure
obtained
ET is to be drawn
43 shows a situation
package,
truncated
43-b the final
1 (figure
layer
so that
horizontal
Figure
recharge
model has been progressively
from which
the package to special
in implementation.
sectional
under study,
layer
field
right
of no flow
half
of the
conditions.
be achieved
was carried
from the
out
through
in
the
stages
and
Land Surface
River
Buried
Drain
\
Vertical Cross Section Showing Hypothetical
Field Situation and Finite Difference Grid
Water
Table
a
III Variable Head Cell
q Constant Head Cell
iiii$ Inactive Cell
El
Status of Cells at End of Simulated
Period
b
clx
.
.
.
.
.
.
.
.
.
.
.
-.
I
I
.
.
.
.
I
I
I
I
Cell from Which ET
Is Abstracted
I I I I Ii
Cells from Which ET Is Abstracted
Option 1
C
Under
Layer Indicators Specifield
in the IEVT Array
111111112223333444-
qX
Cells from Which ET Is Abstracted
Option 2
Cell from Which ET
Is Abstracted
Under
d
Figure 43.-Hypothetical
problem showing cells from which ET
will be abstracted under the two options available
in the ET Package.
10-6
that
the user
from which
interacted
evapotranspiration
with
the simulation
process,
designating
was to be drawn as the truncation
developed.
10-7
the
cells
of the mesh
Evapotranspiration
Input to the Evapotranspiration
specified
in IUNIT (5).
Package Input
(EVT) Package is
read from the
unit
FOR EACH SIMULATION
EVTlAL
1.
Data:
Format:
NEVTOP
110
IEVTCB
110
FOR EACH STRESS PERIOD
EVTlRP
7-.
Data:
Format:
I NSURF
110
3.
Data:
Module:
SURF
U2DREL
4.
Data:
Module:
EVTR
U2DREL
5.
Data:
Module:
EXDP
U2DREL
I NEVTR
110
I NEXDP
110
INIEVT
110
IF THE ET OPTION IS EQUAL TO TWO
6.
Data:
Module:
IEVT
U2DINT
Explanation
Input
of Fields Used in
Instructions
NEVTOP--is the evapotranspiration
(ET) option code.
ET parameters
(ET
surface,
maximum ET rate, and extinction
depth) are specified
in two-dimensional
arrays,
SURF, EVTR, and EXDP, with one value
for each vertical
column.
Accordingly,
ET is calculated
for one
cell
in each vertical
column.
The option codes determine
for
which cell in the column ET will
be calculated.
1 - ET is
calculated
only
for
2 - The cell for each vertical
user in array IEVT.
10-8
cells
in the top
column
is
grid
specified
layer.
by the
IEVTCB--is
a flag
and a unit
number.
If
IEVTCB > 0, it
If
IEVTCB 2 0, cell-by-cell
is the unit number on which cell-by-cell
flow
terms will
be recorded whenever ICBCFL (see Output
Control)
is set.
flow
terms
will
not be printed
or
recorded.
INSURF--is
the ET surface
If
(SURF) read flag.
INSURF L 0, an array
containing
the ET surface
elevation
will
be
read.
If
INSURF < 0, the ET surface
from the preceding
stress
period
will
be reused.
the maximum ET rate
INEVTR--is
(EVTR) read flag.
If
INEVTR 2 0, an array
If
INEVTR < 0, the maximum ET rate
will
be reused.
INEXDP--is
the extinct
If
ion depth
INEXDP 2 0, an array
containing
the maximum ET rate
from the preceding
will
be read.
stress
period
(EXDP) read flag.
containing
the extinction
depth
(EXDP) will
be read.
depth
INEXDP < 0, the extinction
will
be reused.
If
INIEVT--is
the
option
layer indicator
(IEVT) read flag.
(NEVTOP) is equal to two.
If
INIEVT L 0, an array
be read.
If
INIEVT < 0, layer
containing
indicators
be reused.
will
SURF--is
the elevation
EVTR--is
the maximum ET rate
EXDP--is
the ET extinction
IEVT--is
from the preceding
the
stress
It is used only
layer
used during
indicators
the
period
if
the ET
(IEVT)
will
preceding
stress
period
of the ET surface.
(volume
of water
per unit
area
(Lt-I)).
depth.
the layer indicator
array.
indicates
the layer from which
the ET option is equal to two.
For each horizontal
It
ET is removed.
10-9
location,
it
is needed only
if
m
N(VN0P-lC.l
. . . .
.-lrl4l-l.-il-l
.
.
NhlhlO(Yt-7
. . .
l-ll-lrlrlrlrl
.
.
.
Module Documentation
for
The Evapotranspiration
of which
the
Evapotranspiration
Package (EVTl)
are called
by the MAIN program.
EVTl AL
Allocates
space for
ET rate
(EVTR),
extinction
EVTlRP
Reads arrays
(in
terms
and,
surface
if
option
area to get the
out of the flow
If there
to
location,
is
if
rate.
which
there
ET, add the
HCOF and RHS.
and accumulated
system.
10-11
2
Maximum ET
Determines
cell.
rates
2
(IEVT).
area),
each horizontal
terms
the
option
indicator.
by cell
is at the surface.
Calculates
if
each node as a volumetric
for
appropriate
maximum
(SURF),
indicator
depth,
the layer
is ET from that
EVTlBD
and,
all
the maximum ET rate
extinction
maximum ET for
cell
layer
are multiplied
Determines,
to contain
of a volume per unit
is specified,
EVTlFM
(EXDP),
modules,
are:
elevation
containing
elevation,
rates
surface
the
of four
The modules
arrays
depth
is specified,
consists
Package
volume of ET
Narrative
This
module allocates
for
Module EVTlAL
space in the
X array
to store
data
relating
to
evapotranspiration.
for
1.
Print
a message identifying
7-.
Read and print
cell-by-cell
3.
(not
flow
See if
1 or Z),
allocate
5.
If
terms
depth
7.
If
8.
the
flow
will
space for
(EXDP),
the option
If
NEVTOP is
is illegal.
illeg'al
Do not
array
Calculate
NEVTOP.
terms
are to be recorded,
print
the
unit
be recorded.
ET-surface
(NEVTOP) is
array
equal
array
(EVTR),
the
extinction-
(SURF).
to two,
allocate
space for
a
(IEVT).
and print
the
number of elements
ET package.
9.
legal.
the maximum ET-rate
and the
the ET option
layer-indicator
(NEVTOP) is
print
cell-by-cell
Allocate
array
number
(IEVTCB).
legal,
number (IEVTCB) where they
6.
(NEVTOP) and the unit
STOP.
NEVTOP is
the
package.
indicator
a message saying
storage.
4. 'If
the option
the ET option
print
the
RETURN.
10-12
in the X array
used by
Flow Chart
B
for
NEVTOP is the ET option.
If NEVTOP = 1, ET is
top layer.
Module EVTlAL
(2
ENTER
EVTlAL
from the
If NEVTOP = 2, ET is from the
layer specified
by the user in
the indicator
array (IEVT).
1
PRINT MESSAGE
I Dp6;;;<FAYd;G
cl
IEVTCB is the unit number on which
cell-by-cell
flow terms for ET
will
be written.
EVTR is an array which
maximum ET rate for
cell location.
contains
the
each horizontal
SURF is an array which contains
elevation
of the ET surface.
the
EXDP is an array which contains
extinction
depth for ET.
the
IEVT is an array which contains
the
layer number from which ET is taken
for each horizontal
location.
It
is used only if option 2 has
been specified.
PRINT
IEVTCB
I
ALLOCATE SPACE
FOR EVTR, SURF,
AND EXDP ARRAYS
ALLOCATE
SPACE FOR
IEVT ARRAY
I
PRINT AMOUNT
OF SPACE USED
BLR~~:T
1
1
SUBROUTINE
EVT~AL(ISUMILENXILCIEVT,LCEVTRILCEXDP,LCSURF,
NCQLINROW,NEVTOP,IN,IOUT,IEVTCB)
C
C-----VERSION 1607 12MAY1987
EVTlAL
******************************************************************
C
ALLOCATE ARRAY
STORAGE
FOREVAPOTRANSPIRATION
******************************************************************
C
c
C
C
SPECIFICATIONS:
C
C
Cl---
C
c2---
------------------------------------------------------------------
IDENTIFYPACKAGE.
WRITE(IOUT,l)IN
1 FORMAT(lHDr'EVT1
-- EVAF'OTRANSPIRATION
PACKAGE,
VERSION
l,',
1
' 9/l/87','
INPUTREAD FROM UNIT',131
READNEVTOP
ANDIEVTCB.
READ(IN,3)NEVTOP,IEVTCB
3 FORMAT(2110)
C
C3------ CHECK
TO SEETHATET OPTIONIS LEGAL.
IF(NEVTOP.GE.l.AND.NEVTOP.LE.P)GO
TO200
C
C3A-m-s-IF ILLEGALPRINTA MESSAGE
i%ABORTSIMULATION.
WRITE(IOUT,B)
8 FORMAT(lX,'ILLEGAL
ET OPTION CODE. SIMULATION
ABORTING')
STOP
C
C4------IF THEOPTIONIS LEGAL THEN PRINT THE OPTIONCODE.
200 IF(NEVTOP.EQ.l)WRITE(IOUT,ZOl)
201 FORMAT(lX,'OPTION
1 -- EVAPOTRANSPIRATION FROM TOP LAYER’)
IF(NEVTOP.EQ.2)
WRITE(IOUT,POZ)
202 FOlU4AT(lX,'OPTION
2 -- EVAPOTRANSPIRATION
FROM
ONESPECIFIED',
1
’ NODE IN EACH VERTICAL COLUMN’)
IRK=ISUM
------IF
CELL-BY-CELL TEfW TO BE SAVED THEN PRINT UNIT NUMBER.
IF(IEVTCB.GT.0)
WRITE(IOUT,203) IEVTCB
C
203 FORMAT(lX,'CELL-BY-CELL
FLOWTERNSWILL BE SAVEDONUNIT'rI3)
c6 ------ALLOCATESPACE
FORTHEARRAYS
EVTR,EXDPANDSURF.
LCEVTR=ISUM
ISUM=ISUM+NCOL*NROW
LCEXDP=ISUM
ISUM=ISUM+NCOL*NROW
LCSURF=ISUM
ISUM=ISUM+NCOL*NROW
C
C7------ IF OPTION2 THEN ALLOCATE SPACE FOR THE INDICATOR
ARRAYfIEVT)
LCIEVT=ISUM
IF(NEVTOP.NE.P)GO
TO300
ISUM=ISUM+NCOL*NROW
C
C&-----CALCULATE
8 PRINT AMOUNT OF SPACE USED BY ET PACKAGE.
300 IRK=ISUM-IRK
WRITE(IOUT,4)IRK
4 FOl%!AT(lX,I8,' ELEMENTS OF X ARRAY USED FOR EVAPOTRANSPIRATION')
ISUM1=ISUM-1
WRITE(IOUT,5)ISUMl,LENX
5 FORMAT(lX,IBr'ELEMENTS
OFX ARRAYUSEDOUTOF',181
IF(ISUMl.GT.LENX)WRITE(IOUT,6)
6 FORMAT(1X,'
***X ARRAY MUST BE MADE LARGER***‘)
C
c9 ------RETURN.
RETURN
END
10-14
List
Variable
of Variables
for
Definition
Range
I EVTCB
Package
IN
Package
IOUT
IRK
Global
Module
I SUM
Global
ISUMl
Module
LCEVTR
Package
LCEXDP
Package
LCIEVT
Package
LCSURF
Package
LENX
Global
NCOL
NEVTOP
Global
Package
NRDW
Global
Module EVTlAL
Flag.
If IEVTCB > 0 and ICBCFL f 0, cell-by-cell
flow
terms for the EVTl Package will
be recorded on
UNIT = IEVTCB.
Primary unit number from which input for this package
will
be read.
Primary unit number for all printed
output.
IOUT = 6.
Before this module allocates
space, IRK is set equal
IRK is subtracted
from
to ISUM. After allocation,
ISUM to get the amount of space in the X array
allocated
by this module.
Index number of the lowest element in the X array which
has not yet been allocated.
When space is allocated
for an array, the size of the array is added to
ISUM.
Index number of the last element of the X array
allocated
by this module.
Location
in the X array of the first
element of array
EVTR.
Location
in the X array of the first
element of array
EXDP.
Location
in the X array of the first
element of array
IEVT.
Location
in the X array of the first
element of array
SURF.
Length of the X array in words.
This should always be
equal to the dimension of X specified
in the MAIN
program.
Number of columns in the grid.
ET option:
= 1, ET is from the top layer.
= 2, ET at each horizontal-cell
location
is from
the layer specified
by the user in the layerindicator
array (IEVT).
Number of rows in the grid.
10-15
Narrative
This module
evapotranspiration.
reads data
for
Module EVTlRP
used to calculate
the terms
which
represent
1. Read the values INSURF, INEXDP, INEVTR, and INIEVT which indicate
whether the data contained
in arrays SURF, EXDP, EVTR, and IEVT,
respectively,
used during the last stress period,
are to be used for the
current
stress period.
2. Test INSURF to see where the ET-surface
array (SURF) is coming from,,
If INSURF is less than zero, the ET-surface
elevation
used in the last stress
period will
be used again in this stress period.
Print a message to that
effect
and GO TO 4.
INSURF is
3.
greater
than
or equal
to zero.
CALL UEDREL to
read SURF.
4. Test INEVTR to see where the maximum ET rate (EVTR) is coming from.
If INEVTR is less than zero, the maximum ET rate used in the last stress
period will
be used again in this stress period.
Print a message to that
effect
and GO TO 7.
maxim:;
INEVTR is greater
ET rate (EVTR).
6.
Multiply
than
or equal
the maximum ET rate
to zero.
by the
be used
again
in
this
stress
period.
read the
area to get a volumetric
7. Test INEXDP to see where the extinction
INEXDP is less than zero, the extinction
depth
will
CALL U2DREL to
Print
rate is coming
used in the last
a message
to
rate
from.
stresrs
that
If
per iod
ef rect
and GO TO 9.
8.
If
extinction
9.
If
INEXDP is
depth.
greater
the ET option
than
or equal
(NEVTOP) is
equal
to zero,
to two,
CALL U2DREL to read the
a layer-indicator
array
is needed.
Test INIEVT to see where the layer indicator
is coming from.
If
INIEVT is less than zero, the indicator
array used in the last stress period
Print a message to that effect
will
be used again in this stress
period.
and GO TO 12.
10.
11. If
IEVT array.
12.
INIEVT is
greater
than
or equal
RETURN.
lo-16
to zero,
CALL UEDINT to
read the
Flow Chart
for
JNEVTR is a flag which, when set,
indicates
that the maximum ET rate
EVTR should be read for the current
If it is clear
stress
period.
(less than zero),
maximum ET rates
from the last stress period should
be reused.
INIEVT, INSURF, and INEXDP are flags
similar
to INEVTR used for the
layer indicator
array (IEVT), the
ET surface array (SURF), and the
extinction
depth array (EXDP),
respectively.
Module EVTlRP
INEXDP.
INEVTR,
“REUSE
SURF”
CALL MODULE
UPDREL TO READ
SURF
EVTR is an array containing
the maximum
ET rate for every horizontal
cell
location.
SURF is an array containing
the ET
surface elevation
for each horizontal
cell location.
EXDP is an array containing
depth for each horizontal
location.
the extinction
cell
IEVT is an array containing
a layer
indicator
for each horizontal
cell
For each horizontal
cell
location.
location,
it indicates
the layer
number of the cell at that location
It is used
from which ET is taken.
only if the ET option
(NEVTOP) is
equal to two.
NEVTOP is
CELL AREA
7A
“REUSE
EXDP”
CALL MODULE
UZDREL TO
_ READ EXDP
the ET option.
If NEVTOP = 1, ET is from the top
layer.
If NEVTOP = 2, ET is from the layer
specified
by the user in the indicator
array (IEVT).
1OA
CALL
10-17
MODULE
1
SUBROUTINE EVTlRP(NEVTCP,IEVT,EVTR,EXDPtSURF,DELR,DELC,
NCOL,NROWIIN,IOUT)
--VERSION 1635 24JULl987
EVTlM=
READ EVAPOTRANSPIRATION DATA
SPECIFICATIONS:
------------_----------------------------------------------------CHARACTER*4 ANAME
DIMENSION IEVT(NCOL,NROW),EVTR(NCOL1NROH)rEXDP(NCO).
1
SURF(NCOL,NROW).ANAM(6,4),DELR(NCOL),DELC(NROW)
C
DATA ANAME~l,l~,ANAME~2rl~,ANAME~3,l~,ANAFL~4rl~,ANAM~5.l~,
ANAME(611) /’
1,’
1,’
ET’,’
LAY’,‘ER I’,‘NDEX’/
DATA ANAME(l,Z),ANAME(2,2),ANAME(3,2),ANAME(4,2),ANAME(5,2),
1 ANAME(6.2) /’
1,’
I,’
I,’
ET’,’
SUR’,‘FACE’/
DATA ANAME(1,3l,ANAME(2,3),~~(3,3),~~(4,3),~~(5,3),
1 ANAK(6.3)
/’ EVA’r’POTR’,‘ANSP’.‘IRAT’,‘ION
‘,‘RATE’/
DATA ANAME(1,4),AN~(2,4),ANAME(3,4),ANAME(4,4),ANAM(5,4),
1 ANAK(6.4)
/’
1.1
‘,‘EXTI’r’NCTI’,‘ON
D’.‘EPTH’/
-----------------------------------------------------------------1
C
C
Cl------READ
FLAGS SHOWING WHETHER DATA IS TO BE REUSED.
READ(INr6)INSURF,INEVTR.INEXDPtINIEVT
6 FDRMAT(4110)
C
CP-----TEST
INSURF TO SEE WHERE SURFACE ELEVATION COKS FROM.
IF(INSURF.GE.O)GC
TO 32
C
C2A------IF
INSURF< THEN REUSE SURFACE ARRAY FROM LAST STRESS PERIOD
WRITE(IOUT,3)
3 FOF&tAT(1HO,‘REUSING SURF FROM LAST STRESS PERIOD’)
GO TO 35
i3 -------IF
INSURF=>O THEN CALL MODULE U2DREL TO READ SURFACE.
32 CALL U2DREL(SURF.ANAME(lr2)rNRaJ.KOL.O.IN,IOUT)
C
C4------TEST
INEVTR TO SEE WHERE MAX ET RATE COMES FROM.
35 IF(INEVTR.GE.O)GO
TO 37
C
CQA-----IF
INEVTR<O THEN REUSE MAX ET RATE.
WRITE(IOUT,4)
4 FOfU4AT(lHD.‘REUSIffi
EVTR FROM LAST STRESS PERIOD’)
GO TO 45
C
(%------IF
INEVTR=>D CALL MODULE U2DREL TO READ MAX ET RATE.
37 CALL U2DREL(EVTR,ANAME(lr3)tNROWtNC0L,OrIN,IOUT)
C
C6------MULTIPLY
MAX ET RATE BY CELL AREA TO GET VOLUVETRIC RATE
DO 40 IR=l,NROW
DO 40 IC=ltNCOL
EVTR(IC.IR)=EVTR(IC,IR)*DELR(IC)*DELC(IR)
40 CONTINUE
C
C7------TEST
INEXDP TO SEE WHERE EXTINCTION DEPTH COMES FRCM
45 IF(INEXDP.GE.O)GO
TO 47
C
C‘IA------IF
INEXDPCO REUSE EXTINCTION DEPTH FROM LAST STRESS PERIOD
WRITE(IOUT,5)
5 FOPMAT(lHUt ‘REUSING EXDP FROM LAST STRESS PERIOD’ 7
GO TO 48
-------IF
INEXDP=>O CALL MODULE U2DREL TO READ EXTINCTION DEPTH
47 CALL U2DREL~EXDP.ANANE(1,4),N~,KXlLrOrIN,IOUT)
C
C9------IF
OPTION(NEVTCP) IS 2 THEN WE NEED AN INDICATOR ARRAY.
48 IF(NEVTOP.NE.L)GO
TO 50
-----IF
INIEVTCO THEN REUSE LAYER INDICATOR ARRAY.
XF(INIEVT.GE.O%O
TO 49
WRITE(IOUT,2)
2 FOF@tAT(1HOt’REUSING IEVT FROM LAST STRESS PERIOD’)
GO TO 50
------IF
INIEVT=>O THEN CALL MODULE UPDINT TO READ INDICATOR ARRAY.
49 CALL U2DINT(IEVT,ANAME(1.1)rNR~rNCGLrOrIN,IOUT)
C
c12-----RETURN
50 RETURN
END
lo-18
List
Variable
Module
Global
DELR
Global
EVTR
EXDP
IC
IEVT
Package
Package
Module
Package
IN
Package
INEVTR
Module
Module
l
INIEVT
I NSURF
for
Module EVTlRP
Definition
Range
ANAME
DELC
I NEXDP
of Variables
Module
Module
Label for printout
of the input array.
DIMENSION (NROW), Cell dimension in the column
DELC( I) contains
the width of row I.
direction.
DIMENSION (NCOL), Cell dimension in the row direction.
DELR(J) contains
the width of column 3.
DIMENSION (NCOL,NROW), Maximum ET rate.
DIMENSION (NCOL,NROW), Extinction
depth.
Index for columns.
DIMENSION (NCOL,NROW), Layer number for each horizontal
cell location
from which ET will
be taken if the ET
option (NEVTOP) is equal to two.
Primary unit number from which input for this package
will
be read.
Flag.
be read.
-> 0, EVTR array will
< 0, EVTR array already in memory from the
stress period will
be used.
Flag.
> 0, EXDP array will
be read.
last
< 0, EXDP array already in memory from the
stress period will
be used.
Flag.
be read.
-> 0, IEVT array will
last
< 0, IEVT array already in memory from the
stress period will
be used.
Flag.
> 0, SURF array will
be read.
last
< 0, SURF array already
stress period will
IDUT
IR
NCOL
NEVTOP
NROW
SURF
Global
Module
Global
Package
Global
Package
in memory from the
be used.
Primary unit number for all printed
Index for rows.
Number of columns in the grid.
ET option.
= 1, ET is from the top layer.
= 2, ET at each horizontal-cell
the layer specified
in the
array (IEVT).
Number of rows in the grid.
DIMENSION (NCOL,NROW), Elevation
of
10-19
output.
last
IOUT = 6.
location
is from
layer-indicator
the
ET surface.
Narrative
This
1.
module adds terms
2.
Set the
3.
If
ET to the
location,
determine
appropriate
terms
to the equation
layer
equal
to one.
option
index
2 was invoked,
get the
finite-difference
layer
which
for
index
equations.
layer
ET comes
the cell.
from the
DO STEPS 1-7.
indicator
(IEVT).
4.
If
5.
surface
the
If
is external,
move on to the
the head in the aquifer
elevation,
location.
6.
cell
next
horizontal-cell
SKIP STEPS 5-7.
location.
cell
Module EVTlFM
representing
For each horizontal-cell
from and add the
array
for
If
(ET surface
is greater
than
or equal
add EVTR to RHS and move on to the
next
to the ET-
horizontal-
SKIP STEPS 6 AND 7.
the head in the aquifer
minus extinction
finite-difference
equation.
depth),
is
less
no terms
Move on to the
than
the extinction
need to be added to the
next
horizontal-cell
SKIP STEP 7.
7.
Add the term -EVTR/EXDP to HCOF and subtract
-EVTR(EXDP - SURF)/EXDP from RHS.
8.
RETURN.
10-20
elevation
the term
location.
Flow Chart
IEVT is an array containing
a
layer indicator
for each
horizontal
cell location.
For each horizontal
cell
location,
it indicates
the layer number of the
cell at that location
from
It is
which ET is taken.
used only if the ET option
(NEVTOP) is equal to two.
for
Module EVTlFM
FOR EACH
HORIZONTAL
CELL LOCATION
SET LAYER
INDEX EQUAL
TO 1
SURF is an array containing
the maximum ET rate for
every horizontal
cell
location.
IF OPTION 2
IS SPECIFIED,
GET LAYER
INDEX FROM IEVT
EVTR is an array containing
the maximum ET rate for
every horizontal
cell
location.
RHS is an accumulator
in which
the right
hand side of
the finite-difference
equation
is formulated.
HCOF is an accumulator
which a coefficient
head in the finitedifference
equation
formulated.
in
of
is
NEVTOP is the ET option.
If NEVTOP = 1, ET is
the top layer.
from
If NEVTOP = 2, ET is from
the layer specified
by
the user in the indicator
array (IEVT).
ADD ET TERMS
TO HCOF AND
RHS
10-21
1
SUBROUTINE EVTlFM( NEVTOP,IEVT, EVTR, EXDP, SURF, RHS, HCOF,
IBOUND, HNEW,NCOL,NROW,NLAY)
C
C-----VERSION 1031 lOAPR1985 EVTlFM
**********************~**************************************~~****
C
C
ADD EVAPOTRANSPIRATION
TO RHSANDHCOF
*************************************************************~~****
C
C
C
C
SPECIFICATIONS:
-----------------------------------------------------------------DOUBLE PRECISIONHNEW
DIMENSIONIEVT(NCOL,NROW)rEVTR(NCOLINROW1,EXDP~NCOL,NROW~,
1
SURF(NCOL,NROW),RHS(NCOL,NROW,NLAY)r
2
HCOF(NCOL,NROW,NLAY),IBOUND(NCOLINROWINLAY~,
3
HNEW( NCOL, NROW
, NLAY1
------------------------------------------------------------------
I
c”
Cl ------PROCESS
EACH HORIZONTAL CELL
LOCATION
DO 10 IR=lrNROW
DO 10 IC=lrNCOL
C
C&.--
SET THE LAYER INDEX EQUAL TO 1
IL=1
C
C3------ IF OPTION2 IS SPECIFIEDTHEN GET LAYER INDEX FROM IEVT ARRAY
IF(NEVTOP.EQ.2)IL=IEVT(IC,IR)
C
c4 ------IF
THE CELL IS EXTERNAL IGNOREIT.
IF(IBOUND(IC, IR, IL) .LE.O)GO TO 10
C=EVlR(IC, IR)
S=SURF(IC,IR)
H=HNEW(IC,IR,IL)
C
C5------ IF AQUIFER HEAD IS GREATER THAN OR EQUAL TO SURF, ET IS CONSTANT
1FtH.LT.S)
:5A -----SUBTRACT
C
C+---
GO TO 5
-EVTR FROM RHS
RHS(IC,IR,IL)=RHS(IC,IR,IL)
GO TO 10
+ C
IF DEPTH TO WATER>=EXTINCTION DEPTH THEN ET IS 0
5 D=S-H
X=EXDP(IC,IR)
IF(D.G!t.X)GO TO 10
C
c7------LINEAR RANGE. ADD ET TERMS TO BOTH FU-ISAND HCOF.
RHS(IC,IR,IL)=RHS(IC,IR,IL)+C-C*S/X
HCOF(IC, IR, IL)=HCOF(IC, IR, IL)-C/X
10 CONTINUE
C
C8------RETURN
RETURN
END
1o-22
List
Variable
Range
C
D
EVTR
EXDP
H
HCOF
Module
Module
Package
Package
Module
Global
HNEW
Global
BOUND
Global
IC
IEVT
Module
Package
IL
I OUT
IR
NCOL
NEVTOP
Module
Global
Module
Global
Package
NLAY
NROW
RHS
Global
Global
Global
s
SURF
X
Module
Package
Module
of Variables
for
Module EVTlFM
Definition
Maximum ET rate.
Depth to water.
DIMENSION (NCOL,NRDW), Maximum ET rate.
DIMENSION (NCOL,NROW), Extinction
depth.
Head in the cell.
DIMENSION (NCOL,NROW,NLAY), Coefficient
of head in
the cell (J,I,K)
in the finite-difference
equation.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate of
HNEWchanges at each iteration.
head in each cell.
DIMENSION (NCOL,NROW,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
Index for columns.
DIMENSION (NCOL,NROW), Layer number, for each horizontalcell location,
from which ET will
be taken if the ET
option (NEVTOP) is equal to two.
Index for layers.
Primary unit number for all printed
output.
IOUT = 6.
Index for
rows.
Number of columns in the grid.
ET option.
= 1, ET is from the top layer.
= 2, ET at each horizontal
cell location
is from
the layer specified
in the layer-indicator
array (IEVT).
Number of layers in the grid.
Number of rows in the grid.
DIMENSION (NCOL,NROW,NLAY), Right hand side of finiteRHS is an accumulation
of
difference
equation.
terms from several different
packages.
ET surface elevation
for a cell.
DIMENSION (NCOL,NROW), Elevation
of the ET surface.
Extinction
depth for a cell.
lo-23
Narrative
This module calculates
evapotranspiration.
1.
Clear the
2.
If budget terms
be accumulated.
rate
for
rates
and volumes
accumulator
will
Module EVTlBD
be saved,
clear
will
flow
Process each horizontal-cell
location
t"i evapotranspiration
(STEPS 4-11).
Set the
layer
(IL)
index
equal
If option 2 is in effect,
array (IEVT).
indiczior
6.
If the
cell
8.
If the depth to the water
further
9.
10.
Calculate
Subtract
If the
to tii'buffer
12.
to write
13.
processing
the
the
of this
ET flow
into
ET flow
cell-by-cell
(BUFF).
layer
is greater
cell equal
calculating
bypass
from the
layer-
processing
of the
the model using
accumulator
the
extinction
depth,
linear
approximaition.
(RATOUT).
are to be saved,
add the
If the cell-by-cell
flow terms
the buffer
(BUFF) onto a disk.
are to be saved,
call
the
14. Add RATOUT multiplied
ulators
in VBVL for printing
15.
Move the
16.
Increment
17.
RETURN.
VBVL array
for
ET budget-term
the budget-term
labels
counter
lo-24
length
to VBNM for
(MSUM).
ET rate
module
UBUDSV
by BASlOT.
printing
by the time-step
by BASlOT.
cell.
than the elevation
of the
to the maximum ET rate.
terms
Move RATOUT into
flow
index
is greater than the
cell.
SKIP STEP 9.
from the
(BUFF) in which
one at a time
(IBOUND 5 0),
7. If the head in the aquifer
ET surface,
set the ET rate for the
SKIP STEPS 8 AND 9.
bypass
the buffer
to one.
get the
is external
by
RATOUT.
they
4.
removed from the aquifer
to the
printing
volume accumby BASlOT.
Flow Chart
RATOUT is an accumulator
all flows out of the
are added.
for
to which
aquifer
BUFFER is an array in which values
are stored as they are being
gathered for printing
or
recording.
IEVT is an array containing
a
layer indicator
for each
horizontal
cell location.
For
each horizontal
cell location,
it indicates
the layer number
of the cell at that location
from which ET is taken.
It is
used only if NEVTOP is equal
to two.
SURF is an array containing
the ET
surface elevation
for each
horizontal
cell location.
Q is the flow
individual
to ET from an
cell.
VBVL is a table of budget entries
calculated
by component-of-flow
packages for use in calculating
the volumetric
budget.
VBNM is a table of labels
budget terms.
for
10-25
Module EVTlBD
SUBROUTINE EVTlBDt NEVTOP,IEVT, EVTR, EXDP, SURF, IBOUND, HNEW,
1
NCOL, NROW,NLAY, DELI, VBVL, VBNM,MSUM,KSTP, KPER,
2
IEVTCB, ICBCFL, BUFF, IOUT)
C-----VERSION
1608 12MAY1987 EVTlBD
******************************************************************
:
CALCULATE VOLUMETRIC BUDGET FOR EVAPOTRANSPIRATION
******************************************************************
C
:
C
SPECIFICATIONS:
--------_--------------------------------------------------------CHARACTER*4 VBNM,TEXT
DOUBLE PRECISION HNEW
DIKNSION IEVT(NCOL,NROW)rEVTR(NCOL,NROW)rEXDP(NCO),
1
SURF(NCOL,NROW)rIBOUND(NCOL,NROW,NLAY)r
2
VBVL(4,20)rVBNM(4,20)rHNEW(NCOL,NR~,NLAY~,
BUFF(NCOL,NROW,NLAY)
3
DIMENSION TEXT(4)
DATA TEXT(l)rTEXT(Z)rTEXT(3),~~(4)
/’
‘,’
‘,’
‘,’
ET’/
5
Cl ------CLEAR
ME RATE ACCUMULATOR.
RATOUT=O
C
c2---.IF CELL-BY-CELL FLOW TERMS WILL BE SAVED THEN CLEAR THE BUFFER.
IBD=O
IF(IEVTCB.LE.0
.OR. ICBCFL.EQ.0) GO TO 5
IBD=l
DO 4 IL=lrNLAY
DO 4 IR=lrNROW
DO 4 IC=lrNCOL
BUFF(IC,IR,IL)=O.
4 CONTINUE
C
c3 ------PROCESS
EACH HORIZONTAL CELL LOCATION
5 DO 10 IR=lrNROW
DO 10 IC=l,NCOL
C
c4 ------SET
THE LAYER INDEX EQUAL TO 1
IL=1
C
C5------ IF OPTION 2 IS SPECIFIED THEN GET LAYER INDEX FROM IEVT ARRAY
~F(NEVTOP.EQ.Z)IL=IEVT(IC,IR)
C
(36--IF CELL IS EXTERNAL THEN IGNORE IT.
IF(IBOUND(IC,IR,IL)
.LE.O)GO TO 10
C=EVTR(IC, IR)
S=SURF(IC, IR)
1O-26
H=HNEW(IC,IR,IL)
C
C7------
IF AQUIFER HEAD => SURF,SET Q=MAX ET RATE
1FtH.LT.S) GOTO 7
El-F0 9
C
DEFTH=>EXTINCTION DEPTH, ET IS 0
c8------IF
7 X=EXDP(IC,IR)
D=!3-H
IF(D.GE.X)GO TO 10
& ------LINEAR
RANGE . O.=-EVTR(H-EXEL)/EXDP
Q=C*D/X-C
C
Cl()--ACCUMULATETOTAL FLOW RATE
9 RATOUT=RATOUT-Q
C
Cll--IF CELL-BY-CELL FLOW TERMS TO BE SAVED THE ADD Q TO BUFFER.
IF(IBD.EQ.l) BUFF(IC,IR,IL)=Q
10 CONTINUE
C
C12---IF C-B-C TO BE SAVED CALL MODULEUBUDSV TO RECORDTHEM.
IF(IBD.EQ.11 CALL UBUDSV(KSTP,KPER,TEXT,IEVTCB,BUFF,NCGL,NRW,
NLAY, IOUT)
1
C
Cl3-----
C
Cl4-----
C
Cl5-..---
MOVE TOTAL ET RATE INTO VBVL FOR PRINTINGBY BASlOT.
VBVL(3,MSUM)=O.
VBVL(4,MSUM)=RATOUT
ADD ET(ET-RATE TIMES STEP LENGTH) TO VBVL
VBVL(l,MSUM)=O.
VBVL(2,MSUM)=VBVL(2rMSUM)tRATOUT*DELT
MOVE BUDGET TERM LABELS TO VBNM FOR PRINT BY MODULEBASlOT
VBNM(lrMSUM)=TEXT(l)
VBNM(2rMSUM)=TEXT(2)
VBNM(3rMSUM)=TEXT(3)
VBNM(4rMSUM)=TEXT(4)
C
Cl&---
INCREMENT BUDGET TERM COUNTER
MSUM=MSUM+l
C
Cl7 -----RETURN
RETURN
END
1O-27
List
Variable
of Variables
Global
C
D
DELT
EVTR
EXDP
H
HNEW
Module
Module
Global
Package
Package
Module
Global
IBD
Module
I BOUND
Global
IC
ICBCFL
Module
Global
I EVT
Package
IEVTCB
Package
IL
I OUT
IR
KPER
KSTP
Module
Global
Module
Global
Global
MSUM
NCOL
NEVTOP
Global
Global
Package
NLAY
NROW
Global
Global
Module
Module EVTlBD
Definition
Range
BUFF
DIMENSION (NCOL,NROW,NLAY), Buffer used to accumulate
information
before printing
or recording
it.
Maximum ET rate at a cell.
Depth to water below the ET surface.
Length of the current
time step.
DIMENSION (NCOL,NROW), Maximum ET rate.
DIMENSION (NCOL,NROW), Extinction
depth.
Head in the cell.
DIMENSION (NCOL,NROW,NLAY), Most recent estimz.te of
HNEWchanges at each iteration,,
head in each cell.
Flag.
= 0, cell-by-cell
flow terms for this package will
not be recorded.
f 0, cell-by-cell
flow terms for this package will
be recorded.
DIr4ENsION (NC~L,NR~W,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
Index for columns.
Flag.
= 0, cell-by-cell
flow terms will
not be recorded
or printed
for the current
time step.
+ 0, cell-by-cell
flow terms will
be recorc!ed for
the
Q
for
current
time
step.
DIMENSION (NCOL,NROW), Layer number for each rorizontalcell location
from which ET will
be taken if the El
option (NEVTOP) is equal to two.
Flag.
If IEVTCB > 0 and ICBCFL f 0, cell-by-cell
flow
terms for the EVTl Package will
be recordec on
UNIT = I EVTCB.
Index for layers.
Primary unit number for all printed
output.
IOUT = 6,,
Index for rows.
Stress period counter.
Reset at the start
of each stress
Time step counter.
period.
Counter for budget entries
and labels
in VBVL and VBNM.
Number of columns in the grid.
ET option.
= 1, ET is from the top layer.
= 2, ET at each horizontal-cell
location
is from
the layer specified
in the layer-indicator
array (IEvT).
Number of layers in the grid.
Number of rows in the grid.
Flow from ET into the cell.
(Reverse the sign to get
the flow to ET.)
lo-28
a
a
List
Variable
of Variables
for
Module EVTlBD (Continued)
Definition
Range
RATOUT
Module
S
SURF
TEXT
VBNM
Module
Package
Module
Global
VBVL
Global
X
Module
Accumulator
for the total
flow out of the flow field
to ET.
Elevation
of the ET surface for a cell.
DIMENSION (NCOL,NROW), Elevation
of the ET surface.
Label to be printed
or recorded with the array data.
DIMENSION (4,20),
Labels for entries
in the volumetric
budget.
DIMENSION (4,20),
Entries
for the volumetric
budget.
For flow component N, the values in VBVL are:
(l,N),
Rate for the current
time step into the
flow field.
(2,N), Rate for the current
time step out of the
flow field.
(3,N), Volume into the flow field
during simulation.
(4,N), Volume out of the flow field
during simulation.
Extinction
depth for a cell.
10-29
CHAPTER 11
GENERAL-HEAD BOUNDARYPACKAGE
Conceptualization
The function
cally
similar
of the General-Head
to that
into
or out of a cell
tion
to the difference
assigned
of the River,
i,j,k,
flow
into
the
cell
where Qbi , j ,k iS the flow
into
i,j,k
between
in figure
right
level
hb regardless
i,j,k
is
rises
source
Cell
cell
in figure
of porous
flow
i.e.
is the
holds
hbi,j,k
is the
head in cell
source
the
is
cbi,j,k
i,j,k;
source
the link
44 shows no mechanism to limit
head
relationship
source;
and the external
44, which
by the block
and the
(78)
and cell
and hi,j,k
factors;
in propor-
is established,
from the
The constant-head
44.
of other
represented
i,j,k
hi,j,k,
flow
- hi,j,k)
source
source;
in that
is provided
Thus a linear
(hbi,j,k
The relationship
figure
hbi,j,k.
between the external
on the
and ET Packages,
= Cbi,j,k
to the external
apparatus
(GHB) Package is mathemati-
and head in the cell
head assigned
schematically
Drain
from an external
source,
Qbi,j,k
the conductance
Boundary
between the head in the cell,
to the external
between
and Implementation
is
is shown
represented
source
between the
i,j,k.
by the
head at the
source
and cell
material
Cbi,j,k.
Note that
in either
direction
as hi,j,k
or falls.
A graph of Qbi,j,k
versus
hi,j,k
as given
In contrast
to the
River,
Drain
figure
45.
provides
no limiting
value
of flow
direction;
and as the head difference
increases,
flow
into
by equation
and ET Packages,
to bound the
linear
between cell
or out of the cell
11-l
(78)
continues
i,j,k
the GHB Package
function
in either
and the
to increase
is shown in
source
without
0
hbiJ,k
T
Cell i,j,k
Conductance,
Cbi,j,k
between
source
and
cell i,j,k
Figure 44.-Schematic diagram illustrating
principle of general-head
boundary package.
11-2
Constant-head
Source
Positive
Qb Indicates
Flow into
Aquifer
0
Negative
Qb indicates
Flow into
Boundary Source
Figure 45.-Plot of flow, Qb, from a general-head boundary source
into a cell as a function of head, h, in the cell where
hb is the source head.
11-3
limit.
Care must accordingly
insure
that
during
the
unrealistic
course
Because
it
flows
Qbi,j,k
of equation
left
HCOF and RHS of equation
subtracting
Cbi,j,khbi,j,k
into
the
GHB Package to
or out of the system
do not develop
of simulation.
must be added to the
sions
be used in utilizing
the term
cbi,j,k
from RHSi,j,k
(78)
side
of equation
(26),
from
is defined
this
HaFi,j,k
as the matrix
11-4
as an inflow
(24).
In terms
is accomplished
and subtracting
equations
to the aquifer
of the expres-
in the model by
the term
are assembled.
General-Head
Boundary
Package Input
Input for the General-Head
specified
in IUNIT(7).
Boundary
(GHB) Package is
read from the unit
FOR EACH SIMULATION
GHBlAL
1.
Data:
Format:
IGHBCB
110
MXBND
110
FOR EACH STRESS PERIOD
GHBlRP
2.
Data:
Format:
ITMP
I10
3.
Data:
Format:
Layer
Row
Column
I10
110
110
Boundary
Head
F10.0
(Input item 3 normally
consists
of one record for
ITMP is negative
or zero, item 3 is not read.)
Cond
F10.0
each GHB.
If
Explanation
Input
MXBND--is
of Fields
Used in
Instructions
the maximum number of general-head
IGHBCB--is
a flag
and a unit
boundary
cells
at one time.
number.
If
IGHBCB > 0, it
If
IGHBCB = 0, cell-by-cell
is the unit number on which cell-by-cell
flow
terms will
be recorded whenever ICBCFL (see Output
Control)
is set.
flow
terms
will
not be printed
or
recorded.
If
IGHBCB < 0, boundary
whenever
ITMP--is
a flag
leakage for each cell
ICBCFL is set.
will
be printed
and a counter.
If
ITMP < 0, GHB data
from the preceding
If
ITMP 2 0, ITMP is the number of general-head
current
stress period.
11-5
stress
period
will
boundaries
be reused.
during
the
Layer--is
the layer
boundary.
number of the
cell
Row--is
the
Column--is
the column number of the
boundary.
Boundary
row number of the cell
head--is
the
head on the
Cond--is
the hydraulic
conductance
cell and the boundary.
affected
affected
cell
by the head-dependent
by the head-dependent
affected
boundary.
by the head-dependent
boundary.
of the
11-6
interface
between
the aquifer
I
.
.
-3
-3
3030
I
aOaao”
.
.
11-7
Module Documentation
The General-Head
which
are called
GHBlAL
Boundary
the
Package
Allocates
Calculates
flow
boundary
boundary
boundary
Adds the terms
HCoFi,j,k
an array
the
of four
that
rates
list
head,
(BNDS).
and boundary
containing
m.
accumulators
respectively.
and accumulated
to and from general-head
11-8
modulI?s,
contains
-Cm and -CmHBm to the
and RHSi,j,k,
Package
are:
(Cm) of each cell
general-head
GHBlBD
The modules
general-head
Reads location,
Boundary
(GHBl) consists
space for
conductance
GHBlFM
General-Head
by the MAIN program.
the
GHBlRP
for
volume of
boundaries.
all
of
Narrative
This
module allocates
head boundaries
Print
1.
MXBND (the
unit
indicating
cell-by-cell
that
number for
in the
flow
and initialize
cell-by-cell
point
should
flow
of general-
NBOUND
to the first
is currently
terms
boundaries)
or a flag
be printed).
element
pointing
the amount of space needed for
for
each boundary--row,
add it
to ISUM so that
in
list
maximum number of general-head
terms
to ISUM which
values
element
the
in the boundary
to the
first
unallocated
X array.
Calculate
4.
to store
the package
saving
Set LCBNDS, which will
(BNDS), equal
element
X array
boundaries).
and IGHBCB (the
list
space in the
a message identifying
Read and print
3.
Module GHBlAL
(GHB).
(number of general-head
2.
for
it
column,
continues
the boundary
layer,
head,
to point
to the
list
and conductance)
first
(five
and
unallocated
X.
5.
Print
the
6.
RETURN.
number of elements
in the X array
11-9
used by the GHB Package.
Flow Chart
for
Module GHBlAL
NBOUNOis the number of general-head
boundaries
being simulated
at any
given time.
MXBNO is the maximum number of
general-head
boundaries
simulated.
IGHBCB is
a flag
and a unit
number.
If IGHBCB > 0, it is the unit number
on which cell-by-cell
flow terms will
be recorded whenever ICBCFL is set.
If IGHBCB = 0, cell-by-cell
terms will
not be printed
If IGHBCB < 0, the
for each cell will
whenever ICBCFL is
1
flow
or recorded.
boundary leakage
be printed
set.
READ AND PRINT
MXBND AND
LCBNOS is the location
in the X
array of the list
of general-head
boundaries
data (BNDS).
BNDS is a table containing
general-head
boundaries.
data
for
SET LCBNDS
EQUAL TO
LOCATIOI(I OF
FIRST ELEMENT
OF BNDS LIST
I
I
CALCULATE
AMOUNT OF
SPACENEEDED
FOR BNDS
LIST
PRINT AMOUNT
OF SPACE USED
BY THE GHB
11-10
4
B
SUBROUTINE GHBl AL(ISUM,LENX, LCBNDS,NBOUND,MXBND,IN,
1
IOUT,
IGHBCB)
C
C-----VERSION 1610 12MAY1987GHBlAL
****************************~*************************************
C
C
ALLOCATE ARRAY STORAGE FOR HEAD-DEPENDENTBOUNDARIES
******************************************************************
C
C
C
SPECIFICATIONS:
----------------------------------------------------------------------------------------------------------------------------------c"
El ------IDENTIFY
PACKAGE AND INITIALIZE # OF GENERAL HEAD BOUNDS
WRITE(IOUT,l)IN
1 FORMAT(lHO,‘GHBl -- GHB PACKAGE, VERSION 1, 9/l/87’
#
1' INPUT READ FROM UNIT',131
NBOUND=O
C
C2---
Cg.--
READ AND PRINT MXBND AND IGHBCB(MAX # OF BOUNDS AND UNIT
FOR CELL-BY-CELL FLOW TERMS FOR GHB)
READtIN,
MXBND,IGHBCB
2 FORMAT(2110)
WRITE(IOUT,3) MXBND
3 FORMATtlH r’MAXIMUM OF’,I5,’
HEAD-DEPENDENTBOUNDARYNODES’)
IF(IGHBCB.GT.0) WRITE(IOUT,9) IGHBCB
9 FORMAT(lX,‘CELL-BY-CELL
FLOW WILL BE RECORDEDON UNIT',131
IF(IGHBCB.LT.0) WRITE(IOUT,8)
8 FORMATtlX, ‘CELL-BY-CELL FLOW WILL BE PRINTED WHEN ICBCFL NOT 0’ 1
C
C3------ SET LCBNDS EQUAL TO ADDRESS OF FIRST UNUSED SPACE IN X.
LCBNDS=ISUM
C
c4------CALCULATE AMOUNTOF SPACE USED BY THE GENERAL HEAD LIST.
ISP=S*MXBND
IsuM=IsuMtIsP
C
c5------PRINT
AMOUNTOF SPACE USED BY THE GHB PACKAGE
WRITE(IOUT,4) ISP
4 FORMATtlX, 18,' ELEMENTS IN X ARRAY ARE USED FOR HEAD’,
1
‘-DEPENDENT BOUNDARIES’ 1
ISUMl=ISUM-1
WRITE(IOUT,5) ISUMlrLENX
5 FORMATtlX,18,’ ELEMENTS OF X ARRAY USED OUT OF’ ,181
IF(ISUMl.GT.LENX)
WRITE(IOUT,6)
***X ARRAY MUST BE DIMENSIONED
LARGER***‘)
6 FORMATt1X, ’
C
C6------RETURN
RETURN
END
l
11-11
List
Variable
of Variables
for
Range
Module GHBlAL
Definition
IGHBCB
Package
Flag and a unit number.
> 0, unit number on which the cell-by-cell
flow
terms will
be recorded whenever ICBCFL is set.
= 0, cell-by-cell
flow terms will
not be printed
or recorded.
< 0, boundary leakage for each cell will
be printed
whenever IGHBFL is set.
IN
Package
Primary
will
unit number from which
be read.
IOUT
Global
Primary
unit
ISP
Module
Number of words in the
ISUM
Global
Index number of the lowest element in the X array which
has not yet been allocated.
When space is allocated
for an array,
the size of the array is added to ISUM.
I SUM1
Module
ISUM-1.
LCBNDS
Package
Location
in the X array
BNDS.
LENX
Global
Length of the X array in words.
This should always be
equal to the dimension of X specified
in the MAIN
program.
MXBND
Package
Maximum number of head boundaries
time.
NBOUND
Package
Number of head boundaries
stress period.
number for
11-12
all
input
printed
X array
of the
active
for
by this
element
active
during
package
IOUT = 6.
output.
allocated
first
this
module.
of array
at any one
the
current
Narrative
This
1.
flag
module
reads data to build
Read ITMP.
indicating
that
Test
ITMP.
2.
data
read for
that
effect
the
last
(MXBND).
the general-head
ITMP is
stress
boundary
number of general-head
from the previous
greater
less
period
stress
than zero,
will
the
list.
boundaries
or a
should
be reused.
period
general-head
be reused.
or equal
this
stress
period
If
NBOUNDis
the
to zero,
period.
stress
number of general-head
stress
Print
for
than
(NBOUND) in the current
Compare the
current
period
If
boundaries
head boundaries
5.
data
ITMP is
general-head
4.
ITMP is the
Module GHBlRP
Print
boundary
a message to
and RETURN.
If
3.
for
to the
than
is the number of
Set the
period
number of general-
equal
boundaries
number specified
greater
it
to ITMP.
(NBOUND) in the
as the maximum for
the
simulation
MXBND, STOP.
number of general-head
boundaries
in the
current
stress
(NB~UND).
6.
See if
in the current
there
stress
are any general-head
period
(NBOUND = 0),
boundaries.
bypass
If
further
there
boundary
are none
processing
(SKIP STEP 7).
7.
Read and print
each general-head
8.
the
layer,
row, column,
boundary.
RETURN.
11-13
head,
and conductance
for
Flow Chart
for
Module GHBlRP
ITMP is both a flag and a
counter.
If it is greater
than or equal to zero, it is
the number of general-head
boundaries
to be simulated
during the stress period.
If it is less than zero, it
indicates
that the boundaries
simulated
in the last stress
period should be simulated
in the current
stress period.
2A
PRINT A
MESSAGE SAYING
THAT OLD DATA
WILL BE REUSED
MXBND is the maximum number of
general-head
boundaries
to
be simulated.
SET NUMBER
OF BOUNDARIES~
EQUAL TO ITMP
OF GENERALHEAD BOUNDARIES
t
SUBROUTINE
C
GHB1RP(BNDS,NBOUND,MXBND,INrIOUT)
E-----VERSION
1651 02FEB1983 GHBlRf’
******************************************************************
C
C
C
C
READ DATA FOR GHB
******************************************************************
E
SPECIFICATIONS:
-----------------------------------------------------------------DIMENSION
BNDStSrMXBND)
------------------------------------------------------------------
:
Cl----
C
READ ITMP(#
OF GENERAL HEAD BOUNDS OR FLAG TO REUSE DATA.)
READtIN, ITMP
8 FORMATtIlO)
C2------TEST
ITMP
IF(ITMP.GE.0)
C
(-3.A----
GO TO 50
IF ITMP<OTHEN
WRITE(IOUTs7)
7 FORMAT(lHO,‘REUSING
1
' PERIOD')
GO TO 260
REUSE DATA FROM LAST STRESS
PERIOD
HEAD-DEPENDENT BOUNDS FROM LAST STRESS’,
C
C3------ IF ITMF'=>OTHEN IT IS THEI OF GENERAL HEAD BOUNDS.
50 NBOUND=ITMP
C
c4------IF MAXNUMBER OF BOUNDS IS EXCEEDED THEN STOP
IF(NBOUND.LE.MXBND)
GOTO 100
C
WRITE(IOUT,99)
NBOLJNDrMXBND
99 FORMAT(lHOr’NBOUND(‘,I4,‘)
IS GREATER
C4A-----ABNORMAL
STOP
C
c5 ------PRINT #
THANMXBND('rI4,')')
STOP
OF GENERAL
HEADBOUNDS
THIS STRESSPERIOD
100 WRITE(IOUT,l) NBOUND
1 FORMAT(lHO,//lX,I5,' HEAD-DEPENDENT BOUNDARY NODES’)
C
C&---
IF THERE ARE NO GENERAL HEAD BOUNDS THEN RETURN.
IF(NBOUND.EQ.0)
GO TO 260
:7 ------READ
a PRINT
WRITE(IOUT,3)
DATA FOR EACH GENERAL HEAD BOUNDARY.
3 FORMAT(lHOrl5X,‘LAYER’r5X,‘ROW’,5X
1r'COL ELEVATION
CONDUCTANCE
C
BOUND NO.‘/lX,15X,60(‘-‘1)
DO250 II=lrNBOUND
READ (IN,41
K,I,J,BNDS(4rII),BNDS(5,11)
4 FORMAT(3110,2FlO.O)
WRITE(IOUT, K,I,J,BNDS(4,II)rBNDS(SrII)rII
5 F0RMAT(1X,15X,14,19,18,G13.4,G14.4,18)
BNDS(l,II)=K
BNDS(2,II)=I
BNDS(3,II)=J
250 CONTINUE
C8------RETURN
260 RETURN
END
11-15
List
of Variables
for
Module GHBlRP
Definition
Variable
Range
BNDS
Package
DIMENSION (5,MXBND), Layer, row, column, head and
conductance
from boundary for each generalhead boundary.
I
Module
Row number.
II
Module
Index
IN
Package
Primary
will
unit number from which
be read.
IOUT
Global
Primary
unit
I TMP
Module
Flag or number of boundaries.
2 0, number of bounds active
during the current
stress
period.
< 0, same bounds active
during the last stress
period will
be active
during the current
stress period.
J
Module
Column number.
K
Module
Layer
MXBND
Package
Maximum number of head boundaries
time.
NBOUND
Package
Number of head boundaries
stress period.
for
general-head
boundaries.
number for
all
input
printed
for
this
output.
package
IOUT = 6,,
number.
Ii-16
active
active
during
at an,y one
the
current
Narrative
This
ulators
module adds terms
for
Module GHBlFM
representing
riverhead
boundaries
to zero
in the current
to the accum-
HCOF and RHS.
1.
period,
If
there
NBOUNDis
less
For each boundary
3.
Determine
4.
If
the
cell
boundary
row (IR),
(IC),
is external
(IBOUND(IC,
and go on to the next
If the cell
6.
Add the
to the accumulator
boundaries.
in the BNDS list,
the column
5.
7.
or equal
are no general-head
2.
on this
than
is
internal,
-C*HB term
RETURN.
DO STEPS 3-6.
and layer
IR,
(IL).
IL) 2 0),
bypass
processing
one.
get the boundary
(C is the conductance
RHS and the term
stress
data
and HB is the boundary
-C to the accumulator
RETURN.
11-17
(head and conductance).
HCOF.
head)
Flow Chart
for
RHS is an accumulator
in
which the right
hand side
of the equation
is
formulated.
HCOF is an accumulator
which the coefficient
head in the cell is
formulated.
Module GHBlFM
(iG---)
1
in
of
DETERMINE
ROW. COLUMN,
LAYER
CONDUCTANCE
1
ADD TERMS
TO RHS AND
HCOF FOR THIS
CELL
11-18
6
B
SUBROUTINE
GHBlFM( NBOUND,MXBND,BNDS, HCOF,R-6,
1
IBOUND,
NCOL,NRW, NLAY1
C
GHBlFM
C-----VERSION 1037 lOAPR1985
***********************~******************************************
C
ADD GHB TERMS TO RHS AND HCOF
C
***+************t*************************************************
C
C
SPECIFICATIONS:
C
----------_------------------------------------------------------DIMENSION
BNDS(5rMXBND),HCOF(NCOL,NLAY),
C
1
C
C
Cl---
C
c2---..
RHS(NCOL,NRW,NLAY)rIBOUND(NCOL,NRCW,NLAY1
------------------------------------------------------------------
IF NBOUND<=OTHEN THERE ARE NO GENERAL HEAD BOUNDS.
IF(NBOUND.LE.0)
RETURN
RETURN.
PROCESS EACH ENTRY IN THE GENERAL HEAD BOUND LIST (BNDS)
DO 100 L=l,NBOUND
C
C3------
GET COLUMN, ROW AND LAYER OF CELL CONTAINING BOUNDARY
IL=BNDS(l,L)
IR=BNDS(ZrL)
IC=BNDS(3,L)
C
c4------IF THE CELL IS EXTERNAL THEN SKIP IT.
IF(IBOUND(IC,IR,IL).LE.O) GO TO 100
C
C5------ SINCETHE CELL IS
HB=BNDS(4rL)
INTERNAL GET THE BOUNDARYDATA.
C=BNDS(5rL)
C
@j-m--
C
ADD TERMS TO RHS AND HCOF
HCOF(IC,IR,IL)=HCOF(IC,IR,IL)-C
RHS(IC,IR,IL)=RHS(IC,IR,IL)-C*HB
100 CONTINUE
C7------RETURN
RETURN
END
l
11-19
List
of Variables
for
Module GHBlFM
Definition
Variable
Range
BNDS
Package
DIMENSION (S,MXBND), Layer, row, column, head and
conductance
from boundary for each generalhead boundary.
C
Module
Conductance
HB
Module
Head on boundary.
HCOF
Global
DIMENSION (NCOL,NROW,NLAY), Coefficient
the cell
(J,I,K)
in the finite-difference
IBOUND
Global
DIMENSION (NCOL,NROW,NLAY), Status
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
IC
Module
Index
for
columns.
IL
Module
Index
for
layers.
IOUT
Global
Primary
IR
Module
Index
for
rows.
L
Module
Index
for
boundaries.
MXBND
Package
Maximum
from the external
unit
number for
number
of
all
head
boundary.
of each cell.
printed
boundaries
of head in
equation.
output.
active
113UT= 6.
at an!! one
time.
NBOUND
Package
Number of head boundaries
stress period.
NCOL
Global
Number of columns
NLAY
Global
Number of layers
NROW
Global
Number of rows in the
RHS
Global
DIMENSION (NCOL,NROW,NLAY), Right hand side of the
finite-difference
equation.
RHS is an accumulation
of terms from several different
packages.
11-20
in the
in the
active
during
the
current
grid.
grid.
grid.
Narrative
This module calculates
and general-head
accumulator
2.
to step
3.
the
If
there
13 and put zeros
Test
flag
into
to see if
transferred
flow-term
flag
time
cell-by-cell
between the aquifer
(IBD)
and the
will
terms
terms
flow
(NBOUND = 0),
for
terms
rate
(ICBCFL = 0) or
boundaries
will
be accumulated
general-head
conditions
down
boundaries.
hold:
(2) cell-by-cell
during
be saved for
skip
are to be saved on disk.
of the following
general-head
flow
they
either
step
boundaries
the budget
cell-by-cell
not be saved if
not the proper
in which
cell-by-cell
are no general-head
are not needed for
If
and volumes
(RATOUT).
They will
is
rates
Module GHBIBD
boundaries.
Initialize
1.
for
this
this
(1) this
flow
terms
simulation
package,
clear
(IGHBCB 2 0).
the
(BUFF) and set the cell-by-cell
buffer
flow-term
(IBD).
4.
For each general-head
from or into
5.
of this
general-head
Determine
general-head
6.
the
If
the
boundary,
DO STEPS 5-13 accumulating
flows
boundary.
row, column,
and layer
of the cell
containing
the
boundary.
the
cell
is external
(IBOUND(I,J,K)
5 0),
bypass
further
boundary
list
(BNDS).
boundary.
7.
Get the
8.
Set RATE equal
head minus the
boundary
parameters
from the
to the boundary
head in the
cell
conductance
times
(RATE = C*(HB - HHNEW)).
11-21
the boundary
processing
9.
If
ICBCFL # 0),
10.
If
RATE to the
cell-by-cell
flow
print
RATE.
budget
terms
buffer
(BUFF).
terms
for
individual
cells
Check to see whether
flow
12.
If
RATE is negative,
add it
to RATOUT.
13.
If
RATE is
add it
to RATIN.
14.
See if
saved
cell-by-cell
(IBD = 1).
flow
If they
are,
is into
are to be saved,
11.
positive,
terms
call
(IGHBCB < 0 and
are to be printed
add the
or out of the aquifer.
for
individual
cells
module UBUDSV to
record
are to be
the
buffer
(BUFF) onto disk.
15.
Move RATIN and RATOUT into
Add RATIN and RATOUT multiplied
accumulators
budget-term
16.
Basic
in VBVL for
labels
Increment
Package for
17.
by the time-step
printing
to VBNM for
by BASlOT.
printing
the budget-term
a detailed
the VBVL array
RETURN.
11-22
length
Move the
printing
to the
by BASlOT.
volume
general-head
boundary
by BASlOT.
counter
explanation
for
(MSUM).
See the
section
of VBVL, VBNM, and MSUM.
in the
Flow Chart
for
IBD is a flag
which, if set, causes
cell-by-cell
flow terms for generalhead boundary to be recorded.
Module GHBlBD
(iii-)
1
lNlTlALlZE
FLAG
(IBD)
AND
RATE
ACC”MULATORS
l--l
I
I
EXTERNAL: a cell is said to be external
if it is either
no flow or constant
an equation
is not
head (i.e.,
formulated
for the cell).
RATE is the leakage rate into the
aquifer
from the boundary in a cell.
BUFFER is an array in which values are
stored as they are being gathered
for printing
or recording.
RATOUT is an accumulator
to which all
flows out of the aquifer
are added.
RATIN is an accumulator
flows into the aquifer
ROW. LAYER.
AND COLUMN
to which all
are added.
YES
C is the conductance
between the
boundary and the cell.
HB is the
boundary
HHNEW is the
GET BOUNDARY
PARAMETERS
FROM GENERALHEAD ~~s;NDARY
head.
head in the
6
c
CALCULATE
RATE=C’(HB-HHNEW
cell.
9
IGHBCB is a flag
and a unit
IF IGHBCBCO AND
ICBCFLIO.
PRINT RATE
number.
If IGHBCB > 0, it is the unit number
on which cell-by-cell
flow terms will
be recorded whenever ICBCFL is set.
If IGHBCB = 0, cell-by-cell
terms will
not be printed
flow
or recorded.
If IGHBCB < 0, boundary leakage for
each cell will
be printed
whenever
ICBCFL is set.
ICBCFL is
a flag.
If ICBCFL f 0, cell-by-cell
flow terms
will
be either
recorded or printed
depending on IGHBCB for the current
time step.
11-23
10
IF CELL-BY-CELL
TERMS TO BE
RECORDED (IBDtO)
ADD RATE TO
BVFFER
1
SUBROUTINE GHBlBDt NBOUND,MXBND,VBNM,VBVL, MSUM,BNDS, DELT, HNEW,
NCOL,NROW,NLAY, IBOUND,KSTP,KPER, IGHBCB,ICBCFL,BUFFI IOUT)
C
C-----VERSION
1612 lZMAY1987 GHBlBD
***************************~**~**~****~**************~*******~****
CALCULATE VOLUMETRIC BUDGET FOR GHB
*****************************************************~*******~****
C
C
C
C
C
SPECIFICATIONS:
-------------------I---------------------------------~------------
C
CHARACTER*4 VBNM,TEXT
DOUBLE PRECISION HNEW
DIMENSIONVBNM(4,MSUM)rVBVL(4rMSUM),BNDS(5rMXBND)r
1
HNEW(NCOL,NROW,NLAY)rIBOUND(NCOL,NROW,NLAY~,
2
BUFF(NCOL,NROW,NLAY)
DIMENSIONTEXT(4)
DATA TEXT(l),TEXT(Z)rTEXT(3)rTEXT(4)
/’ HEA’r’D
------_--__------------------------------------------~------------
C
C
Cl---Cl---
INITIALIZE CELL-BY-CELL FLOW TERM FLAG
ACCUMULATORS(RATIN AND RATOUT)
IBD=O
RATOUT=O.
DE’r’P
BO’r’UNDS’/
(IBD) AND
RATIN=O.
C
c2-----
IF NO BOUNDARIES THEN KEEP ZEROES IN ACCUMULATORS.
IF(NBOUND.EQ.0)GOTO 200
C
C3------ TEST TO SEE IF CELL-BY-CELL FLOW TERMS ARE NEEDED.
IF(ICBCFL.EQ.0 .OR. IGHBCB.LE.0) GOTO 10
:3A -----SINCE CELL-BY-CELL FLOW TERMS ARE NEEDED CLEAR BUFFER 8, SET
C3A-m--mTHE FLAG IBD.
IBD=l
DO 5 IL=l,NLAY
DO5 IR=lrNROW
DO5 IDlrNCOL
BUFF(IC,IR,IL)=O.
5 CONTINUE
C
c4------FOR
EACH GENERAL HEAD BOUND ACCUMULATEFLOW INTO AQUIFER
10 DO 100 L=lrNBOUND
C
C5------ GET LAYER, ROW AND COLUMNOF EACH GENERAL HEAD BOUNDARY.
IL=BNDS( 1, L)
C
(3j---
IR=BNDS(ZrL)
IC=BNDS(3,L)
IF CELL IS EXTERNAL THEN IGNOREIT.
IF(IBOUND(IC,IR,IL).LE.O) GOTO 100
11-24
C
C7------
GET PARAMETERSFROM BOUNDARYLIST.
HHNEW=HNEW(IC,IR,IL)
HB=BNDS(4rL)
C=BNDS(5rL)
C
C+---
CALCULATE THE FOW RATE INTO THE CELL
RATE=C*( HB-HHNEW1
C
c9 ------PRINT THE
INDIVIDUALRATES IF REQUESTED(IGHBCB<O).
IF(IGHBC3.LT.O.AND.ICBCFL.NE.O)
WRITE(IOUT,900)(TEXT(N)rN=1,4),
1
KPER, KSTP, L, IL, IR, IC, RATE
BOUNDARY’,14,
900 FORMAT(lHD,4A4,' PERIOD'rI3,' STEP’rI3,’
RATE’ rG15.7)
COL’rI4,’
LAYER',I3r' ROW’rI4,’
1'
C
(-Jl()---
C
Cll--C
IF CELL-BY-CELL TERMS ARE TO BE SAVED THEN PUT RATE IN
IF(IBD.EQ.l) BUFF(IC,IR,IL)=BUFF(IC,IR,IL)+RATE
BUFFER
SEE IF FLOW
IS INTOAaUIFEROR OUT OF AQUIFER.
IF(RATE)94,100,96
FLOW IS OUT OF AQUIFER SUBTRACT RATE FROMRATOUT
94 RATOUT=RATOUT-RATE
GO TO 100
c12---
C
Cl3----- FLOW IS INTOAQIFERADD RATE TO
96 RATIN=RATINtRATE
RATIN
100 CONTINUE
C
Cl4----- IF CELL-BY-CELL TERMS ARE TO BE SAVED THEN CALL
Cl4----- UTILITY MODULEUBUDSV
IF( IBD. EQ. 1) CALL UBUDSV(KSTP,KPERrTEXT, IGtBCB,BUFF,
NCOL,NRW,
NLAY,IOUT)
1
El5-----MOVE
RATES, VOLUMESAND LABELS INTO ARRAYS FOR PRINTING
200 VBVL(3rMSUM)=RATIN
VBVL(lrMSUM)=VBVL(lrMSUM)+RATIN*DELT
VBVL(4,MSUM)=RATOUT
VBVL(2,MSUM)=VBVL(2,MSUM)+RATOUT*DELT
VBNM(l,MSUM)=TEXT(l)
VBNM(2,MSUM)=TEXT(2)
VBNM(3,MSUM)=TEXT(3)
VBNM(4,MSUM)=TEXT(4)
C16---
INCREMENT
THE
BUDGET TERM COUNTER
MSUM=MSUMtl
C
Cl7 -----RETURN
RETURN
END
11-25
List
Variable
Range
BNDS
Package
BUFF
Global
C
DELT
HB
HHNEW
HNEW
Module
Global
Module
Module
Global
IBD
Package
IBOUND
Global
XC
I GHBCB
Module
Package
ICBCFL
Global
IL
IOUT
IR
KPER
KSTP
Module
Global
Module
Global
Global
L
MSUM
MXBND
NBOUND
Module
Global
Package
Package
NCOL
NLAY
NROW
Global
Global
Global
of Variables
for
Module GHBlBD
Definition
DIMENSION (5,MXBND), Layer, row, column, head and
conductance
from the boundary for each generalhead boundary.
DIMENSION (NcOL,NR~W,NLAY), Buffer used to accumulate
information
before printing
or recording
it.
Conductance from the external
boundary.
Length of the current
time step.
Head on boundary.
HNEW (J,I,K),
Single precision.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
of
HNEW changes at each iteration.
head in each cell.
Flag.
= 0, cell-by-cell
flow terms for this package will
not be recorded.
# 0, cell-by-cell
flow terms for this package will
be recorded.
DIMENSION (NCOL,NROW,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
Index for columns.
Flag and a unit number.
> 0, unit number on which cell-by-cell
flow terms
will
be recorded whenever ICBCFL is set.
= 0, cell-by-cell
flow terms will
not be printed
or recorded.
< 0, boundary leakage for each cell will
be printed
whenever ICBCFL is set.
Flag.
= 0, cell-by-cell
flow terms will
not be recorded
or printed
for the current
time step.
f 0, cell-by-cell
flow terms will
be either
printed
or recorded (depending on IGHBCB) for ::he currlent
time step.
Index for
layers.
Primary unit number for all printed
output.
IOUT = 6.
Index for rows.
Stress period counter.
Reset at the start
of each stress
Time step counter.
period.
Index for general-head
boundaries.
Counter for budget entries
and labels
in VBVL and VBNM.
Maximum number of head boundaries
active
at any one time.
Number of head boundaries
active
during the current
stress period.
Number of columns in the grid.
Number of layers in the grid.
Number of rows in the grid.
11-26
List
Variable
of Variables
for
Module GHBlBD (Continued)
Range
RATE
Module
RATIN
Module
RATOUT
Module
TEXT
VBNM
Module
Global
VBVL
Global
Definition
Flow from a bound into a cell.
(Reverse the sign to get
flow into the bound.)
Accumulator
for the total
flow into the flow field
out
of the bounds.
Accumulator
for the total
flow out of the flow field
into the bounds.
Label to be printed
or recorded with the array data.
DIMENSION (4,20),
Labels for entries
in the volumetric
budget.
DIMENSION (4,20),
Entries
for the volumetric
budget.
For flow component N, the values in VBVL are:
(l,N),
Rate for the current
time step into the flow
field.
(2,N),
Rate for the current
time step out of the
flow field.
(3,N), Volume into the flow field
during simulation.
(4,N), Volume out of the flow field
during simulation.
11-27
CHAPTER 12
STRONGLY IMPLICIT
PROCEDUREPACKAGE
Conceptualization
and Implementation
General
The discussion
here uti lizes
analysis
noted
of the Strongly
certain
In addition
provide
equations
cell,
i,j,k,
t CRi,j+l/E,khi,j+l,k
t cvi ,j,ktl/2hi
One equation
expressing
each of the six
equation
the
relationship
grid,
for
for
itself
here.
linear
a single
+ CRi,j-1/2,khi,j-1,
- Cvi ,j,k+1/2
+ HCOPi,j,k)hi,j,k
(7%
for
each cell
the equations
for
the entire
grid
consists
the end of the step.
12-1
step.
of head,
changes from one equation
The solution
in the finite-difference
among the heads at node i,j,k,
up to seven unknown values
the
node,
presented
of simultaneous
nodes at the end of a time
of unknown head values
step.
Procedure
three
- CRi,j-1/2,k
form is written
set
at each time
Implicit
these
= RHSi ,j,k*
adjacent
may involve
material,
t CCitl/2,j,khi+l,j,k
,j,ktl
of this
those
2 to be of the form
- CCi-1/2,j,k
- CCi+l/2,j,k
including
equation
+ CCi-1/2,j,khi-l,j,k
+ (-Cvi,j,k-l/2
- CRi , j+1/2,k
system
difference
.I
was shown in Chapter
Cvi,j,k-1/2hi,j,k-1
grid,
a large
presented
and numerical
reference,
the discussion
The finite
by iteration.
algebra
background
of the Strongly
solving
(SIP)
(1977) or Remson, Hornberger
Crichlow
to supplement
SIP is a method for
of matrix
to general
descriptions
may be consulted
Procedure
in any standard
by Peaceman (1977),
earlier
references
Implicit
concepts
which may be reviewed
and Molz (1971).
which
general
Theory
Because each
and because the
to the
must be solved
of one value
and at
next through
simultaneously
of head for
each
The discussion
notation
of the
notation,
equation
+ hi,j,khi+l,j,k
The coefficients
in equation
they
of equation
equation
(79);
(80)
with
is equivalent
+ Ei,j,khi,j,k
+ Si,j,khi,j,k+l
= Qi,j,k*
all
with
are labelled
the equation
is equivalent
to
for
(430)
the
Thus
(79);
+ HCOFi,j,k)
of
out
in
Chapter
2, the
in matrix
entire
set
of equations
of the form
form as
(‘31)
CA1{hj = id
is the matrix
head values,
(80)
two vectors
that
and (q}
Figure
l
[A]
that
equation
Zi,j,k
right-hand
of the
rows,
are all
of equations
node i,j,k,
for
elements
(h)
that
located
terms
coefficient
four
columns
there
on just
is a vector
of
of equation
matrix
and of t1ie
and two layers.
are very
Notice
few nonzero
seven diagonals,
as
47.
of equation
cLi,j,k-l/2
for
these
of head,
of the
is sparse--i.e.,
in figure
Examination
(80)
is a vector
a mesh of three
the matrix
indicated
of coefficients
46 shows the
for
elements--and
Ei,j,k
and so on.
can be summarized
where [A]
i,j,k
- cci-l/2,j,k
(-cvi,j,k-1/2
- CVi,j,k+1/2
index
node i,j,k.
Of equation
cLi,j,k-l/2
to the eXpreSSiOn
- CCi+l/2,j,k
- CPi,j+1/2k
As pointed
(80)
(80)
(80)
- CPi,j-1/2k
of
are associated
Of equation
z{,j,k
of SIP.
the developers
+ Di,j,khi,j-1,k
+ Fi,j,khi,j+l,k
to show that
here is based on the
(79) may be written.
+ Bi,j,khi-l,j,k
Zi,j,khi,j,k-l-
presented
Stone and Kwan (1969))
of Weinstein,
Using their
SIP procedure
(79)
(79)
and (80)
appears
both
and as the coefficient
node i,j,k-1,
that
will
show that
as the coefficient
S in the
the
term
Z in equation
corresponding
is
(;32)
= Si,j,k-1
12-2
::
2
ooooooooooo~oooooooxoo,w
2 24
a,
0
0
0
0
0
0
0
0
0
0
u-j-0
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0
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0
0
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fo
0
:
oooooo$-ooooooo~ooLLW-nOOmo
u
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m
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uTtic.iOo
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-
0
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0
0
m
;:
2
m
M
&
(D
::
ul
:
P
c:
F.3
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0
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oooo~~ooooooofooo~~oomooo
ul
?
m
2
2
ooooo~ooooooo~OGu.Jn-oomoo
w
M
&
(D
0
M
M
$
oooooooocfjmoooooooIooownoo
0
u
2
ooooooooov)‘oooooooIooGwoo
0
0
E
ul
z
m000000
f
Tr
cn~OOOOOOOOOOOwrnOOmOOOOOOO
2
OOOOOOO~*OO~~WOOOOOOOOOOON
0
0
0
0
0
0
x-0
0
u
z
LLi-0
0
-
;:
r! 0
0
9
0
0
0
0
0
0
0
a
0
I-0
0
U!!,$O
0
0
&
OOOO~OOOwm~OOOOOOOOOONOOO
0
c:
M
ooooox*o00tin~0000000000~00
0
N
0
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0
0
0
0
0
0
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0
0
0
0
m
ooPoo~~w~n~oo~oooooooN'ooooo
co
z
0
I”0
0
LmW*&O
0
UI
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
hi0
0
0
0
0
0
0
0
fOOOWmn~OOmmOOOOOOONSOOOOOOO
*
oou*LJooom*oooooooN-00000000
0
ufuW”dO
0
L&.-W”O”O
W-n”0
0
0
Ii”0
0
0
0
0
0
0
0
0
0
0
0
0
COd
0
0
0
0
0
N-O
0
a”0
m*O
0
N
0
z
I
I
12-3
NCOL * NROW
N
/
NCOL
\
/
1
-
s
-
1
\
/
NCOL
NCOL iNROW
Brackets indicate horizontal spacing, in matrix columns, between
nonzero diagonals (e.g., diagonals E and F are adjacent).
Figure 47.-Structure
of coefficient matrix showing nonzero
diagonals.
12-4
Similarly,
and
Bi,j,k
= Hi-l,j,k
(83)
IIi,j,k
= Fi,j-l,k*
(84)
Replacing
with
each Z, B, and D coefficient
the equivalent
yields
S, H, or F element,
the matrix
of Figure
Thus the coefficient
matrix
sparse.
A system of equations
methods
if
[L*]
in lower
is
[A]
48, which
[A]
triangular
while
are equal
into
form
[U*]
CL*] and [U*]
r el at ive to [A]
has been accomplished,
substitution"
arises
generally
even though
needed to calculate
off
errors
[U],
for
[A]
of their
nonzero
sum matrix
(1)
[A + B] is
"close"
(2)
[L]
form,
is
in lower
and all
form
elements
such that
are on or below the
(all
nonzero
of
Once this
factoring
and forward
However,
matrix,
of computer
elements
on the main diagonal
[A].
a difficulty
CL*] and [U*]
are
memory and time
elements.
easily
into
and [U] meet the following
In addition,
may be
round-
a matrix
[B]
two matrices
such that
CL] and
conditions:
to [A];
triangular
entries
by direct
the characteristics
seeks to find
[A + B] can be factored
CL],
elements
as
large.
Procedure
where [A + B],
- (84),
as well
and [U*],
the solution.
deal
Implicit
[L*]
known as "backward
is a sparse
(82)
symmetric
can be solved
illustrates
and a great
all
is
a 3 x 3 matrix
may become unacceptably
The Strongly
the
(49)
a technique
not sparse,
(81)
and all
can be used to complete
in that,
(81)
nonzero
46
seen to be symmetric.
two matrices
(all
of Figure
by equations
readily
is in upper triagular
Figure
to one.
is
of equation
are on or above the main diagonal),
[U*]
as defined
of the form of
can be factored
main diagonal),
in the matrix
along
form while
is
in upper triangular
the main diagonal
of [UJ are equal
to unity;
12-5
[U]
of
0
0
0
-.
7
c/Y 0
0
f
c
-.
0
“. N.
r r
ur u? 0
0
n!
N
2
“! Z:
0:
0 0 cc 0 0 0 0 IL- J 0 0 f
--.
T.
c/i- 0
N.
--.
0
0
0
Y N.
r c.
w’ G 0
f6 o
4
$
o
o
o
o
o
0
0
0
0
co”
0
0
0
0
r
r
co”
0
0
0
cl?
0
0
0
0
0
0
0
0
0
0
0
f
0
3
UY
f
0
0
r
r
ll.Y
-.
c.
IL-
0
7.
2
N.
_
IL- w- 0
2
f
0
0
*fj
-. 2 2
r
c.
r ‘.
7 r
w- Ii- 0
f
Liti
0
x
-.
m
-.
7.
F;-
0
f
0
0
0
-.
7
co’ 0
12-6
.-P
.-c
cp
E
u”
.
Id
[I
1
1
2
-1
0
[
-3
3
Figure 49.-Decomposition
of a coefficient matrix into lowerand
upper triangular matrices.
12-7
(3)
CL1and GUIare
(4)
both
[L]
and [U]
Suppose a matrix
conditions;
both sparse;
have just
[B]
the term
[B]
and
four
nonzero
is constructed
{h}
diagonals.
in an attempt
to satisfy
can be added to each side
these
of equation
(81)
to give
CA + Bl{h)
A solution
for
vector
equation
(81).
equation
(85)
approach
to the
preceding
is,
{h)
+ CBl( h}
equation
(85)
The presence
presents
is utilized
where {ha)
is a vector
of head values
used
postulated
and [U],
above,
appropriate
matrix
of the matrices
is subtracted
If
[B].
from each side
CA + Bl {ha}
(86)
[B]
{h"-1)
were
to the
into
and backward
is equivalent
That
is actually
known,
solution
properties
the
sparse
matrices
substitution.
to that
the
a vector
solution
The term
Thus
of finding
is
pursued
an
in
[A + B] {hg-I}
(86) to yield
= {q)
or
= {q)
right.
R, and {ha-I}
easily
CL] and [U].
- [A + B] {ha-l}
CA + B] {hg - ha-I}
of h from the
on the
(86),
according
however,
[A + B],
of
an iterative
(86)
matrix
be factored
In practice,
[A],
of
{ha-I}
the
for
equation
sides
if
values
from iteration
the use of forward
of solving
Z),
In equation
{ha}.
[A + B] could
allowing
+ [B]
a-1.
be straightforward;
the problem
terms
to
on both
vector
in the form
= {q}
iteration
(h}
head vector
of head values
as an approximation
of (86) would
[L]
from
be a solution
however,
(chapter
may be expressed
[A + B] {hfi)
must also
difficulty;
may be used in the
(85)
(85)
of the vector
an immediate
solution
iteration
equation
for
= {q)
-[A]
{ha-I)
12-8
- [A]
{ha-l}
(87)
In order
that
the conditions
B] may be satisified,
were not present
additional
for
relationship
[U]
is
in [A],
diagonals
following
elements
[U],
new terms
which
of these
into
the equation
to i,j,k.
of [A + B] and the elements
The
of [L]
where as indicated
equations,
to elements
of [U] above the main diagonal,
and [A +
diagonals
effect
heads at nodes not adjacent
50 and 51, a, b, c, and d, refer
to elements
[L],
nonzero
50; the
is to introduce
between the elements
in the
six
as shown in figure
involving
as given
above for
[A + B] must contain
nonzero
node i,j,k,
specified
of CL],
e, f,
and capital
in figures
and g, refer
letters
refer
to
of [A + B].
z'i,j,k
= ai,j,k
(89-a)
A'i,j,k
= ai,j,kei,j,k-1
(89-b)
T'i,j,k
= ai,j,kfi,j,k-l
(89-c)
B'i,j,k
= bi,j,k
(89-d)
c'i,j,k
= ei-l,j,kbi,j,k
(89-e)
D'i,j,k
= ci,j,k
(89-f)
E'i,j,k
= ai,j,kgi,j,k-1
+ bi,j,kfi-l,j,k
(89-g)
+ ei,j-l,kci,j,k+di,j,k
If
and
(89-h)
F'i,j,k
= di,j,kei,j,k
G'i,j,k
= fi ,j-l,kci
H'i,j,k
= fi,j,kdi,j,k
(89-j)
U'i,j,k
= bi,j,kgi-l,j,k
(89-k)
R'i,j,k
= gi,j-l,kci,j,k
(89-1)
s'i,j,k
= gi,j,kdi,j,k
(89-m)
the
subscript
outside
of the
The 13 equations
of an element
grid
boundary,
contain
(89-i)
,j,k
in equations
the element
20 unknown values,
12-9
(89-a...m)
places
the element
is assumed to be equal
the
elements
of [L],
to zero.
[U],
and
NCOL * NROW
*
/
NCOL
/
A
\
1
-
/
\
NCOL
*
1
-
* Marks Diagonals
Which Are Not in
Matrix x
\
1
L
-
-
1
Brackets indicate horizontal spacing,
in matrix columns, between nonzero diagonals
(e.g., diagonals E and D are adjacent); asterisks
mark nonzero diagonals which are not present
in matrix [A].
\
/
/
NCOL
f
NCOL * NROW
Figure 50.-Structure
of matrix [A+B] showing
nonzero diagonals.
12-10
1
\
NCOL
\
-
1
/
Brackets indicate vertical spacing, in matrix rows, between
nonzero diagonals (e.g., diagonals d and e are adjacent).
Figure 51 .-Structure,
showing nonzero diagonals, of the lower triangular
factor [L] and the upper triangular factor [U] of matrix [A+B].
12-11
[At
B].
This
added to [A]
matrices
indicates
so that
of the
must be "close"
that
the
are many matrices
sum can be factored
form of [L]
to [A],
there
into
or equivalently
which
can be
upper and lower
However, the
and [U].
[B]
requirement
triangular
that
[I\ + B]
that
(90)
CA+ Bl {h) = CA1{h)
has not yet been used.
associated
with
an individual
Z'i,j,khi,j,k-1
of the elements
node,
t U’i,j,khi-l,j,ktl
t S'i,j,khi,j,ktl
fj z,j,khi,j,k-1
+ U'i,j,khi,j-1,k
t R’i,j,khi,j-l,k+l
t Fi,j,khi,j+l,k
’ Hi,j,khitl,j,k
(91)
,k+l
(91) can be rearranged
not present
in [A]
so that
are all
is made up of differences
corresponding
elements
(zi ,j ,k-z'
i,j,k)hi,j,k-l
on the
between
of matrix
the terms
right
elements
[A + B],
t (Fi,j,k-F'i,j,k)hi,jtl,k
t (Hi,j,k-H'i,j,k)hi+l,j,k
t (Si,j,k-S’i,j,k)hi,j,ktl
n A’i,j,khi,j+l,k-1
t C’i,j,khi-l,jtl,k
t U'i,j,khi-1,jktl
The terms
side,
six
nonzero
while
the
[A]
and
of matrix
t G’i,j,khi+l,j-1,k
(92)
t B'i,j,khi,j-1,ktl
on the
right
side
of [A t B] not appearing
involve
the
left.
t (Bi,j,k-B'i,j,k)hi-l,j,k
t (Ei,j,k-E'i,j,k)hi,j,k
+ T'i,j,khitl,j,k-1
from the
i.e.
+ (Di , j ,k-D' i,j,k)hi,j-1,k
B, and all
that
t Bi,j,khi-l,j,k
+ Ei,j,khi,j,k
t si,j,khi,j
diagonals
implies
{h)
t G’i,j,khi+l,j-1,k
+ H'i,j,khitl,j,k
diagonals
(90)
and [$I
t T'i,j,khi+l,j,k-1
t F’i,j,khi,jtl,k
+ Di,j,khi,j-1,k
of [A + B] {h)
equation
t C’i,j,khi-l,jtl,k
t E'i,j,khi,j,k
Equation
i,j,k,
t A'i,j,khi,jtl,k-1
+ B'i,j,khi-l,j,k
side
In terms
of (92),
in [A],
corresponding
are all
heads at nodes not adjacent
12-12
to the
derived
to node,
six
nonzero
from the matrix
i,j,k;
by contrast,
the terms
involve
on the
left
side
of (92) are derived
the heads at i,j,k
and the six
To reduce the effect
of the terms
to i,j,k,
three
zero
and one, are introduced
side
of equation
((85)
or (86))
iteration
is
implemented,
They are brought
parameters.
(zi , j,k-Z'
i,j,k)hi,j,k-1
of the terms
solution
multipliers
into
on the
on the
equation
right
role
equations
of
(92) as follows:
+ (Bi,j,k-B'i,j,k)hi-l,j,k
t (Ei,j,k-E’i,j,k)hi,j,k
+ (Fi,j,k-F'i,j,k)hi,j+l,k
+ (Hi,j,k-h'i,j,k)hi+l,j,k
+ (Si,j,k-S’i,j,k)hi,j,k+l
(J d’i,j,khi,j+l,k-1
+ fiT’i,j,khi+l,j,k-1
+ $‘i,j,khi-l,j+l,k
+ YG’i,j,khi+l,j-1,
k + BU’i,j,khi-1,jktl
(93)
,j,khi-l,k+l
Next the heads on right
adjacent
to i,j,k,
adjacent
to i,j,k.
jtl,
lies
which
and
chosen between
of the matrix
take
+ (Ui,j,k-U'i,j,k)hi,j-1,k
+ d’i
and [B],
to nodes not adjacent
a, B and y, and all
as the
these
[A]
nodes.
corresponding
as multipliers
Ultimately,
(92).
adjacent
here termed
parameters,
from both
k-l
are:
interpolation
side
are expressed
This
i,j+l,k;
illustrated
(93),
in terms
is done by noting
at the corner
i,j,k-1;
of
corresponding
of heads at nodes which
that,
of a rectangle,
and i,j,k.
in figure
to nodes not
for
example,
the other
Thus using
52, hi,j+l,k-1
by
three
the
node i,
corners
rules
is given
are
of
in
approximately
= hi,j+l,k
+ hi,j,k-1
- hi,j,k*
(94-a)
hi+l,j,k-l
= hi,j,k-l
+ hi+l,j,k
- hi,j,k
(94-b)
hi-l,j+l,k
= hi-l,j,k
+ hi,j+l,k
- hi,j,k
(94-c)
hi,j+l,k-1
Similarly,
12-13
Suppose the Functionf
1
Is Known at 2,3 and 4.
2
By interpolation the Function
at the Center Can be Approximated
f,(c)
by
* f (2) +f (3)
2
and
f*(c) - f (1) +f (4)
2
Suppose
f, @I -f*
(cl
Then
f (2) +f
(3) =f
2
3
(1) +f (4)
2
4
Therefore
f (1) -f
(2) +f (3) -f (4)
Figure 52.-Estimation
of a function at one corner of a rectangle in
terms of the values of the function at the other three
corners.
12-14
hi+l,j-l,k
= hi+l,j,k
+ hi,j-l,k
- hi,j,k
(94-d)
hi-l,j,k+l
= hi,j,k+l
+ hi-l,j,k
- hi,j,k
(94-e)
hi,j-l,k+l
= hi,j,k+l
+ hi,j-l,k
- hi,j,k*
(94-f)
Substituting
equations
(94-a...
- zi,j,k
+ d'i,j,k
(z'i,j,k
+ BT'i,j,k)
(93)
+ @J'i,j,k)
hi-l,j,k
+ (U'i,j,k
- Ui,j,k
+ s'i,j,k
+ d'i,j,k)
hi,j-l,k
+ (E'i,j,k
- Ei,j,k
- d'i,j,k
- BT'i,j,k
- $'i,j,k
- BU'i,j,k
- d'i,j,k)
- Fi,j,k
+ d'i,j,k
+ "C'i,j,k)
+ (H'i,j,k
- Hi,j,k
+ BT'i,j,k
+ *'i,j,k)hi+l,j,k
+ (S'i,j,k
- Si,j,k
+ BU'i,j,k
+ d'i,j,k)hi,j,k+l
approximately
in equation
equal
to zero.
gives
hi,j,k
+ (F'i,j,k
expressed
and reorganizing
hi,j,k-1
+ $'i,j,k
hi,j+l,k
(95) can be satisfied
Setting
these
(95)
m0
coefficients
if
each coefficient
equal
to zero
the equations
z'i,j,k
- zi,j,k
+ d'i,j,k
+ BT'i,j,k
= 0
(96-a)
B'i,j,k
- Bi,j,k
+ $'i,j,k
+ BU'i,j,k
= 0
(96-b)
U'i,j,k
- Ui,j,k
+ fi'i,j,k
+ d'i,j,k
= 0
(96-c)
E'i,j,k
- Ei,j,k
- d'i,j,k
- BT'i,j,k
- $'i,j,k
- *'i,j,k
- Bu'i,j,k
- &'i,j,k
= 0
(96-d)
F'i,j,k
- Fi,j,k
+ d'i,j,k
+ $'i,j,k
= 0
(96-e)
H'i,j,k
- Hi,j,k
+ BT'i,j,k
+ $'i,j,k
= 0
(96-f)
S'i,j,k
- si,j,k
+ 8U'i,j,k
+ d'i,j,k
= 0
(96-d
Equations
(96-a...g)
and (89-a...
unknowns which when solved,
[U]
equation
- Bi,j,k
The relation
yields
into
+ (B'i,j,k
- YG'i,j,k
is
f)
such that
[A + B] is
will
"close"
m) form a system
yield
the entries
to [A],
12-15
of 20 equations
of [A t B],
and can be readily
in 20
[L]
factored
and
into
[L]
lower
and [U],
where [L]
triangular
equations
and [U]
are both sparse
and upper triangular
(89-a,
-b,
and -c)
into
forms.
equation
and have the
For example,
(96-a)
required
substituting
and rearranging
yields
= zi,j,k/(l
+ *i,j,k-1
+ @fi,j,k-I)*
(97-a)
bi,j,k
= Bi,j,k/(l
+ Vei-l,j,k
+ @i-l,j,k)
(97-b)
ci,j,k
= Di,j,k/(l
+ Yfi,j-1,k
+ agi,j-1,k)
(97-c)
ai,j,k
Similarly,
A'i,j,k
= ai,j,kei,j,k-1
(97-d)
c'i,j,k
= ei-l,j,kbi,j,k
(97-e)
G'i,j,k
= fi, j-l,kci
R'i,j,k
= gi,j-l,kci,j,k
(97-g)
T'i,j,k
= ai,j,kfi,j,k-1
(97-h)
U'i,j,k
= bi,j,kgi-l,j,k
(97-i )
di,j,k
= Ei,j,k
(97-f)
, j,k
+ d'i,j,k
+ *'i,j,k
+ BT'i,j,k
+ @'i,j,k
+ @J'i,j,k
+ d'i,j,k-ai,j,kgi,j,k-l-bi,j,kfi-l,j,k
(97-j 1
- ei,j-l,kci,j,k
ei,j,k
= (Fi,j,k-d'i,j,k-$'i,j,k)/di,j,k
(97-k)
f*l,j,k
= (Hi,j,k-BT'i,j,k-$'i,j,k)/di,j,k
(97-l)
gi,j,k
= (Si,j,k-d'i,j,k'BU'i,j,k)/di,j,k
(97-m)
Using these
relations
be replaced
with
[LJ[UJ
where again
to provide
the product
{ha-ha-l}
[L][U]
= {q) - [A]
the superscript
t-1 to the preceding
the elements
iteration
in
of [L]
and [U],
[A + B] may
(88) to yield
(98)
{ha-l)
R refers
level.
to the
current
We next
12-16
define
iteration
the
level,
vector
and
{RESR} by
{RE$}
= {q}
Using this
- [A]
notation
the
{v)
D-1 {v)
{hR-hRB1}
in the equation
{hg-ha-l}.
{hR-hR-l}
In earlier
The vector
substitution
to solve
53-a.
used to calculate
53-b.
to solve
the coefficients
were identified
the elements
in this
for
way is then
the vector
linear
by the
indices
the process
using
elements
equation
of the equations
of the vector
sequentially
Because all
first
determined
(102)
To illustrate
renumber the equations
in [L]
{v),
a single
of the cells,
of forward
it
and hence the
substitution,
is convenient
index,
by matrix
to
as shown in
above the main diagonal
represented
as
equation
are
(101)
d1v1 = RESla
In equation
(97-j),
the
is
(103)
(103),
the term dl
and RESIR has been calculated
vector
for
= {v)
discussions,
shown in figure
{v)
of back substitution
of the matrices
the
forward
and backward
(101)
in a process
zero,
involves
of forward
= {REg)
ultilized
figure
by a process
in the equation
= [U]
elements
(100)
step
where {v)
[U]
can be written
can now be solved
The first
vector
(98)
= {RE$)
(100)
substitution.
(99)
equation
[L][U]{hR-hg-I}
Equation
{hE-l}
(RES');
The second equation
thus
(103)
represented
has been determined
through
can be solved
by matrix
c2v1 + d2v2 = RES2'
through
equation
(99)
immediately
for
equation
(101)
equation
as an element
the
value
of
of vl.
is
(104)
12-17
Layer 1
Layer 2
(a) Cell Numbering With 3 Indices
3ow 1
2
.
Layer
1
Layer 2
(b) Cell Numbering
Figure 53.-Cell
With 1 Index
numbering schemes for a grid using three
indices and using one index.
12-18
Again,
c2 and d2 are known from equations
equation
(104)
(99);
using
the
can be solved
The general
for
value
(97),
of VI from the
and RESZR is known from
solution
of equation
(103),
v2.
equation
for
an element
of {v)
has the
form
(105)
Vn = (RESnR-anVn-NRC-bnVn-NCOL'CnVn-l)/dn
where NRC is the number of cells
columns
in the model,
through
equations
The terms
(97)
This
of {v)
triangular
The process
that,
calculation
it
through
of {v}
determined
equation
determined
substitution,
is possible
CL]--i.e.,
is next
(99).
[L]
of back substitution
is
{h a-1}
vector
the
[U]
When the
reversed.
corresponding
of {v),
has only
in the
lower
zeros
the elements
solving
to that
to
{hg-ha-I}
to obtain
{hg),
of the
equation
of forward
is upper triangular,
vector
to iteration
problem
thus
is similar
because the matrix
In summary,
the
(102).
substitution
order
of
has been calculated,
the vector
of head
R.
of solving
the equation
CAl{h~ = {s)
(106)
has thus
been converted
matrices
[L]
IRESt}
the
and
the elements
because of the
because
((103)
earlier
in which
used to calculate
from the elements
is added to the
values
and dn are all
of the main diagonal.
{h R -h a-1}
except
number of
and second eqations
elements
in sequence,
Back substitution
vector
first
of forward
form of the matrix
right
NCOL is the
an,bn,cn
the
involves
procedure
are determined
layer,
and RESnR is determined
an and bn are zero for
sequence.
the
the coefficeints
and each equation
(104));
in the
and [U]
is calculated
preceding
iteration;
into
an iterative
are determined
using
(3)
the
vector
equation
process
using
equations
{q),
(100)
12-19
in which:
the matrix
is then
(97);
[A]
solved
(1) the
(2) the
vector
and heads from
using
forward
and backward
vector
substitution
{h"-l}
However,
aspects
to obtain
is added to the
while
these
the
vector
are the essential
steps
the coefficient
seven nonzero
diagonals.
Rather
SIP Package,
only
of the matrix,
only
CC, CR, and CV.
and the
the
matrix
2.
The latest
Output
lower
vector
{hi}.
of the SIP procedure,
diagonals
matrix
passing
The main diagonal
is formed
HCOF described
{q),
estimate
in HNEW replacing
several
from SIP consists
Procedure
to the
matrix
arrays:
2.
lower
only
to the
diagonals
arrays
hand side
RHS described
(ha-l),
are
conductance
The right
array
estimates.
in Ctapter
corresponds
by SIP,
Thus input
they
of
to the
are
to SIP
CC, CR, CV, RHS, HCOF, and HNEW.
of a new HNEWarray.
inside
with
and because of symmetry
of head are calculated
the previous
may be modified
the entire
from the three
of the head distribution
is
sparse,
to the conductance
in Chapter
corresponds
of the following
is
and the three
correspond
array
[A]
are needed;
diagonals
HNEW. As new estimates
arrays
than
the main diagonal
equation,
the Formulate
input
the nonzero
The three
needed.
consists
the
of Arrays
previously,
stored
to obtain
and (4) the
of the method remain to be discussed.
As noted
array
{hg-he-l};
{hfi-ha-l}
Transfer
arrays
vector
the
iteration
at each iteration.
12-20
As explained
loop;
in Chapter,
therefore,
the
3,
Order of Calculation
Experience
solved
has shown that
in two different
iterations
needed to converge
in the discussion,
the first
order,
to this
ascending
proceed
in ascending
order.
51, equations
on alternate
the
last
column order,
to equations
= zi ,j,k/(l+*
bi,j,k
= Bi,j,k/(l+Yei+l,j,k+@i+l,j,k)
ci,j,k
= Di ,j,kl(l+Yf
i,j,k+l+Bfi,j,k+l)
= ai,j,kei,j,k+l
C'i,j,k
=
G’i,j,k
= fi ,j-1,kci
R'i,j,k
= gi,j-l,kci,j,k
T'i,j,k
= ai,j,kfi
U'i,j,k
=
di,j,k
assumed
column,
column
An alternative
layer,
is
and to
and descending
names used in figure
can be developed.
They
are
(107-a)
(107-b)
i,j-l,k+@i,j-1,k)
(107-c)
(107-d)
(107-e)
ei+l,j,kbi,j,k
(107-f)
,j,k
(107-g)
(107-h)
,j,k+l
(107-i )
bi,j,kgi+l,j,k
= Ei,j,k
last
row order,
of diagonal
The order
in ascending
order.
are
number of
at the first
row, and the
(g7-a...m)
ai,j,k
A'i,j,k
layer
descending
the
reduced.
and to proceed
Using the same ordering
similar
is
has been to begin
and ascending
column,
equations
iterations,
to a solution
layer,
row order,
at the first
the finite-difference
point,
row, and the first
to start
layer
orders
if
+ aA'i,j,k+@T'i,j,k
+YC'i,j,k+fi'i,j,k
+BU'i,j,k
t~‘i,j,k-ai,j,k9i,j,k+l’bi,j,kfi+l,j,k
(107-j)
-ei,j-l,kci,j,k
12-21
ei,j,k
= (Fi,j,k-d'i,j,k-s'i,j,k)/di,j,k
(1107-k)
f. l,j,k
= (Hi,j,k-BT'i,j,k-fi'i,j,k)/di,j,k
(307-l)
gi,j,k
= (%,j,k-a'i,j,k-BU'i,j,k)/di,j,k
(107-m)
In the model described
(97-a . ..m)
are in effect
The model program
variables
(107)
indices.
actually
achieved
to the cell
through
in these
n; the
equations,
each been replaced
Note that
section.
the
equation
n.
This
as the
for
equation
of these
one additi
nrl
onal
vn, the element
of the
can be added inasmuch
[L]
of values
general
in which
of
(97)
assigned
equations,
calculated,
the
but in the
are defined
a,
w as explained
equation
iterations.
of equations
parameters
parameter
and equation!;
The ordering
and ncl
iteration
nth rows of the matrices
equations
layer
indices
by a single
set
indices.
the sequence
list
the
(107-a...m)
in successive
uses one general
in the previous
and column as cell
equations
alternately
by single
In the following
refers
Also,
invoked
are identified
is then
herein,
or 01'
to the
index
nil
same row
analogously.
B and y
have
,in the following
has been added to the
vector
the
{v) corresponding
as Vn can be calculated
and [U] have been calculated.
list-to cell
as soon
The
are
an = Zn/(l
+ den11
+ fnll))
:108-a)
bn = Bn/(l
+ den,1
+ Snr1))
:108-b)
Cn = Dn/(l
+ dfncl
+ gncl >I
(108-c)
A'n
( 108-d )
= anenll
C'n = bnenrl
(108-e)
G'n = cnfncl
(108-f)
R'n = Cngncl
(108-g)
T'n
(108-h)
= anfnll
(108-i )
U'n = bngnrl
12-22
dn = En t @(A‘,
- angnll
t T'n
t C'n t G'n + U'n + R'n)
- bnfnrl
(108-j )
- cnencl
en = (Fn - w(A’n + C’n))/dn
( 108-k )
fn = (Hn - w(T’n + G’n))/dn
(108-l)
Sn = (Sn - o(R’n
(108-m)
+ U’n))/dn
Vn = (RESn - anvnll
Since
the backward
- bnvnrl
- CnVncl 11%
substitution
requires
all
vn, space is allocated
in the SIP Package for
values.
arrays
the
Each of these
(108-n)
values
four
has as many elements
of en, fn,
arrays
gn, and
to store
as there
those
are cells
in
grid.
Iteration
While
in their
theoretical
parameter,
however,
development,
o must be cycled
satisfactory
rates
iteration
a single
a series
of values
of convergence.
calculated
determining
to
the sequence
The value
and WSEED is the
rules
outlined
in turn
P29 and p3 are calculated
for
between that
neighbors,
and its
by a single
side
of the equation;
in successive
iterations
herein,
to be used;
x is an index
is the corresponding
iteration
below,
wu
parameter
and used as a basis
"seed",
for
of w values.
of WSEED is
cell
in practice.
In the model described
from 1 to NPARM; w(x)
value;
according
parameters
x=1,2. . ..NPARM
number of u values
values
parameter
right
iteration
value
(93) are replaced
= l-(WSEED)(x-l)/(NPARM-1)
on integral
three
from the expression
where NPARM is the total
taking
utilize
each term on the
through
of w are calculated
w(x)
they
a, 8 and y of equation
W, which multiplies
to achieve
values
Stone and Kwan (1969) define
Weinstein,
Thus the terms
Parameters
developed
each cell
as follows.
in the mesh using
as follows
12-23
The terms
~1,
the conductances
where CCmax for
cci+l/&
j,k,
CRmax is the
smaller,
ccmax + cvmax
p1 = ------------CRmin
(110)
CRmax + CVmax
p2 = ---w-----m--CCmin
(111)
CRmax + ccmax
P3 = ------------CVmin
(112)
a given
CCmin is the
larger
of CRi,j-l/2,k
.2
-------------2(NCOL)2(l+pl)
columns
for
the
cell
cell
WSEED value
each time
produces
well
values
in the
value
grid,
set
for
each of these
IT2
---------..---2(NLAY)2(:.+P3)
NCOL is the number of
three
WSEED, is then
parameters,
w(X),
12-24
as average
of
from t.he
iterations,
recycling
sequence
Stone and Kwan
points
the
is taken
generated
the
same range and that
First,
number
each NPARM iterations).
calculating
several
terms
taken
in successive
used by Weinstein,
selection.
while
number of rows and NLAY is the
from that
However,
CRmin is the
cvi,j,k+l/2,
where again
above for
parameter
while
and
has been used (i.e.,
are in the
and similarly
the terms
described
that
and
cci-l/2,j,k
values;
and
CVi,j,k-1/2
used sequentially
in many problems.
iteration
of these
values,
The iteration
the entire
slightly
Of
The seed term,
are then
of
and CRi,j+l/2,k,
NROWis the
seeds.
The process
differs
each cell
seed.
larger
n2
-------------2(NROW)2(l+p2)
and the minimun
to be the
smaller
larger
'
in the model,
of layers;
is the
Using these
smaller.
are computed
i,j,k,
while
and CVmax iS the
CVmin is the
all
cell,
appear
should
process
be
of w values
(1969), but
to function
made regarc!ing
is essentially
empirical,
and there
better
is
than
convergence
the final
little
understanding
another.
Second,
but
(assuming
solution.
convergence
is extremely
This
multiplier
which
the
ACCL is
simply
Weinstein
user.
As a genera 1 rule,
values
cycled,
in the
rate
Experience
always
produce
required
iteration
is consistently
of this
on the
of
influence
rate
of
from o.
functions
type
as a
is not to
similar
1977,
a single
be given
should
If
parameter,
be pursued
problems
value
a value
of this
by the
of one,
through
with
to
page 130)
do not employ a parameter
initially
below.
it
Parameters
is assigned
should
and
adjustment
convergence
persist,
one can be tried.
setting
seed value
convergence
from the optimum
occur
not
performs
iteration
program,
of one.
the acceleration/relaxation
calculated
optimum convergence--that
large,
parameters
of SIP (Peaceman,
of convergence
the
deviate
oscillations
it
has shown that
to achieve
change is too
a value
but rather
than
(ACCL) to 1 and using
rate
should
to distinguish
ACCL in the
versions
as explained
of ACCL other
the
an additional
parameter
, Stone and Kwan (1969)
ACCL is not
of the seed term,
for
where a parameter
assigned
We.
improvement
of the
provides
is designated
ACCL have been used in various
although
is achieved)
influence
acceleration
of {RESR1; thus
be used,
chosen affect
convergence
herein
to here as the
parameter,
parameters
of parameters
significant.
The model described
referred
the
that
Third,
of why one sequence
if
is,
by the
either
the computed
too
small
value
Convergence
does not
as the head change repeatedly
rates
will
of head change in each
or too
head overshoots
12-25
program
the number of iterations
is not minimum.
the absolute
parameter
large.
When the head
the correct
reverses
value,
and
to compensate
for
the overshoot.
overshoot
the
Severe overshoot
simply
opposite
slows
problem
monotonically,
satisfied
down convergence.
occurs;
but very
at each iteration
slowly.
points,
even though
from the correct
values.
budget
will
imbalance
Weinstein,
with
single
time
one iteration
this
iteration
step.
either
this
trend
overall
of the test)
sign)
that
is often
far
small,
on the
other
trend.
For proper
run for
a number of iterations
for
evaluation
convergence
the
some variation
in the
convergence.
later
the trial
before
12-26
this.
but
head
continue;
it
convergence;
that
is
iterations
(reversals
*in
however,
computed
Head changes which
by a very
to 4 or 5 times
occurs
in which
indicating
are indicated
equal
parameters,
trend
during
of a
in head change from
Some oscillations
of the trend,
or chosen
iterations
as iterations
most evident
optimal
and error
can be done b:y
of iteration
on an overall
here.
hand,
This
for
is a sign of overshoot,
great
a trial
of head change per iteration,
head change are normal
are too
unless
is
volumetric
by the program
is observed
or decrease
is of interest
head changes are too
that
The trend
superimposed
(which
oscillation
parameters,
convergence
heads are still
of seed.
due to the cycling
to increase
of the computed
repeated
ACCL=l.
number,
next
is often
change tends
for
value
head changes
a significant
suggest
the choice
There is normally
to the
variation
the computed
the seed calculated
and using
increasing
the criterion
and Kwan (1969)
run using
from experience,
the
small,
occur.
Stone,
an initial
moderatsa
the correct
situations,
In such situations,
method can be used to improve
making
to approach
In severe
that
while
When head change is too
head tends
may be so small
at all
causes divergence,
flat
should
the
overal'!
generally
be
number of iteration
Fo llowing
two and ten
divided
too
if
initial
trial,
head changes
the
in the
seed is multiplied
initial
by a number between two and ten
small.
tion
the
If
the trend
or division
made using
of the
the
level
is again
trial
to see if
converged,
examined.
the
if
they
The trial
is usually
division
remain
satisfactory
for
example,
additional
to carry
be noted
the more strongly
the main diagonal,
norma lly
changes
modifications
if
procedure
be.
seepage,
tend
of such terms
refine
runs have
required
for
is based on
the
choice
or divided
too
far;
developed
Thus,
which
However,
by this
in boundary
it
or
procedure
conditions
problems
arise
can be repeated.
source
affect
to make the choice
terms
only
It
matrix,
or
after
should
the
less
such as
coefficients
of seed less
to a mode1 seldom necessitates
12-27
by
multiplication
the coefficient
seed.
of
in the model are introduced--
convergence
diagonal
of seed will
or stream
of the
both
initial
2 is seldom warranted.
seed value
and error
evapotranspiration
addition
than
However,
the trial
and the
less
stresses,
in the model mesh.
the choice
If
iteration
of the
of the procedure.
the process
even though
such changes,
important
those
comparison
be multiplied
a satisfactory
will
that
to further
will
seed by factors
In most cases,
a second run is
iteration's.
numbers at each step
not worthwhile
of the
changes
in the final
the
and
multiplica-
of head change vs.
has improved.
great,
appear to be
either
In any case,
to converge,
seed value
smaller
is unclear
are compared with
runs can be continued
progressively
head changes
is based on the number of iterations
have failed
the
those
and the trend
of convergence
observed
in general
appear to be too
trial
The results
comparison
the head changes
seed;
rate
initial
trial
seed may be tried.
new seed value,
the
convergence;
in the
if
by a number between
on
critical;
modification
For each iteration,
IAh&]
refers
iteration
value
the entire
each stress
of these
steps
which
fall
value,
of
each entry
Output
evaluations
the
IAhpJmax values
in the
the acceleration
increases
in the
can be used for
ACCL should
rate
where
time
step,
indicating
time
Module !iIPlAP
IAhg[miix
node at which
whether
assumption
of the
or for
to the
of the
of
a
In addition
indices
step
option,
for
of convergence
case as well;
be attempted
is sometimes
necessary
cells
convergence
of iterations,
that
time
(See Narrative
of the
parameter,
from
of head overshoot
optimal
under the
last
each iteration
can be used in the
ACCL.
in head change.
this
never
to prevent
result
for
every
the
the change was
head change trend
that
the
behavior
of
behavior
of head change
can also
be obtained
Increases
head change at each iteration,
cause decreases
order
JAhglmax,
at the user's
D.)
representative
adjusting
It
for
shdws the
table
above,
is
of
the mesh.
Improvements
will
output;
and a sign
This
described
throughout
JAhgJmax values
in Appendix
in the table
or negative.
value
For the
intervals.
maximum change was recorded,
positive
iteration.
may be printed
at specified
and Sample Problem
the
of the head change computed during
in the program
values
stores
and [Ahg lmax is the maximum such absolute
node,
a table
is printed
table
value
mesh in that
period,
step
program
absolute
9. at a given
for
time
to the
the
but
does not involve
cannot
rather
The trial
however
in the
to slow the
procedure
process
be considered
in the
head overshoot.
12-28
smallest
The procedure
in ACCL
z.bove
seed and in
runs.
of convergence
condition
In these
convergence
cause
described
in the
to the no-flow
an iteration.
convergence
decreases
same set of trial
converting
during
in ACCL will
while
changes
by
in
as a
situations,
in the minimum rumber
number of iterations
of examining
head
l
change per iteration
to determine
when this
and adjusting
condition
iteration
parameters
is being met,
seed or ACCL terms.
12-29
can again
and to develop
the
be used
required
Strongly
Implicit
Procedure
Input to the Strongly
the
unit
Implicit
in IUNIT(9).
specified
Package Input
(SIP) Package is read from
Procedure
FOR EACH SIMULATION
SIPlAL
1.
Data:
Format:
MXITER
110
NPARM
110
SIPlRP
2.
Data:
Format:
ACCL
HCLOSE
F10.0
F10.0
Explanation
Input
I PCALC
110
IPRSIP
110
WSEED
F10.0
of Fields Used in
Instructions
MXITER--is the maximum number of times through the iteration
loop in one
time step in an attempt to solve the system of finite-differerxe
Fifty
iterations
are generally
sufficient.
equations.
NPARM--is the number of iteration
are generally
sufficient.
parameters
to be used.
Five
parameters
It must be greater than zero and is
ACCL--is the acceleration
parameter.
If a zero is entered,
it is changed to one.
generally
equal to one.
HCLOSE--is the head change criterion
for convergence.
When the maximum
absolute
value of head change from all nodes during an iteration
is less than or equal to HCLOSE, iteration
stops.
IPCALC--is
a flag
0 - the
indicating
seed will
1 - the seed will
problem
where the
be entered
iteration
parameter
seed will
come from.
by the user.
be calculated
at the
start
of the
simulation
from
parameters.
It
WSEED--is the seed for calculating
iteration
specified
if IPCALC is equal to zero.
parameters.
IPRSIP--is
IPRSIP is equal
change (positive
step whenever the
also occurs at
of IPRSIP.
the printout
interval
for SIP.
If
The maximum head
is changed to 999.
printed
for each iteration
of a time
This printout
even multiple
of IPRSIP,
stress
period regardless
of the value
12-30
is only
to zero, it
or negative)
is
time step is an
the end of each
12-31
Module Documentation
for
The Stongly
Procedure
modules
Implicit
the
and two submodules.
Strongly
Implicit
Package (SIPl)
SIPlAL
Allocates
of three
SIPlRP
Reads control
Modules
space for
SIP work arrays.
information
needed by the
Package and calculates
iteration
the seed is specified
Performs
consists
Package
They are:
Primary
SIPlAP
Procedure
SIP
parameters
if
by the user.
one iteration
of the strongly
implicit
procedure.
Submodules
SSIPlP
Prints
the
SSIPlI
Calculates
largest
head change for
iteration
is calculated
parameters
by the
12-32
program.
each iteration.
when the
seed
primary
Narrative
Module SIPlAL
arrays,
allocates
space in the
EL, FL, GL, and V hold
Each of these
process.
Additionally,
three
that
iterations
holds
allowed
iteration
iteration
1.
Print
2.
Read and print
3.
Allocate
4.
Calculate
used by SIP is
is
5.
for
HDCG holds
the cell
and is specified
One element
its
location
the
at
in HDCG is MXITER, and
by the user.
in W is used for
Array
each of the
W
NPARM
by the user.)
functions
in the following
order:
the SIP Package.
MXITER and NPARM.
required
space in the
(ISUM) is saved in variable
space required
far
step
a message identifying
the
the solution
each model cell.
and LRCH holds
(NPARM is specified
performs
The four
MXITER, where MXITER is the maximum number of
in a time
parameters.
during
The number of elements
parameters.
Module SIPlAL
pointer
times
for
SIP arrays.
HDCG, LRCH, and W are required.
the maximum occurred.
in LRCH is three
for
results
one element
maximum head change each iteration
which
X array
intermediate
contains
arrays,
Module SIPlAL
for
ISOLD prior
SIP can be calculated
and print
ISUM - ISOLD.
X array.
in step
to allocation
ISUM - 1.
RETURN.
12-33
location
so that
the
4.
the space used in the
The total
The X-array
X array.
space allocated
by all
The space
packages
so
'
Flow Chart
for
Module SIPlAL
X array is the pool of memory space
from which space is allocated
for
arrays used by various
packages.
r
c
1
PRINT A MESSAGE
IDENTIFYING
SIP PACKAGE
READ AND PRINT
MAXIMUM # OF ITERATIOI’JS
AND # OF ITERATION
PARAMETERS
12-34
1
SUBROUTINE SIPlAL(ISUM,LENX,LCEL,LCFL,LCGL,LCV,LCHDCG,LCLRCH,
LCWIMXITERINPARMINCOL,NRC~V,NLAY,IN,IOUT)
C
C-----VERSION
C
C
C
******************************************************************
ALLOCATE STORAGE IN THE X ARRAY FOR SIP ARRAYS
*************************************************************~****
C
C
E
C
C
Cl---
1110 31DEC1986 SIPlAL
SPECIFICATIONS:
----------------------------------------------------------------------------------------------------------------------------------PRINT A MESSAGE IDENTIFYING SIP PACKAGE
WRITE ( IOUT, 1) IN
1 FORMAT(lHO,'SIPl -- STRONGLY IMPLICIT PROCEDURESOLUTIONPACKAGE’
I,', VERSION 1, 9/l/87','
INPUT READ FROM UNIT',131
C
C2---
READ AND PRINT MXITERANDNPARM
READtIN, MXITER,NPARM
2 FORMAT(21101
WRITE( IOUT,
MXITER,NPARM
3 FORMATt1X, ‘MAXIMUM OF’ ,14, ’ ITERATIONS ALLOWED FOR CLOSURE’/
1
1X,12,' ITERATION PARAMETERS’)
C
C3------
ALLOCATE SPACE FOR THE SIP ARRAYS
ISOLD=ISUM
NRC=NROW*NCOL
ISIZ=NRC*NLAY
LCEL=ISUM
IsuM=IsuM+IsIz
LCFL=ISUM
IsuM=IsuM+IsIz
LCGL=ISUM
IsuM=IsuM+IsIz
LCV= ISUM
IsuM=IsuM+IsIz
LCHDCG=ISUM
ISUM=ISU~JI+MXITER
LCLRCH=ISUM
ISUM=ISUMt3*MXITER
LCW=ISUM
ISUM=ISUM+NPARM
C
c4------CALCULATE
AND PRINT THE SPACE USED IN THE X ARRAY
ISP=ISUM-ISOLD
WRITE(IOUTa4) ISP
4 FORMAT(lX,I8,’
ELEMENTS IN X ARRAY ARE USED BY SIP')
ISUMl=ISUM-1
WRITE(IOUT,S) ISUMlr LENX
5 FORMAT(lX,I8,' ELEMENTS OF X ARRAY USED OUT OF’,181
IF(ISUMl.GT.LENX) WRITE(IOUT,6)
6 FORMATt1X, ’
C
CS------RETURN
RETURN
END
:
***X
ARRAY MUST BE DIMENSIONED LARGER***‘)
12-35
List
Variable
Module SIPlAL
for
Definition
Range
IN
Package
IOUT
ISIZ
I SOLD
Global
Module
Package
ISP
ISUM
Module
Global
ISUMl
LCEL
Module
Package
LCFL
Package
LCGL
Package
LCHDCG
Package
LCLRCH
Package
LCV
LCW
LENX
Package
Package
Global
MXITER
NCOL
NLAY
NPARM
NRC
NROW
of Variables
Package
Global
Global
Package
Module
Global
Primary unit number from which input for this package
will
be read.
Primary unit number for all printed
output.
1OUT = 6,)
Number of cells
in the grid.
Before this module allocates
space, ISOLD is c;et equal
ISOLD is subtracted
to ISUM. After allocation,
from ISUM to get ISP, the amount of space in the X
array allocated
by this module.
Number of words in the X array allocated
by this module.
Index number of the lowest element in the X array which
has not yet been allocated.
When space is allocated
for an array,
the size of the array is added to ISIJM.
ISUM-1.
Location
EL.
Location
FL.
Location
GL.
Location
HDCG.
Location
LRCH.
Location
Location
Length
of
in the X array
of the
first
element
of array
in the
X array
of the first
element
of array
in the
X array
of the
first
element
of array
in the
X array
of the
first
element
of array
in the
X array
of the
first
element
of array
of the first
of the first
element
element
of array
of array
in the X array
in the X array
the
X array
in
words.
This
equal to the dimension of X specified
program.
Maximum number of iterations.
Number of columns in the grid.
Number of layers in the grid.
Number of iteration
parameters.
Number of cells
in a layer.
Number of rows in the grid.
12-36
should
always
in the MAIN
V.
W.
be
Narrative
Module SIPlRP reads data
parameter
(ACCL), the
seed (WSEED), a flag
by the user
If
for
closure
1.
and the
iteration
less
The defaults
steps.
2.
Print
the data
3.
Check
IPCALC which
(a)
and the
Print
If
Print
iteration
If
is
in the
WSEED as the
following
substitute
order:
of 1.0.
a default
an interval
(IPRSIP).
If
of 999 time
to the user.
1.
a flag
that
iteration
not zero,
indicates
submodule
parameters
of this
IPCALC is
zero,
parameter
= 1 - (wsEED)
the
source
of
the
(Ii)
SSIPlI
at the start
will
of the
calculate
first
a seed
iteration.
option.
use WSEED to calculate
is given
NPARM-l.
the parameters.
4.
using
as a convenience
i-l
Ii
are calculated
substitute
to zero,
read in step
TPCALC is
a message telling
The i-th
head change
or specified
seed (WSEED).
resulting
(b)
printing
functions
are provided
iteration-parameter
for
parameters
than or equal
iteration-parameter
WSEED is to be calculated
interval
its
the acceleration
(HCLOSE), the
If ACCL is zero,
Read the data.
IPRSlP is
the SIP package:
whether
Module SIPlRP performs
seed.
Module SIPlRP
criterion
indicating
(IPCALC),
IPCALC is zero,
for
RETURN.
12-37
iteration
by the expression
parameters.
Flow Chart
for
,Module SIPlRP
ACCL is a rmltiplier
of
calculated
head change
which is used to control
the convergence rate.
HCLOSE is the head change
When
closure
criterion.
head change in all model
cells
is less than or
equal to HCLOSE, iteration
stops.
WSEED is the seed, specified
by the user, on which the
calculation'of
iteration
parameters
is based if
IPCALC is zero.
IPRSIP is the time step
interval
for printing
the
maximum head change for
each iteration
of a time
Head
change
is
step.
printed
every IPRSIP time
step.
Head change is
printed
at the end of a
stress period regardless
of the interval.
READ AND PRINT
ACCL. HCLOSE.
WSEED, IPCALC.
AND IPRSlP
3A
PRINT MESSAGE
EXPLAINING THAT
ITERATION
PARAMETERS WILL BE
CALCULATED
FROM
MODEL $;;ULATED
1
IPCALC is a flag.
If it is
set equal to one, iteration
parameters will
be calculated
from a seed calculated
within
the program.
If it
is clear (equal to zero),
iteration
parameters will
be calculated
from a seed
provided
by the user.
12-38
1
SUBROUTINE SIP1RF’(NPARM,MXITER,ACCL,HCLOSE,W,IN,IPCALC,IF’RSIP,
IOUT)
C
C-----VERSION
0925 16DEC1982 SIPlRP
********+*********************************************************
READ DATA FOR SIP
+*****************************************************************
E
C
C
C
C
C
SPECIFICATIONS:
-----------------------------------------------------------------DIMENSION W(NPARM)
------------------------------------------------------------------
:
Cl-----
READ ACCLrHCLOSE,WSEEDrIPCALC,IPRSIP
READ(IN,l)
ACCLrHCLOSErIF’CALC,WSEED,IPRSIP
1 F0RMAT(2F10.0,110,F10.0,110~
IF(ACCL.EQ.O.1
ACCL-1.
C
C2------PRINT
DATA VALUES JUST READ
WRITE(IOUT,lOO)
100 FO~AT(lHO,///57X,‘SOLUTION
BY THE STRONGLY IMPLICIT PROCEDURE’
1/57x,43 ( ‘- ’ 1)
WRITE(IOUT,1151
MXITER
115 FORMAT(lH0,47X,‘MAXIMUM
ITERATIONS ALLOWED FOR CLOSURE =‘,I91
WRITE(IOUT,120)
ACCL
120 FORMATtlH r63Xn’ACCELERATION PARAMETER =‘rG15.5)
WRITE(IOUT,125)
HCLOSE
125 FORMATt1H ,52X, ‘HEAD CHANGE CRITERIONFOR CLOSURE =’ rE15.5)
IF(IPRSIP.LE.O)IF’RSIP=999
WRITE(IOUT,130)
IPRSIP
130 FORMATflH r52X,‘SIP
HEAD CHANGE PRINTOUT INTERVAL =‘,I91
C
C3-----CHECK IF SPECIFIED VALUE OF WSEED SHOULD BE USED OR IF
C3-----SEED SHOULD BE CALCULATED
IF(IPCALC.EQ.0)
GO TO 150
C
C3 A---- -CALCULATE SEED 8 ITERATION PARAMETERS PRIOR TO 1ST ITERATION
WRITE(IOUT,140)
140 FORMAT(lHO,52X,‘CALCULATE
ITERATION PARAMETERS FROM MODEL’,
1’ CALCULATED WSEED’)
GO TO 1000
l
SPECIFIED VALUE OF WSEED
:3Ek ----USE
c35 ----CALCULATE
AND PRINT ITERATION PARAMETERS
150 Pl=-1.
P2=NPARM-1
DO 160 I=lrNPARM
Pl=Pl+l.
160 W(I)=l.-WSEED**(Pl/P2)
WRITE(IOUT,161)
NPARMrWSEED,(W(JlrJ=l,NPARM)
161 FORMAT(lHO,/,IS,’
ITERATION PARAMETERS CALCULATED FROM’,
1
’ SPECIFIED WSEED =‘rF11.8,’
:‘//(lOX,6E15.7))
C
c4 ------RETURN
1000 RETURN
END
12-39
List
of Variables
for
Module SIPlRP
Definition
Variable
Range
ACCL
Package
Acceleration
HCLOSE
Package
Closure
I
Module
Index
IN
Package
Primary
will
unit number from which
be read.
IOUT
Global
Primary
unit
I PCALC
Package
Flag.
parameter.
criterion
for
iteration
for
the
procedure.
parameters.
number for
+ 0, seed for
program.
= 0, seed will
iterative
all
iteration
input
printed
will
be specified
,Tor this
output.
be calculated
package
IOUT = 6.
in the
by the user.
IPRSIP
Package
Frequency (in time steps) with which the maximum head
changes for each iteration
will
be printed.
J
Module
Index
MXITER
Package
Maximum number of iterations.
NPARM
Package
Number of iteration
Pl
Module
I - 1.
P2
Module
NPARM - 1.
W
Package
DIMENSION (NPARM), Iteration
WSEED
Module
Seed for
for
iteration
calculating
12-40
parameters.
parameters.
iteration
parameters.
parameters.
Narrative
Module SIPlAP performs
(SIP)
algorithm
time,
all
indexes
for
arrays
used to access
time
is
achieved
computational
identical
if
requires
Checks are made to detect
Double
to allow
Improvement
of the geometry
Procedure
normally
in computational
is used to increase
are not
repeated
FORTRAN addressing
for
routines
were used.
partly
the same calculations
This
uses the same computer
are calculated
and column indexes
be done by internal
the equations.
Implicit
The one-dimensional
and because calculations
subscripts
that
row,
Strongly
To save computational
dimensions.
module is somewhat complex,
of ordering
that
equation.
layer,
in three
as would
three-dimensional
process
from the
efficiency,
of the
one dimensional.
because knowledge
indices
This
the flow
are declared
the arrays
Module SIPlAP
one iteration
solving
are calculated
for
be performed
is implemented
statements
which
because the SIP solution
two methods
by a generalized
to handle
ordering
with
both ordering
scheme is used,
algorithm
schemes.
and array
indexes
accordingly.
precision
accurate
is used for
answers to be calculated
Mixed precision
arithmetic
variables
equal
to single-precision
precision
variables
where necessary
most calculations
has been avoided
to generate
by doing
the
values
fully
reverse
expressions.
12-41
for
in this
a wide
by setting
and then
double-precision
to generate
fully
module in order
range of problems.
double-precision
using
the double-
expressions,
single
and
precision
In the
explanations
use of an assignment
amount of text
care should
this
no attempt
below,
statement
would
to change precision,
However,
require.
be used to maintain
as mixed precision
has been made to discuss
expressions
expressions
because of the
when changing
that
this
have unmixed
can cause erroneous
results
each
large
module,
precision,
with
some
compilers.
Module SIPlAP
performs
its
functions
If the user has specified
1.
should
be calculated
in the
following
(IPCALC f 0) that
by the program,
order:
iteration
SSIPlI
CALL submodule
parameters
to calculate
both the seed and the parameters.
2.
Assign
values
3.
Initialize
to fields
the
that
variables
are constant
that
track
during
an iteration.
maximum head change c.uring
an
iteration.
4.
Clear
5.
Determine
(IDIR)
SIP work
the
accordingly.
Calculate
indexes
of neighboring
substitution.
therefore,
diagonals
ponding
ordering
This
flag
alternates
and set the ordering
between
IDNRC and IDNCOL which
the matrix
The elements
they
[U]
flag
1 and -1 each iteration,,
are used when calculating
and intermediate
in matrix
are not saved.
in the matrix
field
of equations
locations
cells.
Calculate
6.
arrays.
In the
[L]
names in the program
are used as they
explanation
[U] were designated
"e,"
are EL (e lower
12-42
vector
of
"f,"
{V) using
are calculated;
SIP concepts,
and "g."
case),
forward
FL (f
the
The correslower
case),
and GL (g lower
I,,,,,
Ilb,"
llc,l,
Similarly,
case).
and I'd" in the explanation
in the program.
The codes for
are the same in the program.
explanation
are followed
explanation
is ZP (Z prime)
in the explanation
(a)
the
equation
reverse
this
cell
indexes
which
"CL,"
and "DL"
"BL,"
in matrix
[A]
diagonals
in the program.
in
are
in the explanation
[A+B]
in the
Hence, Z' in the
The intermediate
vector
{V)
"V" in the program.
II,
indexes,
JJ, KK.
is the same as the order
loop
"AL,"
[LJ array
of the
For normal
loop
I and K are inverted
indexes
to produce
ordering,
I,J,K.
For
the proper
of cells.
(b)
If
The codes for
in the
by a "P" in the program.
Set current
order
are
the diagonals
is the array
ordering,
sequence
the diagonals
cell
Calculate
the one-dimensional
is constant
head or no flow,
subscript
skip
of the current
calculations
for
cell.
this
cell
and go on to the next.
(c)
Calculate
the one-dimensional
subscripts
for
the six
neighboring
(d)
Calculate
the one-dimensional
subscripts
for
conductance
cells.
each of the six
assigned
stores
neighboring
to array
elements
conductance
cells.
at specific
between cells
conductance
subscripts
neighboring
cells
on equation
ordering.
Since
as calculated
cells
I,J,K
are not simply
(for
the cell
6(c).
between cells
example,
and I,J+l,K),
in step
12-43
conductances
Also,
are
CR(I,J,K)
the four
locations
to
or five
of the six
the subscripts
depend
(e)
substitution
cell
Calculate
and involve
is outside
(f)
matrices
of the
[U]
This
is one row back.
(2)
Neighboring
cell
is one row ahead.
(3) Neighboring
cell
is one column back.
(4)
Neighboring
cell
is one column ahead.
(5)
Neighboring
cell
is one layer
back.
(6)
Neighboring
cell
is one layer
ahead.
and CL],
7.
of that
If
this
and go to the
are set
residual
so that
forward
to zero.
of the upper and lower
are the factors
calculations
of matrix
{RES}.
[A+BJ.
The calculation
the calculation
triangular
will
of HNW times
HCOF
have precision
made in the formulation
modules,
all
of
precision.
Calculate
the
intermediate
vector
the forward-substitution
the cells
Set current
used for
cell
the
precision
Step through
(b)
which
Calculate
completes
(a)
variables
the components
for
Whenever a neighboring
cell
use single
step
cells.
are required
(1) Neighboring
to similar
(h)
neighboring
that
the
is done in single
comparable
variables
grid,
Calculate
(g)
which
or assign
forward
cell
process
solving
indexes
substitution
for
JJ, KK.
(step
6(a)).
the one-dimensional
is constant
head or no flow,
12-44
which
for
is stored
subscript
skip
back substitution.
The ordering
is the
of the current
calculations
in array
one cell.
head change using
II,
Calculate
next.
{V},
for
this
cell.
cell
reverse
V.
(c)
cells
the
Calculate
behind
current
(relative
Back substitute,
V in place
up of storage
this
Save the
(f)
8.
and its
step
Also,
to get a new estimate
cell
If
the step;
location
neighboring
ordering)
values
of vector
of additional
location
in arrays
the
Print
head change
{V).
This
computer
storage.
value
where this
doubling
is
largest
head
of the head change.
iteration
to head from the previous
value
HDCG and LRCH.
step.
is
greatest
iteration
is complete,
print
the
this
These may be printed
Set the convergence
is met.
flag
iteration
in
to one if
number of iterations
for
RETURN.
the maximum head change and cell
period
Store
of head.
criterion
the SIP printout
11.
the three
back-substitution
head change.
the head change whose absolute
otherwise,
of a stress
value
Add the head change this
Store
for
save the cell
and the absolute
the convergence
10.
for
of head change whose absolute
10 at the end of the time
9.
of the
intermediate
value
iteration.
change occurred
iteration
of the
solving
is used to save the cost
(e)
during
to the direction
subscripts
cell.
(d)
in array
the one-dimensional
interval
(IPRSIP)
regardless
is
reached.
of the interval.
RETURN.
12-45
location
each iteration
Printout
occurs
if
at the end
Flow Chart
for
If it is set
IPCALC is a flag.
equal to one, the program
calculates
a seed from which
iteration
parameters
are
It may be set
calculated.
by the user at the beginning
It is
of the simulation.
cleared during the first
SSIPlI will
iterations.
never be called more than
If IPCALC is not set
once.
equal to zero, the user
specifies
the seed for the
iteration
parameters.
Module SIPlAP
SET, CALL SSlPl I.
CLEAR IPCALC
IDIR indicates
whether the
ordering
of equations
is
(-1).
normal (1) or reverse
INDICATE
NORMAL
FOR EACH CELL
SSIPlI
is a submodule
calculates
iteration
parameters.
which
DIAGONALS
IN MATRIX U AND
INTERMEDIATE
VECTOR V
CHANGE
12-46
FOR THIS
c 1
EXPANSION
“‘6 ~N~cfs
A3E ON THE
NEXT PAGE
Flow Chart
for
Module SIPlAP
(Continued)
Sing1 e Cell Index: In this module,
a single
index is used to identify
This is in opposition
each cell.
to the three indices
(I,J,K) used
in most other modules.
LJ
SET UP
TtWC;LL
(i)
CALCULATE
SINGLE CELL
r-
I
A
SET UP
THREE CELL
INDICES
CALCULATE
SINGLE CELL
INDICES OF
THE SIX
ADJACENT CELLS
0
CALCULATE
SINGLE CELL
INDEX
CALCULATE
INDICES
.--- .- . FOR
_ON-D~CTA&~~
TO SIXC;WtCENT
CALCULATE
SINGLE CELL
INDEX FOR
NEIGHBORING
D
BACK SUBSTITUTE
FOR HEAD CHANGE
ST;E~M&N
L
I
ELEMENTS
INLANDU
FOR THIS CELL
I
CHANGE IF IT
IS THE MAXIMUM
.
G
1
I
CALCULATE THE
RESIDUAL
I
CALCULATE THE
ELEMENT IN V
FOR THIS ELEMENT I
12-47
ADD HEAD CHANGE
TO HEAD AT START
OF INTERATION TO
GET HEAD AT END
OF ITERATION
SUBROUTINESIP~AP(HNEW,IBOUND,CR,CC,CV.HCCF,RHSIEL.FL,GL,V.
w, cocci, LRCH,NPAR~KITER, HaosE, Aca, ICNVG, Km, KPER,
2
IPCALC, IFRSIPIMXITER, NSTP,NCCL,NRCW,NLAY, NODES,IOUT)
C-----VERSION 1656 24JUL1987 SIPlAP
1
C
**********I**************~********************~*****~*******u*~***
SOLUTIONBY THE STRONGLYIMPLICIT PROCEDURE-- 1 ITERATION
***t*******P**~*****~~***~**~~**********~~**************~**~*****~*
E
C
i
SPECIFICATIONS:
DOUBLEPRECISION HNEW,DITPAR,AC, HHCCF,RR-IS,XI, DZERO.DONE,RES
DOUBLE PRECISIONZ,B,D,E,F,HtS,AP,TP,CPtGP,UP.RP
DOUBLE PRECISIONZHNEW,BHNEW,DHNEW,FHNEW,HHNEW,SHNEW
DOUBLE PRECISION AL,BL,CL,DL,ELNCLrFLNCL,GLNCL
DOUBLE PRECISIONELNRrFLNRLtGLNRLrELNLLtFLNLL,GLNLL
DOUBLE PRECISION VNRIVNCL,VNLL~ELXI,FLXI,GLXI,VN,HCFHNW
C
1
2
C
DIMNSION HNEW(NODES1, IBDUND(NOCES1, CR(NODESlr CC(NODESlr
CV(NODES1, HCCF(NOCES1, RHS(NODES1, EL(NODESlr FL(NODES)r
GLLNODES), V(NODESlr WLNPARM), HDCGLMXITER), LRCHL3,MXITERl
-----------------------------------------------------------------
El ------CALCULATE
ITERATION PARAMETERSIF FLAG IS SET. THEN
Cl------CLEAR
THE FLAG SO THAT CALCULATION IS DONE ONLY ONCE.
IF(IPCALC.NE.0)
1
CALL SSIPlI(CR,CC,CV,IBOUND,NPARMtW,NCDLrNRCW.NLAY,ICUT1
IPCALOO
------ASSIGN
VALUES TO FIELDS THAT ARE CONSTANTDURING AN ITERATION
DZERO=O.
DONE=l.
AC=ACU
NRC=NROW*NCOL
NTH=MOD(KITER-lrNF’ARM)t1
DITPAR=W(NTHl
C
Q------INITIALIZE
VARIABLE THAT TRACKS MAXIbUMHEAD CHARGEDURING
C3------THE
ITERATION
BIGOO.
$------CLEAR
SIP WORKARRAYS.
DO 100 I=l,NOCES
EL(I)=O.
FL(I)=O.
GL(Il=O.
100 V(I)=O.
C
B------SET
NOFUML/REVERSEEQUATION OROERINGFLAG (1 OR -11 AND
CS------CALCULATE INDEXESDEPENDENTON ORDERING
IDIR=l
IFMOD(KITER,2).EQ.O)IDIR=-1
IDNRC=IDIR*NRC
IDNCOL-IDIR'NCOL
C
C&-----STEP
THROUGHCELLS CALCULATING INTEWEDIATE VECTORV
c6 ------USING FORMRD SUBSTITUTION
DO 150 K=l,NLAY
DO 150 I=l,NRCW
DO 150 J=l,NCOL
UP CURRENTCELL LOCATION INDEXES. THESE ARE DEPENDENT
THE DIRECTION QF EQUATION ORDERIt&.
IF(IDIR.LE.O)GO TO 120
CSA-----ON
II=1
JJ=J
KK=K
GO TO 122
120 II=NRW-I+1
JJ=J
KK-NLAY-Ktl
12-48
c’
(%&----CALCULATE 1 DIMENSIONAL SUBSCIW’T OF CURRENTCELL AND
W&----SKIP
CALCULATIONS IF CELL IS NOFLOWOR CONSTANTHEAD
122 N=JJ+(II-l)*NCOL+(KK-l)*NRC
IF(IBOUND(N).LE.O)GO TO 150
Fix
-----CALCULATE 1 DIMENSIONAL SUBSCRIPTS FOR LOCATING THE 6
‘XC-----SURROUNDING CELLS
NRN=N+IDNCOL
NF(L=N-IDNCOL
NCN=N+l
NU=N-1
NLN=N+IDNRC
NLL-N-IDNRC
n
:6D- ----CALCULATE 1 DIKNSIONAL SUBSCRIPTS FOR CONWCTANCETO THE 6
C6D-----SURROUNDING CELLS. THESE DEPENDON ORDERINGOF EQUATIONS.
IF(IDIR.LE.O)GO
TO 124
NCF=N
NCD=NCL
NW=NR
NR-I-N
NLS=N
NLZ=NLL
GO TO 126
124 NCF=N
NCD=NCL
NB=N
NRi=NRN
NLS=NLN
NLZ=N
C
@E--ASSIGN VARIABLES IN MATRICES A 6 U INVOLVING ADJACENTCELLS
C6El ----NEIGHBOR IS 1 ROWBACK
126 B=DZERO
ELNRL=DZERO
FLNR=DZERO
GLNRL=DZERO
BHNEW=DZERO
VNRL=DZERO
IF(I.EQ.l)
GO TO 128
B=CC(NRB)
ELNRL=EL(NRL)
FLNRL=FL(NR)
GLNF(L=GL(NRL)
BHNEW=B+HNEW
(NR 1
VNRL=V(NRL)
c
C6E2----NEIGHBOR IS 1 RCWAHEAD
128 H=DZERO
HHNEW=DZERO
IF(I.EQ.NRW)
GO TO 130
H=CC(NRH)
HHNEW=H*HNEW
(NRN)
C
C6E3----NEIGHBOR IS 1 COLUMI BACK
130 D=DZERO
ELNCL=DZERO
FLNU=DZERO
GLNa=DZERO
DHNEW=DZERO
VNCL=DZERO
IF(J.EQ.l)
GO TO 132
D=CR(NCD)
ELNCL=EL(NU)
FLNCL=FL(NcL)
GLNa=GL( NCL1
DHNEW=D*HNEW(NCL)
VNa=V(NU)
12-49
C6E4----NEIGHBOR IS 1 COLUMNAHEAD
132 F=DZERO
FHNEW=DZERO
IF(J.EQ.NCOL) GO TO 134
F=CR(NCF)
FHNEW=F*HNEW(NCN)
C
C6E5----NEIGHBOR IS 1 LAYER BEHIND
134 Z=DZERO
ELNLL=DZERO
FLNLL=DZERO
GLNLL=DZERO
ZHNEW=DZERO
VNLL=DZERO
IF(K.EQ.1)
GO TO 136
Z=CV(NLZ)
ELNLL=EL (NLL)
FLNLL=FL(NLL)
GLNLL=GL(NLL)
ZHNEW=Z*HNEW(NLL)
VNLL=V(NLL)
C
C6E6----NEIGHBOR IS 1 LAYER AHEAD
136 S=DZERO
SHNEW=DZERO
IF(K.EQ.NLAY) GO TO 138
S=CV(NLS)
SHNEW=S*HNEW(NLN)
i&E7 ----CALCULATE THE NEGATIVE SUM OF ALL CONWCTANCESTO NEIGRBORING
C6E7----CELLS
138 E=-Z-B-D-F-H-S
C
C6F-----CALCULATE COMPONENTS
OF THE UPPER AND LUVER MATRICES, WHICH
C6F-----ARE THE FACTORSOF MATRIX (A+B)
AL=Z/(DONE+DITPAR*(ELNLL+FLNLL) 1
BL=B/(DONE+DITPAR*(ELNRL+GLNRL))
a=D/(DONE+DITPAR*(FLNCL+GLNa))
AP=AL*ELNLL
CPBLYLNRL
GP=CL*FLNU
RP=a*GLNCL
TF=AL*FLNLL
UP=BL’GLNR
HHCOF=HCOF(N)
DL=E+HHCOF+DITPAR*(AP+TP+CP+GPtUPURP)-ALBLNLL-BL*FLNR-CL*ELNU
EL(N)=(F-DITPAR*(AP+CP))/DL
FL(N)=(H-DITPAR*(TPtGP))/M
GL(N)=(S-DITPAR+(RP+UP))/DL
C
C6G----CALCULATE THE RESIDUAL
RRHS=RiS(N)
HNW=HNEW
(N)
HCFHMd=HNW*HCQF(N)
RES=RRHS-ZHNEW-BHNEW-DHNEW-E~NEW(N)-HCMNW-FHNOII-HHNEW-SHNM
C
C6t!-----CALCULATE THE INTERMEDIATE VECTORV
V(N)=(AC*RES-AL*VNLL-BL+VNR-CL*VNU)/DL
C
150 CONTINUE
C
C7------STEP
THROUGHEACH CELL AND SOLVE FOR HEAD CHANGEBY BACK
C7------SUBSTITUTION
DO 160 K=lrNLAY
DO 160 I=lrNRW
DO 160 J=l,NCOL
c
1240
C7A-----SET UP CURRENTCELL LOCATION INDEXES. THESE ARE DEPENDENT
C7Am.--- ON THE DIRECTION OF EQUATION ORDERING.
IF(IDIR.LT.0)
GO TO 152
KK=NLAY-K+l
II=NR@V-I+1
JJ=NCOL-J+l
GO TO 154
152 KK=K
II=1
JJ=NCOL-J+l
C7&----CALCULATE 1 DIMENSIONAL SUBSCRIPT OF CURRENTCELL AND
C7B---- SKIP CALCULATIONS IF CELL IS NOFLW OR CONSTANTHEAD
154 N=JJ+(II-l)‘NCOL+(KK-l)“NRC
IF(IBOUND(N).LE.O)GO TO 160
C7C-----CALCULATE 1 DIMENSIONAL SUBSCRIPTS FOR THE 3 NEIGHBORINGCELLS
C7C--BEHIND (RELATIVE TO THE DIRECTION OF THE BACK SUBSTITUTION
C7C-----ORDERING) THE CURRRENTCELL.
NC=N+l
NF+N+IDNCOL
NL=N+IDNRC
C7D-----BACK SUBSTITUTE, STORING HEAD CHANGEIN ARRAY V IN PLACE OF
C7D-----INTEMDIATE
FORWARDSUBSTITUTION VALUES.
ELXI=DZERO
FLXX=DZERO
GLXI=DZERO
IF(JJ.NE.NCOL) ELXI=EL(N)*V(NC)
IF(X.NE.l)
FLXI=FL(N)*V(NR)
IF(K.NE.l)
GLXI=GL(N)*V(NL)
W=‘/(N)
V( N)=VN-ELXI-FLXI-GLXI
C
C7E-----GET THE ABSOCUTEHEAD CHANGE. IF IT IS MAX OVER GRID SO FAR.
C7E-----THEN SAVE IT ALONGWITH CELL INDICES AND HEAD CHANGE.
TCHK=ABS(V(N) 1
IF ITCHK.LE.BIGG) GO TO 155
BIGG=TCHK
BIG=V(N)
IB=II
38555
KB=KK
C
C7F-----ADD HEAD CHANGETHIS ITERATION TO HEAD FROMTHE PREVIOUS
C7F-----ITERATION
TO GET A NEW ESTIMATE OF HEAD.
155 XI=V(N)
HNEW(N)=HNEW(N)+XI
C
160 CONTINUE
C
CS------STORE THE LARGEST ABSOLUTEHEAD CHANGE (THIS ITERATION) AND
CS------AND
ITS LOCATION.
HDCG(KITER)=BIG
LRCH(lrKITER)=KB
LRCH(2rKITER)=IB
LRCH(3rKITER)=JB
ICNVG=O
IF(BIGG.LE.HCLOSE) ICNVG=l
------IF
END OF TIME STEP, PRINT I OF ITERATIONS THIS STEP
IF(ICNVG.EQ.0 .AND. KITER.NE.MXITER) GD TO 600
IF(KSTP.EQ.l)
WRITE(IOLIT,500)
500 FORMAT(lt0)
WRITE(IOUT,SOl) KITER,KSTP,KPER
501 FORMAT(lX,I5,’
ITERATIONS FOR TIME STEP’rI4,’
IN STRESS PERIOD’,
1
13)
ClO-----PRINT
HEAD CHANGEEACH ITERATION IF PRINTOUT INTERVAL IS REACHED
IF(ICNVG.EQ.0 .OR. KSTP.EQ.NSTP .OR. MOD(KSTP,IPRSIP).EQ.O)
1
CALL SSIP1P(HDCG,LRCH,KITERtMXITERtIOUT)
~~-----RETLIRN
600
RETURN
C
END
12-51
List
Variable
Range
AC
ACCL
AL
Module
Package
Module
AP
Module
B
Module
BHNEW
BIG
BIGG
BL
Module
Module
Module
Module
cc
Global
CL
Module
CP
Module
CR
Global
cv
Global
D
Module
DHNEW
DITPAR
DL
Module
Module
Module
DONE
DZERO
Module
Module
Module
EL
Module
ELNCL
ELNLL
ELNRL
F
Module
Module
Module
Module
Module
FHNEW
FL
Module
Module
FLNCL
FLNLL
FLNRL
Module
Module
Module
ELXI
of Variables
for
Module SIPlAP
Definition
Double-precision
acceleration
parameter (ACCL).
Acceleration
parameter.
Diagonal from the lower factor.
(AL stands for
A-lower case.)
Diagonal element in the modified
coefficient
matrix.
(AP stands for A-prime.)
Diagonal label in the coefficient
matrix--conduc:tance
from the adjacent
node which is in the last row.
Head in the adjacent
cell which is in the last row.
Largest head change for an iteration.
Largest absolute
value of head change for an iteration.
(BL stands for
Diagonal from the lower factor.
B-lower case.)
DIMENSION (NCOL,NROW,NLAY), Conductance in the column
CC(J,I,K) contains
conductance
between
direction.
and (J,I+l,K).
nodes (J,I,K)
(CL stands for
Diagonal from the lower factor.
C-lower case.)
Diagonal element in the modified
coefficient
matrix.
(CP stands for C-prime.)
DIMENSION (NCOL,NROW,NLAY), Conductance in the row
CR(J, I ,K) contains
conductance
between
direction.
and (J+l,I,K)
nodes (J,I,K)
DIMENSION (NCOL,NROW,NLAY-l), Conductance in the vertical
CV(J,I,K) contains
conductance
between
direction.
nodes (J,I,K)
and (J,I,K+l).
Diagonal label in the coefficient
matrix.
Conductance
from the adjacent
node which is in the last c.olumn.
Head in the adjacent
cell which is in the last column.
Double-precision
iteration
parameter.
Diagonal from the lower factor.
(DL stands for
D-lower case.)
Double-precision
field
containing
a one.
Double-precision
field
containing
a zero.
Main diagonal
in the coefficient
matrix.
DIMENSION (NODES), Diagonal from the upper factor.
(EL stands for E-lower case.)
EL (E-lower
case) from the cell in the last column.
EL (E-lower case) from the cell in the last layer.
EL (E-lower
case) from the cell in the last row.
Intermediate
result.
Diagonal label in the coefficient
matrix--conductance
from the adjacent
node which is in the next column.
Head in the adjacent
cell which is in the next column.
DIMENSION (NODES), Diagonal from the upper factor.
(FL stands for F-lower case.)
FL (F-lower
case) from the cell in the last column.
FL (F-lower
case) from the cell in the last layer.
FL (F-lower
case) from the cell in the last row.
12-52
.
8
List
l
0
Variable
Range
FLXI
GL
Module
Module
GLNCL
GLNLL
GLNRL
GLXI
GP
Module
Module
Module
Module
Module
H
Module
HCFHNW
HCLOSE
HCOF
Module
Package
Global
HDCG
HHCOF
HHNEW
HNEW
Package
Module
Module
Global
HNW
I
IB
IBOUND
Module
Module
Module
Global
ICNVG
Global
IDIR
Module
I DNCOL
I DNRC
II
IOUT
I PCALC
Module
Module
Module
Global
Package
IPRSIP
Package
3
JB
JJ
K
KB
KITER
Module
Module
Module
Module
Module
Global
of Variables
for
Module SIPlAP
(Continued)
Definition
Intermediate
result.
DIMENSION (NODES), Diagonal from the upper factor.
(GL stands for G-lower case.)
GL (G-lower case) from the cell in the last column.
GL (G-lower case) from the cell in the last layer.
GL (G-lower case) from the cell in the last row.
Intermediate
result.
Diagonal element in the modified
coefficient
matrix.
(GP stands for G-prime.)
Diagonal label in the coefficient
matrix.
Conductance
from the adjacent
node which is in the next row.
Product of head and HCOF for a cell.
Closure criterion
for the iterative
procedure.
DIMENSION (NCOL,NROW,NLAY), Coefficient
of head in the
cell
(J,I,K)
in the finite-difference
equation.
DIMENSION (MXITER), Maximum head change for each iteration.
Double-precision
HCOF.
Head in the adjacent
cell which is in the next row.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
of head
HNEWchanges at each iteration.
in each cell.
Temporary field
for HNEW(N).
Index for nodes and rows.
Row number of the cell having the largest
head change.
DIMENSION (NCOL,NROW,NLAY), Status of each cell.
c 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
Flag is set equal to one when the iteration
procedure
has converged.
Indicator
for direction
of solution
algorithm.
+l - forward
-1 - reverse
Intermediate
result
used to calculate
indices.
Intermediate
result
used to calculate
indices.
Row number.
Primary unit number for all printed
output.
IOUT = 6.
Flag.
= 0, iteration
parameter seed (WSEED) is entered
by the user.
= 1, seed is calculated
in the program.
Frequency (in time steps) with which the maximum head
changes for each iteration
will
be printed.
Index for columns.
Column number of the cell having the largest
head change.
Column index.
Index for layers.
Layer of the cell having the largest
head change.
Reset at the start
of each time
Iteration
counter.
step.
12-53
List
Variable
of Variables
Module
Global
Global
LRCH
Package
MXITER
N
NC
NCD
Package
Module
Module
Module
NCF
Module
NCL
Module
NCN
Module
NCOL
NL
NLAY
NLL
Global
Module
Global
Module
NLN
Module
NLS
Module
NLZ
Module
NODES
NPARM
NR
NRB
Global
Package
Module
Module
NRC
NRH
Module
Module
NRL
Module
NRN
Module
NROW
NSTP
NTH
RES
RHS
Global
Global
Module
Module
Global
Module SIPlAP
(Continued1
a
Definition
Range
KK
KPER
KSTP
for
Layer index.
Stress period counter.
Reset at the start
of each stress
Time step counter.
period.
DIMENSION (MXITER), Layer, row, and column of the cell
containing
the maximum head change (HDCG) for each
iteration.
Maximum number of iterations.
Cell index.
Index for the adjacent cell in the last column.
One-dimensional
subscript
of conductance
to the adjacent
cell which is in the last column.
One-dimensional
subscript
of conductance
to the adjacent
cell which is in the next column.
One-dimensional
subscript
of the cell index of the
adjacent
cell which is in the last column.
One-dimensional
subscript
of the cell index of the
adjacent
cell which is in the next column.
Number of columns in the grid.
Index for the adjacent
cell in the last layer.
Number of layers in the grid.
One-dimensional
subscript
of the cell index of the
adjacent
cell which is in the last layer.
One-dimensional
subscript
of the cell index of the
adjacent
cell which is in the next layer.
One-dimensional
subscript
of conductance
to the adjacent
cell which is in the next layer.
One-dimensional
subscript
of conductance
to the adjacent
cell which is in the last layer.
Number of cells
(nodes) in the finite-difference
grid.
Number of iteration
parameters.
Index for the adjacent
cell in the last row.
One-dimensional
subscript
of conductance
to the adjacent
cell which is in the last row.
Number of cells
in the layer.
One-dimensional
subscript
of conductance to the! adjacent
cell which is in the next row.
One-dimensional
subscript
of the cell index of the
adjacent
cell which is in the last row.
One-dimensional
subscript
of the cell index of the
adjacent
cell which is in the next row.
Number of rows in the grid.
Number of time steps in the current
stress period.
Index for iteration
parameters.
Residual.
DIMENSION (NCOL,NROW,NLAY), Right hand side of the
finite-difference
equation.
RHS is an accumulation
of terms from several
different
packages.
12-54
a
List
Variable
Range
RP
Module
RRHS
S
Module
Module
SHNEW
TCHK
TP
Module
Module
Module
UP
Module
V
VN
VNCL
Package
Module
Module
VNLL
Module
VNRL
Module
W
XI
Z
Package
Module
Module
ZHNEW
Module
of Variables
for
Module SIPlAP
(Continued)
Definition
Diagonal element in the modified
coefficient
matrix.
(RP stands for R-prime.)
Double-precision
right hand side of the equation.
Diagonal label in the coefficient
matrix--conductance
from the adjacent
node which is in the next layer.
Head in the adjacent
cell which is in the next layer.
Absolute value-of
head change for a sing le cell.
Diagonal element in the modified
coeffic ient matr ix.
(TP stands for T-prime.)
Diagonal element in the modified
coeffic ient matr ix.
(UP stands for U-prime.)
DIMENSION (NODES), Intermediate
result.
Temporary double-precision
V(N).
Element in the intermediate
vector for the cell in
the last column.
Element in the intermediate
vector for the cell in
the last layer.
Element in the intermediate
vector for the cell in
the last row.
DIMENSION (NPARM), Iteration
parameters.
Double-precision
V(N).
Diagonal label in the coefficient
matrix--conductance
from the adjacent
node which is in the last layer.
Head in the adjacent cell which is in the last layer.
12-55
Narrative
Submodule SSIPlP prints
all
cells
location
for
each iteration
the
for
Module SSIPlP
largest
of a time
(LRCH) where the change
value
step.
occurs.
no numbered comments are used and no flow
12-56
of head change
Also
printed
The submodule
chart
is
(HDCG) out of
is the cell
is so short
provided.
that
SUBROUTINE SSIPlP(HDCG,LRCH,KITER,MXITER,IOUT)
C
C
C-----VERSION
1636 24JUL1987 SSIPlP
C
C
C
C
C
C
C
C
C
*****f***~~**f**+*+*~*~~**~*~~~***~~*********~***~*~*********~****
PRINT MAXIMUM
HEAD CHANGE FOR EACH ITERATIONDURINGA TIME STEP
******************************************************************
SPECIFICATIONS:
-----------------------------------------------------------------DIMENSIONHDCGtMXITER),LRCH(3rMXITER)
-----------------------------------------------------------------WRITE(IOUT,S)
5 FORMATtlHOr'MAXIMUM
HEADCHANGEFOREACHITERATION:'/
1
lHO,S(" HEAD CHANGE LAYER,ROW,COL’)/lX,132(‘-‘1)
WRITE (IOUT,lO) (HDCG(J),(LRCH(I,J),I=lr3),J=lrKITER)
10 FORMAT((lX,S(G12.4,’
~‘,13,‘,‘,13,‘,‘,13,‘~‘~~~
WRITE(IOUT,ll)
11 FORMATt1HO1
C
RETURN
C
END
l
12-57
List
of Variables
for
Module SSIPlP
Definition
Variable
Range
HDCG
Package
DIMENSION (MXITER),
iteration.
I
Module
Index
IOUT
Global
Primary
Module
Index
KITER
Global
Iteration
step.
LRCH
Package
DIMENSION (MXITER), Layer, row, and column of the cell
containing
the maximum head change (HDCG) for each
iteration.
MXITER
Package
Maximum number of iterations.
for
cell
unit
for
Maximum head change for
each
location.
number for
all
printed
output.
IOUT = 6.
iterations.
counter.
12-58
Reset at the
start
of each time
Narrative
Submodule SSIPlI
conductance
values
calculates
and grid
the method of calculation
for
each active
Finally,
all
the
seed is also
printed.
Submodule SSIPlI
the
average
performs
constants
cell
seed,
These are initialized
seed.
Since
1.0.
this
The three
a*/Z(NCOL)2,
3-.
seed,
value
all
grid
functions
in the
following
variables.
than
one,
and n2/2(NLAY)2,
grid
order:
In order
to calculate
seeds)
and
are required.
the smallest
it
is
CCOL, CROW, and CLAY are set
cells,
This
a seed is calculated)
be less
is selected.
seed.
AVGSUM (sum of the cell
which
required,
The minimum cell
WMINMN is used to store
coefficients,
Loop through
the
its
must always
r2/2(NROW)2,
to give
parameters.
to zero.
seed is
seeds be calculated
iteration
for
model-
the minimum of the three,
and initialize
cells
a single
the
accumulators
NODES (sum of the active
seed using
three-directional
seeds are averaged
used to calculate
Calculate
that
Then a cell
cell
Although
dimensions.
seed is then
1.
an iteration-parameter
requires
cell.
Module SSIPlI
for
cell
initialized
equal
to
to
respectively.
calculating
a cell
seed for
each active
cell.
(a)
cells.
Conductance
(b)
direction
vertical
that
Find
Find
the
conductances
across
from the cell
the grid
boundary
a neighbor
is set equal
(ZSMX, ZSMN).
is no flow),
If
in the
(BHMX, BHMN), and in the
the minimum is
set the minimum equal
12-59
adjacent
to zero.
the maximum and minimum of the two conductances
(DFMX, DFMN), in the column direction
direction
to each of the six
zero
(which
indicates
to the maximum.
row
(c)
Calculate
three-directional
seeds
(WCOL, WROW, WLAY) u:;ing
the
relations
WCOL = CCOL/(l.
+ (BHMX + ZSMX)/DFMN);
WROW= CROW/(l.
+ (DFMX + ZSMX)/BHMN); and
WLAY =
If
cLAY/(l.
the minimum conductance
are zero),
cell
any valid
with
the
be less
(d)
Select
it
is the
Accumulate
the
the
(that
to 1.0.
minimum-directional
seed will
If
so that
is zero
set the seed equal
seed (the
seed.
+ (DFMX + BHMx)/ZSMN).
3.
Calculate
the
minimum
4.
Calculate
This
seed)
than
both the minimum and the maximum
value
smallest
of all
the
is selected
cell
grid
seed used so far,
seeds and the total
cell
seed (the
average
cell
and print
iteration
parameters
.x-a
where
i-th
NPARM is the
..
5
Z(d)
bec:ause
seeds as the cell
store
it
in WMINMN.
number of active
seeds can be calculated
= 1 - (SEED) NPARM - 1
is the
in step
when the
1.0.
i-l
Ii
be ignored
seed)
in step
cells
3.
and print
it
along
seed.
relation
Ii
will
the minimum of the three-directional
sum of the cell
average
is,
iteration
parameter,
number of iteration
and
parameters.
RETURN.
12-60
using
the
grid
seed with
Flow Chart
for
Module SSIPlI
Seed: the "grid seed" is the
single
parameter used to
calculate
the iteration
To calculate
parameters.
the grid seed, several
intermediate
variables,
called
"cell
seeds," are
For each cell,
used.
three "directional
seeds"
are calculated.
The minimum
directional
seed for a cell
is the "cell
seed."
The
"grid seed" is the average
of the cell seeds.
AVGSUMis an accumulator
to
which each cell seed is
It is then divided
added.
by the number of cells to
obtain the average cell
seed which is used as the
grid seed.
.AND MINIMUM OF THE
TWO CONDUCTANCES
IN EACH PRINCIPAL
COORDINATE
DIRECTION
CALCULATE THE
THREE i;I;;TlONAL
A
2D
IF THIS IS THE
MINIMUM CELL SEED
SO FAR, SAVE IT
I
CALCULATE THE
AVERAGE CELL SEED
AND PRINT THE
AVERAGE AND
MINIMUM SEEDS
+
4
CALCULATE AND PRINT
ITERATION
PARAMETERS USING
THE AVERAGE CELL
SEED
I
12-61
SUBROUTINE SSIPlI (CR,CC,CV,
1
IBOUND,NPARM,WINCOL,NROW,NLAY,
IOUT)
C
C-----VERSION 1417 12MAY1987SSIPl I
*****************************************************~********~***
C
C
CALCULATE AN ITERATIONPARAMETERSEED AND USE IT TO CALCULATE SIP
C
ITERATION PARAMETERS
C
C
C
C
a
*****************************************************~************
SPECIFICATIONS:
-------------i----,-,,,,,,,,,,,,,,,,,,,,--------~-------------,---DIMENSIONCR(NCOL,NROW,NLAY)rCC(NCOLINROn’rNLAY)
1
rCV(NCOL,NROW,NLAY)rIBOUND(NCOL,NROW,NLAY~,W~NPARM~
C
DOUBLE PRECISIONDWMIN,AVGSUM
--------------------------------------------------------------.---c”
Cl-----
CALCULATE CONSTANTS AND
INITIALIZE VARIABLES
PIEPIE=9.869604
R=NROW
C=NCOL
ZL=NLAY
CCOL=PIEPIE/(Z.+WC)
CRW=PIEPIE/(Z.*R*R)
CLAY=PIEPIE/(Z.*ZL*ZL)
WMINMN=l.
AVGSUM=O.
NODES=0
C
(-32----c2-----
LOOP THROUGHALL CELLS, CALCULATING A SEED FOR EACH CELL
THAT IS ACTIVE
DO 100 K=lrNLAY
DO 100 I=lrNROW
DO 100 J=lrNCOL
IF(IBOUND(J,I,K).LE.O)
GOTO 100
C
C2A----C2/+-..--
CONDUCTANCEFROM THIS CELL
TO EACH OF THE 6 ADJACENT CELLS
D=O.
IF(J.NE.l) D=CR(J-lrI,K)
F=O.
IF(J.NE.NCOL) F=CR(J,I,K)
B=O.
IF(I.NE.l)
B=CC(J,I-1rK)
H=o.
IF(I.NE.NROW) H=CC(JrIrK)
z=o.
IF(K.NE.l) Z=CV(J,IrK-1)
s=o.
IF(K.NE.NLAY) S=CV(J,I,K)
C
c2B----- FIND THE MAXIMUM
ANDMINIMUMOF THE 2 CONDUCTANCECOEFFICIENTS
C2&---- IN EACHPRINCIPALCOORDINATE
DIRECTION
12-62
a
DFMX=AMAXl(D,F)
BHMX=AMAXl(B, H)
ZSMX=AMAXl( Z, S)
DFMN=AMINl(D,F)
BHMN=AMINl(B,H)
ZSMN=AMINl(Z,S)
IFtDFMN.EQ.0.) DFMN=DFMX
IF(BHMN.EQ.0.)
BHMN=BHMX
IF(ZSMN.EQ.0.)ZSMN=ZSMX
C
(yJc---
CALCULATE A SEED IN EACH PRINCIPAL
COORDINATE
DIRECTION
WCOL=l.
IF(DFMN.NE.0.)
WCOL=CCOL/(l.+(BHMX+ZSMX)/DFMN)
WROW=l.
IF(BHMN.NE.0.)
WLAY=l.
WROW=CROW/(l.+(DFMX+ZSMX)/BHMN)
IF(ZSMN.NE.0.)WLAY=CLAY/(l.+(DFMX+BHMX)/ZSMN)
C
C2’)--C2D---
C
SELECT THE CELL SEED, WHICH
IS THE MINIMUM
SEED OF THE 3.
SELECT THE MINIMUM SEED OVER THE WHOLEGRID.
WMIN=AMINl(WCOL,WROW,WLAY)
WMINMN=AMINl(WMINMN,WMIN)
C2E-w-vQE---
C
ADD THE CELL SEED TO THE ACCUMULATORAVGSUMFOR USE
IN GETTING
THE AVERAGE SEED.
DWMIN=WMIN
AVGSUM=AVGSUM+DWMIN
NODES=NODES+l
100 CONTINUE
------CALCULATE
THE AVERAGE SEED OF THE CELL SEEDS, AND PRINT
C3------ THE AVERAGE AND MINIMUM SEEDS.
TMP=NODES
AVGMIN=AVGSUM
AVGMIN=AVGMIN/TMP
WRITE(IOUT,lOl)AVGMIN,WMINMN
101 FORMAT(lHO,‘AVERAGE SEED =‘rF11.8/1X,‘MINIMUM
SEED =‘rF11.8)
C
ANDPRINTITERATION
PARAMETERSFROM THE AVERAGE SEED
c4 ------CALCULATE
Pl=-1.
P2= NPARM-1
DO 50 I=lrNPARM
Pl=Pl+l .
50 W(I)=l.-AVGMIN**(Pl/P2)
WRITE(IOUT,150)NPARM,(W(J)rJ=lrNPARM)
150 FORMAT(lHO,/rIS,' ITERATION
PARAMETERSCALCULATED FROM’,
1
’ AVERAGE SEED:‘//(lOX,6E15.7))
l
C
C5------RETURN
RETURN
END
12-63
List
Variable
of Variables
for
Module SSIPlI
Definition
Range
AVGMIN
Module
Mean WMIN.
AVGSUM
Module
Sum of all
B
Module
Conductance
BHMN
Module
Minimum of B and H (if
maximum).
BHMX
Module
Maximum of B and H.
C
Module
Number of columns.
cc
Global
DIMENSION (NCOL,NROW,NLAY), Conductance in the column
CC(J,I,K)
contains
conductance
between
direction.
nodes (J,I,K)
and (J,I+~,K).
CCOL
Module
Intermediate
factor.
CLAY
Module
Intermediate
factor.
CR
Global
DIMENSION (NCOL,NROW,NLAY), Conductance in the
CR(J,I,K)
contains
conductance
direction.
between nodes (J,I,K)
and (J+l,I,K).
CROW
Module
Intermediate
cv
Global
DIMENSION (NCOL,NROW,NLAY-l), Conductance
CV(J,I,K)
contains
vertical
direction.
between nodes (J,I,K)
and (J,I,K+l).
D
Module
Conductance
DFMN
Module
Minimum of D and F (if
maximum).
DFMX
Module
Maximum of D and F.
DWMIN
Module
Double
F
Module
Conductance
between this
node and the
one to the
right.
H
Module
Conductance
between this
node and the
one to the
front.
I
Module
Index
IBOUND
Global
DIMENSION (NCOL,NROW,NLAY), Status
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
of WMIN’s.
between this
one to the
the minimum is 0, it
rear.
is the
row
factor.
between this
precision
for
node and the
node and the
the minimum is
in the
conductance
one to the
0, it
left.
is the
WMIN.
rows.
12-64
of each cell.
List
Variable
of Variables
Module SSIPlI
for
Range
(Continued)
Definition
IOUT
Global
Primary
J
Module
Index
for
columns.
K
Module
Index
for
layers.
NCOL
Global
Number of columns
NLAY
Global
Number of layers
NODES
Module
Number of variable-head
NPARM
Package
Number of iteration
NROW
Global
Number of rows in the
PIEPIE
Module
PI squared.
Pl
Module
Index
P2
Module
NPARM-1.
R
Module
Number of rows.
S
Module
Conductance
TMP
Module
Temporary
W
Package
DIMENSION (NPARM), Iteration
parameters.
WCOL
Module
Seed in the column direction
for
WLAY
Module
Seed in the
WMIN
Module
Minimum of (WCOL, WLAY, WROW).
WMIl@lN
Module
Minimum WMIN.
WROW
Module
Seed in the
row direction
Z
Module
Conductance
between this
ZL
Module
Number of layers.
ZSMN
Module
Minimum of Z and S (if
ZSMX
Module
Maximum of Z and S.
unit
for
number for
the
all
in the
printed
output.
IOUT = 6.
grid.
in the grid.
(IBOUND > 0) cells
in the
grid.
parameters.
grid.
number of parameters.
between this
field
for
layer
node and the one below.
nodes.
direction
12-65
for
for
a cell.
a cell.
a cell.
node and the one above.
minimum is
0, it
is the maximum).
CHAPTER 13
SLICE-SUCCESSIVE OVERRELAXATION PACKAGE
Conceptualization
Successive
of linear
overrelaxation
equations
model discussed
Package.
is another
method for
herein
through
material
the Slice
on the
in many standard
by Peaceman (1977),
Successive
successive
references,
Crichlow
(1977)
solving
large
It is implemented
by means of iteration.
Background
can be found
and Implementation
in the
Overrelaxation
overrelaxation
including
systems
those
(SSOR)
approach
already
and Remson, Hornberger
noted
and Molz
(1971).
The successive
Package by dividing
shown in figure
overrelaxation
the finite
values
they
successive
iterations.
The set
adjacent
slices
as known quantities
computed
values
of head for
equations
for
multiplied
the
results
the slice
the
slice
into
for
(that
processed).
in this
Gaussian
SSOR
"slices,"
discrete
these
as
sets,
sets
of
in a new set of estimated
each slice
slices
elimination
parameter,
values
13-1
W, generally
slice
the terms
for
the most recently
as "known"
The values
head between
to the
treating
inserting
head
are processed,
corresponding
is,
the adjacent
final
vertical
iteration,
elimination,
being
as the
in the
of the change in computed
by Gaussian
by an acceleration
are taken
node equations
of equations
solved
implemented
into
In every
in terms
is then
computed for
directly
grid
As the equations
expressed
is
resulting
in turn,
each slice.
are first
the
to a slice.
are processed
for
difference
54, and grouping
each set corresponding
equations
technique
values
in the
of head change
process
taken
are then
between
of head change in that
each
1 and 2;
iteration
Slice 4
Full Grid
Figure 54.-Division
of the three-dimensional
model array into
vertical slices for processing in the SSOR package.
13-2
for
They are added to the
the slice.
preceding
for
iteration
that
until
thus
to obtain
This
slice.
all
completing
in successive
a single
It
should
equations
for
not direct
values
values
continue
flow
through
for
below with
have been processed,
sequence
until
is then
a direct
is
less
than
method of solution
each iteration
to process
the overall
solution
Each direct
solution
produces
as successive
of solution
consideration
cell,
the addition
repeated,
the differences
iterations
slice,
to change until
an individual
iteration,
in sequence
slices
closure
is
described
the
procedure
only
is
interim
of head change based on the most recently
slices;
The process
detail
is used within
but iterative.
heads in adjacent
array
of slices,
even though
each individual
or estimates
each slice
the
nodes in the mesh.
be noted that
elimination)
for
computed in successive
from the
of head for
The entire
the series
at all
(Gaussian
estimates
repeated
iteration.
between the head values
criterion
is
head values
in the three-dimensional
passes through
the closure
the final
procedure
of the slices
respective
computed
are processed,
the
computed
achieved.
above can be illustrated
in more
of the node equations.
The equation
as developed
2, is
in chapter
of a second superscript
of
reproduced
to indicate
iteration
level
md
w
+ GRi,j-1/2,khi,j-1,k
+ Gci-1/2,j,khi-l,j,k
GVi,j,k-l/ZhY$,k-I
+ (- GVi,j,k-l/2
- GGi-l/E,j,k
- GRi,j-1/2,k
- GRi,j+l/E,k
m, II
- Gvi,j,k+l/2
- GGi+l/2,j,k
w
+ CCi+l/2,j,khi+l,j,k
+ HGGFi,j,k)hi,j,k
w
+ GRi,j+l/2,khi,j+l,k
m, fi
+ CVi,j,k+l/Ehi,j,k+l
13-3
= RH%,j,k
(113)
In equation
(113),
the superscript
of (113)
side
R refers
is written
of equation
equation,
the superscript
the
to the
for
iteration
the following
(113)
result
m refers
is then
level.
If
iteration
subtracted
can be written
to the time
step,
an equation
a+l,
level,
from each side
while
of the form
and the
of the
left
new
as
+CCi-l/*,j,k(hTI~~~,k-h~~~,j,k)
CVi
,j,k-1/2,(h~:gf:-l-h::g.k-l)
m, a+1
+ (- CVi,j,k-l/2
+ CRi,j-1/2,k(hi,j-I,k-hl:ja_l,k)
- CRi,j+l/2,k
- CRi ,j-1/2,k
m,R+l
m,a
+ HCOFi ,j,k)(hi,j,k-hi,j,k)
t CCi+l/2,j,k(h~~~rj,k-h~~~,j,k)
w
- CVi,j,k-1/2hi,j,k-1
RHSi,j,k
w
- CRi,j-1/2,khi,j-l,k
- CVi,j,k+l/E
t CRi ,j+l/2,k(hT:~~~,k-h~~~tl,k)
+ cvi , j ,k+l/z(hi
m, a+1
, j ,k+l-h~:~,k+l)
m, 11
- CCi-l/E,j,k
- CRi,j-1/2,k
- cvi , j , k+1/2 + HCOFi,j,k)hy:Q,k
w
m,a
w
- CRi ,j+l/2,khi,j+l,k
=
- cci-1/2,j,khi-l,j,k
- (- CVi,j,k-l/2
- CCi+l/2,j,k
- CRi , j+1/2,k
- CCi+l/E,j,k
- CCi-1/2,j,k
- CCi+l/2,j,khi+l,j,k
- Cvi ,j,k+I/2hi
,j,k+l
(114)
In equation
(114) the
& and iteration
head between iteration
Note that
of (114)
when the
consists
conductance
head already
terms
unknown terms
Gh iterat
entirely
assembled
obtained
during
are taken
QtI--for
as the changes
m,a+l
ion has been completed,
of known terms--it
in the formulation
iteration
R.
13-4
(hi,j,k
example,
the
includes
process,
right
in computed
- h!/:ja,k).
hand side
the RHS and
and estimate:;
of
Now suppose that
rows,
the
we divide
as shown in figure
54, and isolate
nodes of an individual
which
is taken
equation
retain
along
(114),
if
slice--for
values.
Thus the terms
m, a+1
side
(hi+l,j,k
and hTit,j,k
- CCi+l/2,j,k
- CVi,j,k+l/2
m,R
- CRi,j-l/E,k
to row i,
as unknown terms,
side
slices
we
but
to be known
and
of equation
two expressions
that
of
the terms
(114),
are
to the
right
and
in hy':,j,k
- CRi,j+l/2,k
+ HCOFi,j,k)(hyIE:-hl:t,k)
=
m, Et1
- cc-i-1/2,j,khi-l,j,k
- (- CVi,j,k-l/2
- CCitl/2,j,k
- CRi,j+l/2,khi,jtl,k
In terms
+ Cvi,j,ktI/2(h~:jaf:tI-h!i~~,ktI)
- CVi,j,k-I/Eh;:Q,k-I
- CRi , jt1/2,k
we find
54,
leaving
- CCi-1/2,j,k
- CRi,j-I/2,khl:Q-l,k
left
along
with
4 of figure
array.
slice
taken
associated
corresponding
If we move these
and rearrange,
+ CRi,jtI/2,k(hY:tZ:,k-hYIftI,k)
RHSi,j,k
i,
this
on the
- hy;f,j,k).
drop out,
t (- CVi,j,k-l/2
slices
at nodes in the two adjacent
m, a+1
- hyl:,j,k)
cci-1/2,j,k
(hi-l,j,k
as known quantities.
of the equation
slice
dimensional
slice
at nodes within
the head changes
treated
example,
we are processing
consider
vertical
the equations
row 4 of the three
the head changes
CCi+l/Z,j,k
the mesh into
- CCi-1/2,j,k
- CVi,j,ktl/2
- CRi,j-1/2,k
t HCOFi,j,k)h!i:;,k
m, at1
- CCitl/2,j,khitl,j,k
w
- CVi,j,ktl/2hi,j,ktl
(115)
13-5
Now suppose the slices
number,
i;
then
iteration
a
Value
Of
initiated
available.
calculations
side
value
slice
in the processing
TO circumvent
preceding
for
in the
i-l
will
order
of increasing
be completed
row
in each
It follows
that
before calculations
for slice
i are initiated.
m,a+l
will
be available
when the processing
of slice
i is
hi-l,j,k
m, 11+1
in iteration
a+l, whereas a value of hi+I,j,k
will
not be
m,Q+I
directly
Thus the term CCi-I/2,j,khi-l,j,k
can be incorporated
as a known term
cannot.
are processed
difficulty,
mall
hi+I,j,k,
iteration,
of (115).
this
(Thus in effect
of head for
of slice
i,
the
value
is substituted
for
we are using
each adjacent
m,Q+l
but the term CCi+I/2,j,khi+I,,j,k
slice.)
from the
of hy+I,j,k
m, Q+l
hi+I,j,k
on the
the most recently
The resulting
equation
tight
calculated
is
-f"', Q+l
CVi , j ,k-l/2
+ CRi,j-1/2,k(hi,j-l,k-hT:Q_l.k)
(G:gf:-l-hy:q,k-l)
t (- CVi,j,k-l/2
- CCi-1/2,j,k
- CRi,j-1/2,k
+ HCOFi,j,k)(hT:K:-hyzJ,k)
- CCi +1/2, j ,k - Cvi,j,ktl/2
41, Q+l
t cvi ,j,ktl/2(hi,j,ktl-h'~~~,ktl)
t CRi,jt1/2,k(~:9=:,k-h~:g+l,k)
RHSi,j,k
- cvi,j,k-l/2hy:Q,k-l
m,Q
- CRi ,j-1/2,khi,j-1,k
- CRi , jt1/2,k
m,Q
=
m, Q+l
- cci-1/2,j,khi-l,j,k
- (- CVi,j,k-l/2
- CCitl/2,j,k
- CRi,jtl/2,khi,jtl,k
- CRi,jtl/2,k
- CCi-1/2,j,k
- Cvi , j ,k+1/2
m, 11
- CCitl/2,j,khitl,j,k
- CRi,j-1/2,k
m,Q
t HCOFi,j,k)hi,j,k
m,a.
- CVi,j,ktl/$i,j,ktl
(ll6)
In equation
terms
in slice
(116),
the
i at iteration
notation
atl.
K has been introduced
The purpose
13-6
of this
for
notation
the head
will
become
clear
as the solution
slice
is
the
process
at each node.
and an equation
Thus a system
established.
Gaussian
elimination
the entire
three-dimensional
of equations
in matrix
CAli {AK}i
where [AJi
slice
(116)
is
formulated
in NC*NL unknowns is
is usually
small,
the total
enough so that
direct
solution
approach
(note
the larger
set
that
by
such a procedure
of equations
associated
model array.)
associated
with
an individual
slice,
i,
can be
form as
= {R)i
(117)
between iteration
"constant"
slice
for
is the coefficient
-in,R+l
m,Q
, for
hi,j,k-hi,j,k
estimates,
small
is an efficient
not be feasible
The set
the
is generally
in the model and NL
form of
of NC*NL equations
generally
written
of the
Because the number of layers
number of equations
with
The number of nodes in the
NC*NL, where NC is the number of columns
number of layers;
would
is described.
terms,
matrix
for
slice
i;
{bF;}i
is a vector
of
the change in computed head at each node in
R and iteration
representing
the
right
g+l;
side
and {R}i
of equation
is the vector
(116),
of
for
i.
The Gaussian
(117) yields
slice.
elimination
one value
These terms
head from iteration
acceleration
m,R+l
m,a.
hi,j,k
= hi,j,k
applied
estimates
a. tl.
W, and each result
iteration
R+1; that
to the matrix
~,a+1
m,R
(hi,j,k-hi,j,k)
as first
R to iteration
parameter,
iteration
of the term
are taken
head from the preceding
head for
procedure
to obtain
for
for
equations
each node in the
the change in computed
Each is multiplied
by the
is added to the corresponding
the
final
estimate
of
is,
+ w(hy:;f:-h;:;,k)
(118)
13-7
m,R+l
have been computed for
Of hi,j,kl
When values
slice
i,
slice,
the
procedure
itl.
of calculation
When all
and calculations
slices
is
initiated
for
have been processed
are initiated
for
the
each node (j,k)
next
the
in
the succeeding
iteration
iteration
is conplete,
unless
closure
has
been achieved.
As illustrated
equation
equal
only
(117)
to the
the
figure
is symmetric
triangular
in the program
55-b,
with
of the
SSOR to achieve
optimal
to the trial
adjustment
of the
the matrix
and banded,
with
acceleration
and error
SIP "seed"
parameter
of convergence.
procedure
value
storage
as illustrated
In this
For this
described
NL=NC=3.
necessary
purpose,
in Chapter
is
in
example,
is frequently
can be applied.
13-8
of
of the matrix,
this
array,
NL*NC and NL+l.
[A]i
a maximum half-bandwidth
has to be stored;
in a two-dimensional
rates
of coefficients
Because of the symmetry
portion
dimensions
Adjustment
similar
55-a,
number of layers.
lower
provided
in figure
in
methods
12, for
1 a11
a 12
1 a12
I
I a14
a22
a23
a 23
a33
a14
a25
I
I
I
I
I
I
a25
a36
a 44
a45
a 45
a55
a47
a56
(a) Coefficient matrix for an individual slice
(b) Two dimensional
Figure 55.-Coefficient
corresponding
array for storage of matrix elements
matrix for slice equations and
computer storage array.
13-9
Slice-Successive
Input
the unit
to the
Overrelaxation
Slice-Successive
specified
Package Input
Overrelaxation
(SOR) Package is
read from
in IUNIT(11).
FOR EACH SIMULATION
SORlAL
1. Data:
Format:
MXITER
110
SORlRP
2. Data:
Format:
HCLOSE IPRSOR
F10.0
110
ACCL
F10.0
Explanation
Input
MXITER--is
ACCL--is
of Fields Used in
Instructions
the maximum number of iterations
the
HCLOSE--is
acceleration
the
head
absolute
is
IPRSOR--is
less
parameter,
change
value
than
the printout
for
or equal
is
printed
for
SOR.
When the
nodes during
is an even multiple
at the end of each stress
of IPRSOR.
period
13-10
an iteration
IF IPRSOR is equal
of a time
maximum
stops.
The maximum head change
each iteration
step.
1.0 and 2.0.
convergence.
to HCLOSE, iteration
interval
in a time
between
of head change from all
is changed to 999.
step
usually
criterion
it
for
allowed
step
This
regardless
to zero,
(positive
whenever
printout
of the
or negative)
the
also
value
time
occurs
of I:PRSOR.
Module Documentation
The Slice-Successive
primary
modules
for
the
Slice-Successive
Overrelaxation
and one submodule.
Allocates
SORlRP
Reads control
Package
(SORl)
consists
They are:
Primary
SORlAL
Overrelaxation
Modules
space for
arrays.
information
needed by the
SORl Package.
SORlAP
Performs
one iteration
of slice-successive
overrelaxation.
Submodule
SSORlB
Solves
a system
of linear
13-11
equations.
Package
of three
Narrative
Module SORlAL allocates
arrays
the
for
Module SORlAL
space in the
X array
are A, RES, IEQPNT, HDCG, and LRCH.
lower
diagonals
RES holds
the
IEQPNT holds
HDCG holds
location
of the
residual
symmetric
vector
a sequential
of the cell
(row,
column,
1.
Print
2.
Read and print
3.
Allocate
the
(ISUM) is
space required
for
an array,
is
incremented
5.
for
a single
a single
each cell
each iteration.
and layer)
its
functions
a message identifying
the
SOR is
for
slice,,
slice.
in a slice.
LRCH holds
which
and
had the'maximum
the
head
each iteration.
Module SORlAL performs
4.
matrix
number for
The SOR
the main diagonal
hand sides)
identification
the maximum head change for
change for
pointer
right
SOR arrays.
"A" holds
coefficient
(the
for
the
Calculate
required
order:
SOR Package.
space in the
variable
required
and print
variable
X array.
The X-array
ISOLD prior
SOR can be calculated
array-location
by the
following
the maximum number of iterations.
saved in the
for
the
in the
to allocation
in step
is
location
set equal
4.
so that
To allocate
to ISUM.
space
Then ISUM
number of elements.
the
space used in the
ISUM - ISOLD.
RETURN
13-12
X array,
The space used by
Flow Chart
for
Module SORlAL
,X array is the pool of memory space
from which space is allocated
for
arrays used by various packages.
PRINT A MESSAGE
IDENTIFYING THE
SORPACKAGE
READ AND PRINT
THE MAXIMUM
NUMBER OF
ITERATIONS
ALLOCATE SPACE
FOR SOR ARRAYS
CALCULATE AND
PRINT THE AMOUNT
OF SPACE IN THE
X ARRAY USED BY
13-13
SUBROUTINE SORlAL (ISUM,LENX, LCA, LCRES, LCHDCG,LCLRCH, LCIEQP,
1
MXITER,NCOL,NLAY,NSLICE,bf3W,IN,IOUT)
: -----VERSION 1638 24JUL1987 SORlAL
********************************~*~*****************~*************
ALLOCATE STORAGE FOR SOR ARRAYS
************************~***************************~*******~~*****
C
C
C
C
C
C
SPECIFICATIONS:
--------------------____________________------------.--------------
----------------------------------------------------~-------------
C
------PRINT A MiSSAGE IDENTIFYINGSOR PACKAGE
WRITE(IOUT,l)IN
1 FORMAT(lHO,‘SORl -- SLICE-SUCCESSIVE
OVERRELAXATION PACKAGE’
I,', VERSION1, 9/l/87 INPUT READ FROM UNIT’,131
C
(-J&---
READ AND PRINT MXITER (MAXIMUM
# OF ITERATIONS)
READtIN, MXITER
2 FORMATtIlO)
WRITE(IOUT,3) MXITER
3 FORMATt1X, 15, ' ITERATIONSALLOWED FOR SOR CLOSURE’1
------ALLOCATE
SPACE FOR THE SOR ARRAYS
ISOLD=ISUM
NSLICE=NCOL*NLAY
MBW=NLAY+l
LCA=ISUM
ISUM=ISUMtNSLIC~*MBW
LCRES=ISUM
ISUM=ISUM+NSLICE
LCIEQP=ISUM
ISUM=ISUMtNSLICE
LCHDCG=ISUM
ISUM=ISUM+MXITER
LCLRCH=ISUM
ISUM=ISUM+3*MXITER
ISF+=ISUM-ISOLD
i
C
c4------CALCULATE
AND PRINT THE SPACE USED IN THE X ARRAY
WRITE(IOUT,4) ISP
4 FORMAT(lX,I8,' ELEMENTS IN X ARRAY ARE USED BY SOR’)
ISUMl=ISUt+l
WRITE(IOUT,5) ISUMlrLENX
5 FORMAT(lX,I8,' ELEMENTS OF X ARRAY USED OUT OF’,181
IF(ISUMl.GT.LENX) WRITE(IOUT,6)
6 FORMATt1X, ’
***X ARRAY MUSTBE DIMENSIONED
LARGER***‘)
C
c5 ..---+EJ-U~
RETURN
END
13-14
List
Variable
of Variables
for
Module SORlAL
Definition
Range
IN
Package
Primary
will
unit number from which
be read.
IOUT
Global
Primary
unit
ISOLD
Package
Before this module allocates
space, ISOLD is set equal
to ISUM. After allocation,
ISOLD is subtracted
from ISUM to get ISP, the amount of space in the
X array allocated
by this module.
ISP
Module
Number of words in the
ISUM
Global
Index number of the lowest element in the X array which
has not yet been allocated.
When space is allocated
for an array, the size of the array is added to ISUM.
ISUMl
Module
Index number of the
by this module.
LCA
Package
Location
in the
X array
of the
first
element
of array
LCHDCG
Package
Location
in the
HDCG.
X array
of the
first
element
of array
LCIEQP
Package
Location
in the
I EQPNT.
X array
of the
first
element
of array
LCLRCH
Package
Location
in the X array
LRCH.
of the
first
element
of array
LCRES
Package
Location
RES.
of the first
element
of array
LENX
Global
Length of the X array in words. This should always be
equal to the dimension of X specified
in the MAIN
program.
FBW
Package
Maximum bandwidth
MXITER
Package
Maximum number of iterations.
NCOL
Global
Number of columns
NLAY
Global
Number of layers
NSLICE
Package
Number of cells
number for
in the
all
X array
printed
X array
last
input
of the
of the coefficient
in the grid.
in a slice.
13-15
this
output.
allocated
element
in the grid.
for
package
IOUT = 6.
by this
X array
matrix
+l.
module.
allocated
A.
Narrative
Module SORlRP reads data
(ACCL),
also
called
and the time-step
the
following
1.
Read the
zero,
substitute
equal
to 999.
parameter
the
Module SORlRP
SOR package:
factor;
(IPRSOR) for
closure
printing
criterion
its
parameter
(HCLOSE);
head change.
Module SORlRP performs
chart.
Print
acceleration
interval
a default
parameter
for
printing
value
of 1.0.
(ACCL),
This module
functions
(ACCL),
the closure
criterion
RETURN.
13-16
the closure
head change
If
the maximum number of iterations
(IPRSOR).
3.
the
the acceleration
in the
order:
(HCLOSE), and the
2.
relaxation
interval
does not have a flow
for
for
criterion
(IPRSOR),
IPRSOR is
less
(MXITER),
(HCLOSE), and the
If
than
the
ACCL is
one,
set
it
acceleration
head-change
interval
SUBROUTINE SORlRPlMXITER, ACCL, HCLOSE,IN,
IPRSOR,IOUT)
C
C
C-----VERSION 1005 16MAR1983 SORlRP
**************************************************************~***
READ PARAMETERSFOR SOR
**t***~**~**t******+********~*~*****~******~*****~*****~~**~***~**
C
C
c”
C
SPECIFICATIONS:
-----------------------------------------------------------------C
-----------------------------------------------------------------C
C
Cl----- READ THE ACCELERATION PARAMETER/RELAXATION FACTOR (ACCL) THE
Cl---CLOSURE CRITERION (HCLOSE) AND THE NUMBEROF TIME STEPS
Cl--BETWEENPRINTOUTS OF MAXIMUM HEAD CHANGES (IPRSOR).
READtIN,
1
ACCL,HCLOSE,IPRSOR
FORMAT(2F10.0,110)
IF(ACCL.EQ.0.) ACCL=l.
IF(IPRSOR.LT.l) IPRSOR=999
:2------PRINT
A~CL, HCLOSE, IPRSOR
WRITE(IOUT,lOO)
100 FORMAT(lHO,///57X,‘SOLUTION
BY SLICE-SUCCESSIVE
OVERRELAXATION'
1/57X,43('-'))
WRITE(IOUT,llS) MXITER
115 FORMAT(lHO,47X,'MAXIMUM
ITERATIONSALLOWED
FORCLOSURE
=',I91
WRITE (IOUT,
ACCL
120 FORMATtlH ,63X, 'ACCELERATION
PARAMETER
='rG15.5)
WRITE(IOUT,125)
HCLOSE
FORMATtlH,52X,'HEAD CHANGE
CRITERIONFORCLOSURE
='rE15.5)
WRITE(IOUT,130) IPRSOR
130 FORMATtlH ,52X,‘SOR HEAD CHANGEPRINTOUT INTERVAL=',I91
125
C
C3------RETURN
RETURN
END
13-17
List
of Variables
for
Module SORlRP
Definition
Variable
Range
ACCL
Package
Acceleration
HCLOSE
Package
Closure
criterion
IN
Package
Primary
will
unit number from which
be read.
IOUT
Global
Primary
unit
IPRSOR
Package
Frequency (in time steps) with which the maximum head
changes for each iteration
will
be printed.
MXITER
Package
Maximum number of iterations.
parameter.
for
the
number for
13-18
all
iterative
input
printed
procedure,,
for
output.
this
package
IOUT = 6,,
Narrative
Module SORlAP performs
relaxation
(SSOR) algorithm
equations.
are combined,
[A]
and the
single
vector
slice.
which
{RES) on the
are calculated
by slice),
right
Sn the array
SSORlB which
solves
head changes which
of the matrix
[A]
the current
the matrix
are compared to the closure
criterion
matrix
equation
vector
equation
by the
the iteration.
The final
iteration.
procedure
and banded,
and the
changes are added to the heads from the preceding
heads for
HCOF
for
a
only
As heads are calculated,
is then multiplied
head changes for
coefficient
is symmetric
HNEW. The matrix
terms
by the formulation
hand side
are saved.
Over-
of finite-difference
to form the
and NLAY subdiagonals
to get the final
Slice-Successive
the system
matrix
passed to a submodule
factor
solving
Since the coefficient
are stored
of approximate
of the
CC, CR, and CV and the composite
row by row (slice
main diagonals
they
for
(27))
Module SORlAP
one iteration
The conductances
and RHS (see equation
for
The final
iteration
the
a vector
relaxation
head
to get the
head changes for
to see if
for
{RES) are
the
iterative
iteration
procedure
has closed.
Module SORlAP performs
1.
matrix
Calculate
the
its
functions
number of elements
in the following
in the compressed
order:
coefficient
[A].
2.
Process
3.
Clear
4.
Assign
(remember that
the slices
(rows)
one at a time
(DO STEPS 3-7).
the A array.
integers
sequentially
finite-difference
to the active
equations
13-19
cells
are formulated
in the slice
only
for
active
cells).
5.
the
Calculate
residual
If
the elements
vector
the cell
the main diagonal
will
consist
will
be formed
Process
{RES).
is
inactive,
of the coefficient
of HCOF plus
in an accumulator
zero,
the
Determine
cell
(b)
is
(c)
If
the equation
EE and subtract
(d)
there
from EE, and subtract
is
is active,
matrix
[A].
Remember that
to the
left
in step
(e)
If
EE and subtract
(f)
5(c)
there
there
from EE and subtract
adjacent
cells.
They
of EE multiplied
from an
head from the
times
left,
NEQ is
to HCOF and RHS,
last
iteration.
subtract
the
conductance
from
HNEWfrom R.
right,
times
the coefficient
did
If
cell.
EE and R equal
a node to the
subtract
the conductance
HNEW from R; and,
into
matrix
the
if
compressed
is symmetric
the cell
coefficient
so the
conduc:tance
not have to be stored.
is a node to the
the conductance
If
next
move the conductance
right
six
in
of hi,j,k)
number (NED) of the cell.
the conductance
to the
multipliers
and
at a time.
The elements
(HNEW) are subtracted
is a node to the
the conductance
If
cell.
[A]
one cell
The contents
Move on to the
HNEWcontains
there
matrix
residual.
inactive.
Note:
(the
EE.
iteration
Set the accumulators
respectively.
next
to the
called
coefficient
in the slice
matrix
conductances
(R) to form the
(a)
the cells
move on to the
by the head from the previous
accumulator
in the compressed
times
rear,
13-20
the conductance
from
HNEWfrom R.
is a node to the front,
the conductance
subtract
times
subtract
HNEW from R.
the
conductance
Remember that
the
form of the SSOR equations
rows on the
left
(g)
and subtract
If
active,
there
If
there
Move EE into
If
there
the
times
there
is only
residual
it
into
"full"
in the
vector
subtract
{RES).
conductance
from EE
if
below
residual
for
solve
If there
this
it
slice,
iteration)
this
the first
EE times
and leave
the
next
slice.
result
in
are two or more equations,
of head change for
(a)
Subtract
go on to the
directly
(first
in the slice,
row in A corresponds
vector.
for
For each cell
the cell
matrix.
the system of equations
7.
the
The first
row of A.
SSORlB to solve
estimate
from EE
A.
coefficient
are no equations
one equation,
the conductance
HNEWfrom R; and,
the first
in the
HNEW from R and store
If
head in adjacent
HNEWfrom R.
is a node below,
move the conductance
to the main diagonal
6.
times
the conductance
(i)
subtract
is a node above,
the conductance
and subtract
containing
hand side.
(h)
is
does not have terms
the
calculate
slice
leaving
in the
call
the
vector
the head for
submodule
results
{RES).
the current
iteration.
by the
Multiply
relaxation
factor
estimate
to get the final
of head change for
estimate
this
iteration
of head change for
this
iteration.
(b)
the
last
Add the final
iteration
head change for
to get the head for
13-21
this
this
iteration
iteration.
to the
head from
(c)
other
If
cell,
8.
store
Save the
be printed
9.
largest
Compare the
If
(ICNVG) equal
biggest
HCLOSE is
12.
If
the time
for
the
iteration
that
for
any
cell.
so that
it
can
than
(BIGG) to the
BIGG, set the
closure
convergence
criterion
flag
and you have not exceeded
the maximum
number of iterations.
interval
each iteration
13.
of the
than
RETURN.
convergence
step
location
greater
step.
head change
greater
is
to one.
number of iterations,
Print
cell
head change from this
If you have not converged
11.
this
the head change and the
at the end of the time
(HCLOSE).
10.
the head change for
failed,
specified
in this
time
or this
is the
by the user,
step.
RETURN.
13-22
last
print
time
step,
or this
is
the maximum head change
8
Flow Chart
for
Module SORlAP
A is a compressed coefficient
matrix for a slice.
It
contains
the main diagonal
of the full
matrix and the
NLAY diagonals
below it.
(NLAY is the number of layers.)
Sequence Number is a number used
to identify
the internal
(variable-head)
cells
in a
slice
and also the equations
for each internal
cell.
FOR
IN
RES is a vector containing
the
residuals
for a slice.
It
consists
of RHS (from the
basic finite-difference
equation)
plus all of those
terms which are moved to the
right
hand side to get the
equations
ready for solution
in residual
form.
First
estimates
of head change:
these are the head changes
calculated
by simultaneously
solving
the equations
for a
They will
be multislice.
plied by the relaxation
factor
to get final
estimates
of head change.
Final estimates
of head change:
these are the head changes
calculated
by multiplying
first
estimates
by the
relaxation
factor.
They are
added to the heads from the
previous
iteration
to get
head for the current
iteration.
ICNVG is the convergence flag.
It is set in the approximator
and returned
to the MAIN
Program so that the iteration
loop can be terminated.
13-23
SUBROUTINE SORlAP(HNEW, IBOUND,CRrCC,CVr HCOF, RHS, A, RES, IEQPNT,
HDCG,LRCH,KITER,HCLOSE,ACCL,ICNVG,KSTP,KPER,
1
2
IPRSOR,MXITERINSTPINCOL,NROW,NLAYINSLICE,M~W,IOUT)
-----VERSION
0936 09MAY1983 SORlAP
***************************************************~**************
SOLUTION
BY SLICE-SUCCESSIVE
OVERRELAXATION -- 1 ITERATION
*******************************************~************~~*********
:
C
C
C
SPECIFICATIONS:
---------------------------------------------------------.--------DOUBLE PRECISION
HNEW, DIFF,DP, EE, R,HCFHNWr HHCOF
C
DIMENSION HNEW(NCOL,NROW,NLAY)r IBOUND(NCOLrNROW,NLAY)r
CR(NCOL,NROW,NLAY)r
CC(NCOLrNRCW,NLAY)r
CV(NCOLrNROW,NLAY)r
HCOF(NCOLrNROW,NLAY)r
RHS(NCOLrNROW,NLAY)r
HDCGtMXITER),
LRCH(~~MXITER)~A~J~BW,NSLICE)~RES(NSLICE),
3’
IEQPNT(NLAY,NCOL)
--------------------------------------------------------~---------
1
1
C
C
# OF ELEMENTS IN COMPRESSED MATRIX A
Cl ------CALCULATE
Cl--INITIALIZE FIELDS TO SAVE LARGEST HEAD CHANGE.
NA=MBW*NSLICE
BIG=O.
ABSBIG=O.
IB=O
JB=O
AND
KB=O
C
c2---
C
PROCESS EACH SLICE
DO 500 I=lrNROW
Q------CLEAR
A
DO 110 J=lrNSLICE
DO 110 K=l,MBW
110 A(K,J)=O.
E4------ASSIGN
A SEQUENCE # TO EACH VARIABLE HEAD CELL.
NEQT=O
DO 200 J=l,NCOL
DO 200 K=l,NLAY
IEQPNT(K,J)=O
IF(IBOUND(J,I,K) .LE.O) GO TO 200
NEQT=NEQT+ 1
IEQPNT(K,J)=NEQT
200 CONTINUE
C
c5------FOR
EACH CELL LOAD MATRIX A AND VECTOR RES
DO 300 J=lrNCOL
DO 300 K=lrNLAY
&A -----IF
SEQUENCE #
NEQ=IEQPNT(K, J)
IS 0
(CELL
IF(NEQ.EQ.0) GOTO 300
C
C5&---- INITIALIZE ACCUMULATORS
IS
EXTERNAL)
EE AND R
EE=O.
C
R=RHS(J,I,K)
13-24
GO ON TO NEXT CELL
clj(-+---
IF NODE TO LEFT SUBTRACT TERMS FROM EE AND R
IF(J.EQ.l)
GO TO 120
DP=CR(J-lrI,K)
R=R-DP*HNEW(J-1rIrK)
EE=EE-DP
C
C5D-w-n IF NODE TO RIGHT SUBTRACT TERMS FROM EE 8 R, MOVE COND TO A
120 IF(J.EQ.NCOL)
GO TO 125
SF’=CR(J,I,K)
DP= SP
R=R-DP*HNEW(J+lrIrK)
EE=EE-DP
NXT=IEQPNT(K,J+l)
IF(NXT.GT.0)
A(l+NXT-NEQ,NEQ)=SP
C
ME--IF NODE TO REAR SUBTRACT TERMS FROM EE AND R
125 IF(I.EQ.l)
GO TO 130
DP=CC(J,I-1rK)
gR;y;HpNEW’J,I-1rK)
= C
pj F---IF NODE TO FRONT SUBTRACT TERMS FROM EE AND R
130 IF(I.EQ.NROW)
GO TO 132
DP=CC(J,I,K)
;;R;$P;HpNEW(J,I+lrK)
= .
C
IF NODE ABOVE SUBTRACT TERMS FROM EE AND R
CSG---132 IF(K.EQ.l)
GO TO 134
DP=CV(J,I,K-1)
R-R-DP*HNEW(JrI,K-1)
EE=EE-DP
C
C5 H----s IF NODE BELOW SUBTRACT TERMS FROM EE 8 R AND MOVE CDND TO A
134 IF(K.EQ.NLAY)
GO TO 136
SF=CV(J,I,K)
DP=SP
R=R-DP*HNEW(JrIrK+l)
EE=EE-DP
IF(IEQPNT(K+lrJ).GT.O)
A(2rNEQ)=SP
-----MOVE
EE INTO A, SUBTRACT EE TIMS
136 HHCOF=HCOF(J,I,K)
A(l,NEQ)=EE+HHCQF
HNW=HNEW(JrIrK)
HCFHNW=HNW*HCOF(J, 1,Kl
RES(NEQ)=R-EE*HNEW(J,I,KbHCFHNW
300 CONTINUE
LAST HEAD FROM R TO GET RES
NO EQUATIONS GO TO NEXT SLICE, IF ONE EQUATION SOLVE
is6 ------IF
IF 2 EQUATIONS CALL SSORlB TO SOLVE FOR FIRST
c6 ------DIRECTLY,
(3j--ESTIMATE OF HEAD CHANGE FOR THIS ITERATION.
IF(NEQT.LT.l)
GO TO 500
C
C7------
IF(NEQT.EQ.l)
RES(l)=RES(l)/A(lrl)
IF(NEQT.GE.2)
CALL SSORlB(A,RES,NEQT,NA,MBW)
FOR EACH CELL IN SLICE CALCULATE FINAL
DO 400 J=lrNCOL
DO 400 K=l,NLAY
NEQ=IEQF’NT(K, J 1
IF(NEQ.EQ.0)
GO TO 400
C
13-25
HEAD CHANGE THEN HEAD.
C7A-es-- MULTIPLY FIRST ESTIMATE OF HEAD CHANGEBY RELAX FACTORTO ’
C7A----- GET FINAL ESTIMATE OF HEAD CHANGEFOR THIS ITERATION,
DH=RES(NEQ)*ACCL
DIFF=DH
C
C7&---- ADD FINAL ESTIMATE TO HEAD FROMLAST ITERATIONTO GET HEAD
c7B----- FOR THIS ITERATION.
HNEW(J,I,K)=HNEW(J,IIK)+DIFF
FINAL HEAD CHANGEIF IT IS THE LARGEST
ABSDH=ABS(DH)
IF(ABSDH.LE.ABSBIG) GO TO 400
:7c -----SAVE
ABSBIG=ABSDH
BIG=DH
IB=I
JB=J
KB=K
400 CONTINUE
:
500 CONTINUE"
Ei3------SAVE LARGEST HEAD CHANGEFOR THIS ITERATION
HDCG(KITER)=BIG
LRCH(lrKITER)=KB
LRCH(i?rKITER)=IB
LRCH(3rKITER)=JB
k ------IF LARGEST HEAD CHANGEIS SMALLER THAN CLOSURETHEN SET
c9 ------CONVERGE FLAG (ICNVG) EQUAL TO 1.
ICNVGO
IF(ABSBIG.LE.HCLOSE) ICNVGl
C
ClO----- IF NOT CONVERGEDAND NOT EXCEDEDITERATIONS THEN RETURN
IF(ICNVG.EQ.0
IF(KSTP.EQ.l)
600 FORMATt1HO)
.AND.
KITER.NE.MXITER)
WRITE(IOUT,6001
RETURN
C
Cll---
PRINT NU1YBEROF ITERATIONS
WRITE(IOUT,601)KITER,KSTP,KPER
601 FORMAT(lX,I5,' ITERATIONSFORTIME STEP'rI4r' IN STRESSPERIOD',
1
13)
FAILED TO CONVERGEOR LAST TIME STEP OR PRINTOUT
INTERVAL SPECIFIEDBY USER IS HERE THEN PRINT MAXIMUM
HEAD CHANGESFOR EACH ITERATION.
IF(ICNVG.NE.0 .AND. KSTP.NE.NSTP .AND. MOD(KSTP,IPRSORl.NE.O)
1
GO TO 700
El2-----IF
c12--c12---
WRITE(IOUT,5)
5 FORMAT(1HOr’MAXIMUMHEAD CHANGEFOR EACH ITERATION:
'/
1
lHO,4(’
HEAD CHANGE LAYER,ROW,COL')/lX,120('-'1)
WRITE(IOUT,
(HDCG(J)r(LRCH(I,J)rI=lr3)rJ=lrKITER)
10 FORMAT((lX,4(4X,G12.4,' (',13,',',13,',',13,')I)))
WRITE(IOUT,ll)
11 FORMATtlHD)
C
Cl3 -----RETURN
700 RETURN
C
END
13-26
List
Variable
Range
A
Package
ABSDIG
ABSDH
Module
Module
ACCL
cc
Package
Global
CR
Global
cv
Global
DH
DIFF
DP
EE
HCLOSE
HCOF
Module
Module
Module
Module
Package
Global
HDCG
Package
HNEW
Global
I
IB
Module
Module
IBOUND
Global
ICNVG
Global
IEQPNT
Global
IOUT
I PRSOR
Global
Package
J
JB
Module
Module
K
KB
Module
Module
KITER
Global
KPER
Global
of Variables
for
Module SORlAP
Definition
DIMENSION (MBW,NSLICE), Compressed coefficient
matrix
for a slice.
Largest ABSDH for this iteration.
Absolute
value of head change in a cell for the current
iteration.
Acceleration
parameter.
DIMENSION (NCOL,NROW,NLAY), Conductance in the column
CC(J,I,K) contains conductance between
direction.
nodes (J,I,K)
and (J,I+~,K).
DIMENSION (NCOL,NROW,NLAY), Conductance in the row
CR(J,I,K) contains conductance between
direction.
and (J+l,I,K).
nodes (J,I,K)
DIMENSION (NCOL,NROW,NLAY-l), Conductance in the
CV(J,I,K)
contains
conductance
vertical
direction.
and (J,I,K+l).
between nodes (J,I,K)
Change in head in a cell during one iteration.
Double-precision
change in head (DH).
Double-precision
temporary field.
Main diagonal term in the finite-difference
equation.
Closure criterion
for the iterative
procedure.
DIMENSION (NCOL,NROW,NLAY), Coefficient
of head in the
cell
(J,I,K)
in the finite-difference
equation.
DIMENSION (MXITER), Maximum head change for each
iteration.
DIMENSION (NCOL,NROW,NLAY), Most recent estimate
of
HNEWchanges at each iteration.
head in each cell.
..
Index for rows.
Row number of the cell containing
the largest
head
change.
.
DIMENSION (NCOL,NROW,NLAY), Status of each cell.
< 0, constant-head
cell
= 0, inactive
cell
> 0, variable-head
cell
Flag is set equal to one when the iteration
procedure
has converged.
DIMENSION (NLAY,NCOL), Sequence numbers for variablehead cells
in a slice.
Primary unit number for all printed
output.
IOUT = 6.
Frequency (in time steps) with which the maximum head
changes for each iteration
will
be printed.
Index for columns.
Column number of the cell containing
the largest
head
change.
Index for layers.
Layer number of the cell containing
the largest
head
change.
Reset at the start
of each time
Iteration
counter.
step.
Stress period counter.
13-27
List
Variable
of Variables
for
Module SORlAP (Continued)
Definition
Range
KSTP
Global
LRCH
Package
MBW
MXITER
NA
Package
Package
Package
NCOL
NEQ
NEQT
NLAY
NROW
NSLICE
NSTP
NXT
R
Global
Module
Package
Global
Global
Package
Global
Module
Module
RES
RHS
Package
Global
SP
Module
Reset at the start
of each stress
Time step counter.
period.
DIMENSION (MXITER), Layer, row, and column of the cell
containing
the maximum head change (HDCG) for each
iteration.
Maximum bandwidth of the coefficient
matrix +l.
Maximum number of iterations.
Number of elements in the compressed coefficient
matrix
(A).
Number of columns in the grid.
Index for equations
(variable-head
cells)
in a slice.
Number of equations
(variable-head
cells)
in a slice.
Number of layers in the grid.
Number of rows in the grid.
Number of cells
in a slice.
Number of time steps in the current
stress period.
Sequence number of the cell to the right.
Right hand side of the finite-difference
equation
as
modified
(terms for the adjacent
rows moved to the
right)
for solution
by the slice-successive
overrelaxation.
DIMENSION (NSLICE), Residual.
DIMENSION (NCOL,NROW,NLAY), Right hand side of the
finite-difference
equation.
RHS is an accumulation
of terms from several
different
packages.
Single-precision
temporary
field.
13-28
Narrative
for
Module SSORlB uses Gaussian
of the form [A]{X)={B).
"N. " It
is stored
single
the space reserved
The indices
organization.
format
index
for
(B).
vector
the
the first
Modify
inverse
to aT,T which
matrix
as it
is calculated,
are those
index.
rank
55 and uses a
is stored
for
used in the program
in
standard
matrix
are based on the
Module SSORlB performs
N-l rows using
each one,
of the main diagonal
its
functions
in sequence,
as
are indexed
element---aT,T.
(The
element
of column
I in the
row I so that
the terms
corresponding
is the first
each of the
rows after
are eliminated.
MBW-1 equations
Since the
by 'IL."
coefficient
matrix
is
banded,
(where MBW is the maximum half-bandwidth
one) where the term to be eliminated
equation
and banded with
shown in figure
chart
equation
[A].)
term
are only
4.
is symmetric
format
actually
a matrix
order:
Calculate
to the pivot
equation
to solve
row (row I).
compressed
there
{X),
and a single
(ID) points
3.
The vector
Work through
the pivot
2.
[A]
used in the module flow
in the following
1.
The matrix
The indices
compressed
elimination
in the compressed
subscript.
Module SSORlBs
(The equation
is not already
corresponding
equal
to zero.
to row "L"
is
plus
The rows
referred
to as
"L.")
Calculate
the coefficient
and subtracted
C which when multiplied
from equation
13-29
L will
eliminate
by the pivot
a term
in equation
L.
(The index
IB points
of symmetry,
5.
is equal
Calculate
to the
right
matrix
is banded,
pivot.
Therefore,
6.
7.
side
which
for
to the coefficient
of the coefficient
there
at most,
C times
Subtract
L.
is being
MBW-1 coefficients
the
right
(The index
L for
because
each of the terms
eliminated.
MBW-1 nontero
terms
Because the
to the
right
of the
have to be calculated.
in the
in equation
which,
to be eliminated.)
a coefficient
C times
equation
in equation
that
are only
coefficient
of equation
in the pivot
the new coefficients
Subtract
corresponding
to a coefficient
pivot
equation
from the
L.
side
LB points
of the
pivot
to the
equation
coefficient
from the
in equation
right
L
must be calculated.)
8.
Solve
equation
9.
Work backward
N for
X(N) putting
from equation
N-l
the
result
solving
in B(N).
each equation
(equation
X(L).
10.
Set the
11.
Multiply
equation
accumulator
"SUM" equal
the coefficient
L) by the
corresponding
12.
Calculate
the
13.
RETURN.
value
to zero.
to the
value
of X(L)
right
of the main diagonal
of X and add it
and store
13-30
it
to the
in B(L).
sum.
(in
L)
Flow Chart
for
Module SSORlB
MBW is the maximum half bandwidth
of the coefficient
matrix plus one.
FOR EACH ROW I
(I=l... , N-l)
CALCULATE Cl, THE
INVERSE OF THE PIVOT
Cl+$j
-----A
FOR EACH ROW J
3
(J=l.. ., MEW-l)
4
CALCULATE
C=al,l+J’Cl
FOR E&ZH
COLUMN I+K
K=J...., MBW-1
I
SUBTRACT C’B(I)
FROM B(I+J)
L
+
FOR EACH EQUATION
L
8
9
(L=N-1, N-2,..., 1)
10
I
CLEAR THE
ACCUMULATOR
I
ADD_ZH_E TERM
aLIL+J?~aTO SUM
I
h
FOR EACH TERM L+J’
J=l I..., MBW-1
CALCULATE
X(L)=(B(L)SUM)/A(L.L)
13-31
SUBROUTINE SSORlBt A, B, N, NA,MBW)
C
C
C-----VERSION 1359 31MAR1983 SSORlB
******************************************************************
C
C
SOLVE A SYMMETRIC SET OF EQUATIONS
C
A IS COEFFICIENTMATRIXIN COMPRESSEDFORM
C
B IS RIGHTHAND SIDE AND IS REPLACED BY SOLUTION
C
N IS NUMBEROF EQUATIONS
TO BE SOLVED
C
MBWIS BANDWIDTH OF A
C
NA IS ONE-DIMENSION
SIZE OF A
******+***********************************************************
C
C
C
C
SPECIFICATIONS:
-----------------------------------------------------------------DIMENSIONA(NA)rB(N)
------------------------------------------------------------------
C
C
NMl=N-1
MBWl=MBW-1
ID=l-M5W
C
Cl---
SEQUENTIALLY USE EACH OF THE FIRST N-l
Cl ------THE
PIVOT ROW.
ROWSAS
DO20 I=lrNMl
C
C2------CALCULATE THE INVERSEOF THE PIVOT.
ID=IDtMBW
Cl=l./A(ID)
LD=ID
L=I
:3 ------FOR
EACH ROWAFTER THE PIVOT ROW (THE TARGET ROW)
C3------ ELIMINATE THE COLUMNCORRESPONDING
TO THE PIVOT.
Do 15 J=lrMBWl
L=L+l
1FtL.GT.N)
GO TO 20
IB=ID+J
C
THE FACTOR NEEDED TO
------CALCULATE
Y4------TARGET
ROW.
@A(IB)*Cl
LD=LD+MBW
13-32
ELIMINATEA TERM IN THE
l
LB=LD-1
L
C5------ MODIFYTHE REST OF THE TERMS IN THE TARGET ROW.
DO 10 K=J,b8Wl
C
C&---SUBTRACT THE FACTOR TIMES A TERM IN THE PIVOT ROW
(3j-w--w
FROM THE CORRESPONDINGCOLUMNIN THE TARGET ROW.
LB=LB+1
A(LB)=A(LB)-C*A(IDtK)
10 CONTINUE
:7 ------MODIFY THE RIGHT SIDE OF THE EQUATIONCORRESPONDING
C7------ TO THE TARGETROW.
B(I+J)=B(ItJ)-C*B(I)
15 CONTINUE
20 CONTINUE
ID=IDtMBW
n
&------SOLVE
THE LAST
EQUATION.
B(N)=B(N)/A(ID)
------WORKING
BACKWARDSSOLVE THE REST OF THE
EQUATIONS.
DO70 I=lrNMl
ID=ID-MBW
C
Cl(-j---
C
Cll---
C
CLEAR THE ACCUMULATORSUM.
suM=o.o
L=N-I
MBWlM=MINO(MBWl,I)
ADD THE KNOWNTERMS IN EQUATION L TO SUM.
DO 60 J=l,MBWlM
SUM=SUMtA(IDtJ)*B(L+J)
60 CONTINUE
cyJ---
SOLVEFORTHE ONEUNKNOWN
IN EQUATIONL.
B(L)=(B(L)-SUM)/A(ID)
70 CONTINUE
C
C13-----RETURN
RETURN
END
13-33
List
Variable
of Variables
for
Module SSORlB
Definition
Range
A
Package
DIMENSION (MBW,NSLICE),
for a slice.
B
Package
DIMENSION (N),
C
Module
Factor
Cl
Module
Inverse of pivot.
I
Module
Index
IB
Module
Index for elements
ID
Module
Index of pivots.
J
Module
Index
for
columns.
K
Module
Index
for
columns.
L
Module
Index for equations.
LB
Module
Index for elements
the
Compressed
Right-hand-side
needed to eliminate
for
rows in the
matrix
vector.
a term
in the target
SSOR matrix
to the
coefficient
right
(not
of the
in the target
row.
the grid).
pivot.
row to the
right
of
main diagonal.
LD
Module
Index of the main diagonal
MBW
Package
Maximum bandwidth
of the
coefficient
matrix
MBWl
Module
Maximum bandwidth
of the
coefficient
matrix.
MBWlM
Module
Maximum possible
number of the nonzero
the right of the main diagonal.
N
Package
Number of equations
NA
Package
One-dimension
NM1
Module
N-l.
SUM
Module
In back substitution--in
equation
the right
of the main diagonal
size
13-34
elements
in the target
rows.
+l.
elements
to
to be solved.
of compressed
matrix
"A."
L, sum of terms
term (L,L).
to
CHAPTER 14
UTILITY
Utility
to several
modules
different
of a "U" followed
are those
packages.
MODULES
submodules
which
perform
The name of a utility
by a five-character
mnemonic.
general
tasks
module always
There are eight
common
consists
utility
modules:
UBUDSV
Writes an unformatted
record consisting
of
an array with one real number for each cell
in the grid.
ULASAV
Writes an unformatted
record consisting
of
an array with one real number for each cell
in a layer.
ULAPRS
and
ULAPRW
Prints one two-dimensional
array which contains
one real number for each cell in a layer.
ULAPRS prints,
in strip
form, the first
N columns
(where N is the number of values that can fit
on
one print
line)
of each row and then the next N
columns, etc.,
until
all columns of each row are
printed
(fig.
56).
ULAPRWprints,
in wrap form,
all of row 1, all of row 2, and all of row 3, etc.
The format for printing
arrays is shown in table 2.
UCOLNO
Prints column numbers at the top of each page
of data printed
by ULAPRS and ULAPRW.
UZDREL
Reads a two-dimensional
array
of real
U2DINT
Reads a two-dimensional
array
of integers.
UlDREL
Reads a one-dimensional
array
of real
14-1
numbers.
numbers.
1:
122
13”
14”
155
16
6
177
8
9
10
1
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
2
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
3
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
4
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
5
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
6
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
7
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
WRAP FORM
1
2
3
4
5
6
7
8
9
10
1
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
2
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
3
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
4
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
5
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
6
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
7
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
11
12
13
14
15
16
17
1
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
2
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
3
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
4
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
5
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
6
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
7
1325.79 1325.79 1325.79 1325.79 1325.79 1325.79 1325.79
STRIP FORM
Figure 56.~Illustration
of wrap and strip forms of printed
for a layer containing 7 rows and 17 columns.
14-2
output
l
codes for
2 .--Print-format
ULAPRS and ULAPRW.
Table
utility
modules
IPRN
FORMAT
1
11610.3
2
9613.6
3
15F7.1
4
15F7.2
5
15F7.3
6
15F7.4
7
2OF5.0
8
20F5.1
9
20F5.2
10
20F5.3
11
20F5.4
12
10611.4
14-3
Input
Instructions
For Array
Reading
Utility
Modules
The real two-dimensiohal
array reader (UZDREL), t&&integer
two-dimensional
array reader (U2DINT), and the real one-dimensional
array
reader (UlDREL) read one array-control
record and, optionally,
a data
array in a format specified
on the array-control
record.
The control
record is read from the input unit number specified
for the major option
For example, the Recharge Package uses
that is requesting
the array.
The input unit for the recharge option is
U2DREL to read the RECH array.'
contained
in IUNIT (8), and accordingly,
the RECH array control
record is
read on this input unit.
FDR REAL ARRAY READER (U2DREL or UlDREL)
Data:
Format:
LOCAT
CNSTNT
FMTIN
IPRN
110
F10.0
5A4
110
FMTIN
5A4
IPRN
110
FOR INTEGERARRAYREADER(U2DINT)
Data:
Format:
LOCAT
ICONST
110
110
Explanation
of Fields
Used in
Input Instructions
LOCAT--indicates
If
the
location
of the data which
LOCAT < 0, the sign is reversed
which an unformatted
will
be put
to give the
record will
If LOCAT = 0, every element in the array will
value CNSTNT/ICONST.
in the array.
unit number from
be read.
be set
equal
to the
If LOCAT > 0, it is the unit
read in the
array-control
CNSTNT/ICONST--is a constant.
number from which data values will
be
format specified
in the third
field
of the
record (FMTIN).
Its use depends on the value of LOCAT.
If LOCAT = 0, every element
in the
array
is
set equal
to
CNSTNT/ICONST.
If LOCAT f 0, and if CNSTNT/ICONST
f 0, every element in the
array is multiplied
by CNSTNT/ICONST.
FMTIN--is the format of records containing
the array values.
It is used
only if the first
field
in the array-control
record (LOCAT) contains
The format must be enclosed in parentheses;
for
a positive
number.
example, (15F5.0) for real data and (1515) for integer
data.
14-4
IPRN--is
a flag indicating
that the array being read should be printed
and
a code for indicating
the format that should be used.
It is used only
if LOCAT is not equal to zero.
The format codes are different
for each
of the three modules.
IPRN is set to zero when the specified
value
exceeds those defined
in the chart below.
If IPRN is less than zero,
the array will
not be printed.
IPRN
UZDREL
U2DINT
UlDREL
10612.5
0
10611.4
10111
1
11610.3
6011
2
9613.6
4012
3
15F7.1
3013
4
15F7.2
2514
5
15F7.3
2015
6
15F7.4
7
2OF5.0
8
20F5.1
9
20F5.2
10
20F5.3
11
20F5.4
12
10611.4
14-5
Narrative
Utility
dimensioned
module UBUDSV writes
(NCOL, NROW, NLAY).
by an unformatted
information
consists
record
Module UBUDSV
an unformatted
The record
containing
record
containing
identifying
consisting
the
array
information.
of an array
is
preceded
The identifying
of:
KSTP
current
time
KPER
current
stress
TEXT
label
character
NCOL
number of columns
integer
1 word
NROW
number of rows
integer
1 word
NLAY
number of layers
integer
1 word
Documentation
a list
for
of this
step
period
module consists
of variables.
14-6
only
integer
1 word
integer
1 word
string
of comments in the
4 words
program
and
l
BUFF, NCOL,NROW,NLAY, IOUT)
SUBROUTINE UBUDSV(KSTP, KPER, TEXT, IBDCHN,
C
C
C-----VERSION
1637 12MAY1987 UBUDSV
************************************************~*****************
RECORDCELL-BY-CELL FLOW TERMS FOR ONE COMPONENTOF FLOW.
****~************************************************************~
C
C
C
SPECIFICATIONS:
--------------_---------------------------------------------------
:
C
CHARACTER*4 TEXT
DIMENSION TEXT(4) rBUFF(NCOL, NROW,NLAY)
-----_---c_-------------------------------------------------------
C
C
Cl ------WRITE AN UNFORMATTEDRECORDCONTAINING
IDENTIFYING
Cl---
C
INFORMATION.
1) TEXT, IBDCHN,
KSTP,KPER
WRITEtIOUT,
1 FORMAT(lX,‘“‘,4A4,‘”
BUDGET VALUES WILL BE SAVED ON UNIT',I3,
1
' AT END OF TIME STEP',I3,', STRESS PERIOD',131
C
c2---(-&L--c2---
C
C3------
WRITE(IBDCHN)KSTP, KPER, TEXT, NCOL,NROW,NLAY
WRITE AN UNFORMATTEDRECORDCONTAINING
VALUES FOR
EACH CELL IN THEGRID. THE ARRAY IS DIMENSIONED
(NCOL,NROW,NLAY)
WRITE(IBDCHN)BUFF
RETURN
RETURN
END
14-7
List
Variation
of Variables
for
Module UBUDSV
Definition
Range
BUFF
Global
DIMENSION (NCOL,NROW,NLAY), Buffer used to accumulate
information
before printing
or recording
it.
IBDCHN
Module
Unit
IOUT
Global
Primary
KPER
Global
Stress
KSTP
Global
Time step
period.
NCOL
Global
Number of columns
NLAY
Global
Number of layers
NROW
Global
Number of rows in the
TEXT
Module
Label
number on which
the array
unit
number for
period
counter.
all
will
printed
Reset at the
counter.
in the
in the
to be printed
14-8
be recorded.
output;
start
IOUT = 6.
of each stress
grid.
grid.
grid.
or recorded
with
the array
data.
Narrative
Utility
array
module ULASAV writes
dimensioned
by an unformatted
information
for
consists
(NCOL, NROW).
record
Module ULASAV
an unformatted
The record
containing
record
containing
identifying
consisting
the
information.
array
of an
is preceded
The identifying
of:
integer
1 word
integer
1 word
elapsed time in the
current
stress
period
real
1 word
TOTIM
elapsed time
simulation
real
1 word
TEXT
label
character
NCOL
number of columns
integer
1 word
NROW
number of rows
integer
1 word
ILAY
layer
integer
1 word
KSTP
current
time
KPER
current
stress
PERTIM
step
period
in the
number
14-9
string
4 words
SUBROUTINE ULASAV( BUF, TEXT, KSTP, KPER, PERTIM, TOTIM,
NCOL,
NROW,ILAY,ICHN)
1
C
C-----VERSION
C
C
C
C
C
C
C
C
Cl----
Cl--C
c2--c2----
C
1642 12MAY1987
ULASAV
***t**************************************************************
SAVE 1 LAYER ARRAY ON DISK
******************************************************************
SPECIFICATIONS:
-----------------------------------------------------------------CHARACTER*4 TEXT
DIMENSION
BUF(NCOL,NROW)rTEXT(4)
------------------------------------------------------------------
WRITEAN UNFORMATTEDRECORDCONTAINING
IDENTIFYING
INFORMATION.
WRITEt
ICHN) KSTP,KPER, PERTIM,TOTIM,TEXT,
NCOL,NROW,ILAY
WRITE AN UNFORMATTEDRECORDCONTAINING
ARRAY
VALUES
THE ARRAY IS DIMENSIONED (NCOL,NROW)
WRITEtICHN)((BUF(IC,IR)rIC=lrNCOL),IR=lrNROW)
C3------RETURN
RETURN
END
14-10
l
List
Variable
l
of Variables
for
Module ULASAV
Definition
Range
BUF
Module
Buffer
containing
IC
Module
Index
ICHN
Module
Unit
I LAY
Module
Layer
number.
IR
Module
Index
for
KPER
Global
Stress
KSTP
Global
Time step
period.
NCOL
Global
Number of columns
NROW
Global
Number of rows in the
PERTIM
Package
Elapsed
TEXT
Module
Label
TOTIM
Package
Elapsed
for
data to be printed
or recorded.
columns.
number on which
the array
is to be recorded.
rows.
period
counter.
counter.
time
during
to be printed
time
Reset at the
in the
of each stress
grid.
grid.
the
current
or recorded
in the simulation.
14-11
start
stress
with
period.
the array
data.
Narrative
Module ULAPRS prints
using
one of twelve
the following
set
it
equal
2.
Use the
Calculate
and the
format
If
code (IP).
form
its
(fig.
56)
tasks
in
it
is less
than
1 or greater
than
12,
default).
format
code (IP)
the
to determine
number of spaces
Initialize
(NSTRIP).
last
column
Loop through
5.
Calculate
6.
Print
7.
Call
8.
Loop through
9.
in strip
Module ULAPRS performs
FORTRAN formats.
4.
appropriate
array
the
number of values
(NCAP)
on one line.
number of strips
(Jl)
a two-dimensional
to 12 (the
to be printed
3.
Module ULAPRS
order:
Get the
1.
for
(52)
the
the
first
a title
for
strips
(Jl)
the
each value
fields
(NCPF) and the
to store
the
column for
this
first
column
each strip.
(DO STEPS 5-8).
and last
(52)
strip.
on each strip.
module UCOLNOto print
format
used for
the
rows printing
the
column numbers above each strip.
columns
(IP).
RETURN.
14-12
Jl
through
52 using
the
Flow Chart
for
Module ULAPRS
(x-y)
IPRN is a code indicating
the
format to be used in printing
array values.
If it is not
between 1 and 12, it is set
equal to 12.
GET THE FORMAT
CODE - - - IPRN
I
DETERMINE THE
NUMBER OF VALUES
TO BE PRINTED IN
ONE LINE
I
CALCULATE THE
NUMBER OF STRIPS
NEEDED
I
FOR EACH STRIP
4
CALCULATE THE
FIRST AND LAST
COLUMN FOR THIS
6
I
PRINT A TITLE
AT THE TOP OF
THE STRIP
,
I
PRINT THE VALUES IN
THE ROW THAT BELONG
IN THIS STRIP ACCORDING
TO THE FOsRyh;lpARTSPECIFIED
I’
14-13
SUBROUTINE ULAPRStBUF,TEXT,KSTP,KPER, NCOL,NROW,ILAY, IPRN, IOUT)
C
1640 12MAY1987 ULAPRS
: -----VERSION
******************************************************************
C
PRINT A 1 LAYER ARRAY IN STRIPS
******************************************************************
:
C
SPECIFICATIONS:
C
-----------------------------------------------------------------C
CHARACTER*4 TEXT
DIMENSIONBUF(NCOLrNR@iW)
rTEXT(4)
-----------------------------------------------------------------:
Cl---MAKE SURE THE FORMATCODE (IP OR IPRN) IS BETWEEN1
Cl------AND
12.
C
c2---
C
C3------
IP=IPRN
IF(IP.LT.l
.OR. IP.GT.12) IP=12
DETERMINE THE NUb8ER OF VALUES (NCAP) PRINTED ON ONE LINE.
IF(IP.EQ.l) NCAP=ll
IF(IP.EQ.2) NCAP=9
IF(IP.GT.2 .AND. IP.LT.7) NCAP=lS
IF(IP.GT.6 .AND. IP.LT.12) NCAP=20
IF(IP.EQ.12) NCAP=lO
CALCULATE ME NUMBEROF STRIPS(NSTRIP).
NCPF=129/NCAP
ISP=O
IF(NCAP.GT.12)
ISP=3
NSTRIP=(NCOL-l)/NCAP + 1
Jl=l-NCAP
J2=0
C
THE STRIPS.
c-4------LOOP THROUGH
DO 2000 N=lr NSTRIP
:5 ------CALCULATE
THE FIRST(J1)
8 THE LAST(J2)
Jl=Jl+NCAP
J2=JZ+NCAP
IF(J2.GT.NCOL) J2=NCOL
COLUMNSFOR THIS STRIP
ii5-------PRINT TITLE ON EACH STRIP
WRITE(IOUT,l) TEXT,ILAY,KSTP,KPER
1 FORMAT(lHlrlOX,4A4,' IN LAYER’rI3,’
AT END OF TIME STEP’rI3,
1
' IN STRESS PERIOD'rI3/11Xr71('-'1)
C
c7 ------PRINT COLUMNNUMBERSABOVE THE STRIP
CALL UCOLNO(Jl,J2rISP,NCAPINCPFIIOUT)
C
C&-aLOOP THROUGHTHE ROWSPRINTING COLS Jl THRU 52 WITH FORMAT IP
DO 1000 I=lrNROW
GOT0(10,20,30,40,50,60r70r80r90r10011101120~, IP
C
10610.3
C------------FORMAT
10 WRITE(IOUT,ll) I,(BUF(J,I),J=Jl,J2)
11 FORMAT(1HO,I3r2X,1PGlO.3,lO~lX,GlO.3))
GO TO 1000
C
C------------FORMAT
8613.6
14-14
20 WRITE(IOUT,El) I,(BUF(J,I)rJ=JlrJ2)
21 FORMAT(1HO,I3r2X,1PG13.6,8~lX,Gl3.61~
GO TO 1000
~------------FORMAT
15F7.1
30 WRITE(IOUT,31) I,(BUF(J,I)rJ=JlrJ2)
31 FORMAT(1HO,I3,lX,15(lX,F7.1))
GO TO 1000
C
C------------FORMAT
15F7.2
I,(BUF(J,I)rJ=JlrJ2)
41 FORMAT(lHO,I3,lX,15(lX,F7.2))
GO TO 1000
40 WRITE(IOUT,41)
C
15F7.3
C------------FORMAT
50 WRITE(IOUT,Sl) I,(BUF(J,I)rJ=JlrJ2)
51 FORMAT(1HO,I3rlX,15(lX,F7.3))
GO TO 1000
n
L----------FORMAT
15F7.4
60 WRITE(IOUT,61) I,(BUF(J,I)rJ=JlrJ2)
61 FORMAT(1HO,I3rlX,15(lX,F7.4))
GOTO 1000
C
2OF5.0
C------------FORMAT
70 WRITE(IOUT,71) I,(BUF(J,I)rJ=JlrJ2)
71 FORMAT(1HO,I3rlX,20(lX,F5.0))
GO TO 1000
C
20F5.1
C------------FORMAT
80 WRITE(IOUT,81) I,(BUF(J,I),J=JlrJ2)
81 FORMAT(1HO,I3rlX,20(lX,F5.l))
GO TO 1000
C------------FORMAT
20F5.2
90 WRITE(IOUT,91) I,(BUF(J,I)rJ=JlrJ2)
91 FORMAT(1HO,I3rlX,20(lX,F5.2))
GOTO 1000
~------------FORMAT
20~5.3
100 WRITE(IOUT,lOl)
I,(BUF(J,I)rJ=JlrJ2)
101 FORMAT(1HOrI3rlX,20(1X,F5.3))
GO TO 1000
L-----------FORMAT
20~5.4
110 WRITE(IOUT,lll) I,(BUF(J,I)rJ=JlrJ2)
111 FORMAT(1HO,I3rlX,20(lX,F5.4))
GO TO 1000
C
9611.4
C------------FORMAT
120 WRITE(IOUT,121) I,(BUF(J,I)rJ=JlrJ2)
121 FORMAT(1HO,I3r2X,1PGll.4r9(1XIG11.4))
C
1000 CONTINUE
2000 CONTINUE
C
c9------RETURN
RETURN
END
14-15
List
Variable
of Variables
for
Module ULAPRS
Definition
Range
BUF
Module
Buffer
containing
I
Module
Index
for
ILAY
Module
Layer
number.
IPUT
Global
Primary
unit
IP
Module
Format
code.
IPRN
Module
Code for
to be printed
ISP
Module
Number of spaces.
J
Module
Index
for
Jl
Module
First
column
52
Module
Last
KPER
Global
Stress
KSTP
Global
Time step
period.
counter.
N
Module
Index
strips.
NCAP
Module
Number of columns
on a line.
NCOL
Global
Number of columns
in the
NCPF
Module
Number of columns
per field.
NROW
Global
Number of rows in the
NSTRIP
Module
Number of strips.
TEXT
Module
Label
or recorded.
rows.
the
number for
format
all
printed
output.
to be used when printing
IOUT = 6.
arrays.
columns.
column
period
for
data
in a strip.
in a strip.
counter.
Reset at the
to be printed
14-16
start
of each stress
grid.
grid.
or recorded
with
the array
data.
Narrative
Module ULAPRW prints
using
the
than
one of twelve
following
2.
Set the
in wrap form
Module ULAPRW performs
its
(fig.
56)
tasks
in
it
a header.
equal
format
Call
4.
Loop through
If
code (IP).
to 12 (the
3.
5.
array
order:
Print
the appropriate
Module ULAPRW
a two-dimensional
FORTRAN formats.
1.
12, set
for
format
is less
than
1 or greater
default).
the module UCOLNOto print
the
it
rows printing
code.
RETURN.
14-17
column numbers.
each one in its
entirety
using
Flow Chart
for
Module ULAPRW
IPRN is a code indicating
the
format to be used in printing
If it is not
array values.
between 1 and 12, it is set
equal to 12.
CODE - - IPRN
PRINT COLUMN
FOR EACH ROW
PRINT THE
ARRAY VALUES
ACCORDING
TO
FORMAT IPRN
14-18
SUBROUTINE ULAPRW(BUF,TEXT, KSTP, KPER, NCOL,NROW,ILAY, IPRN,
IOUT)
C
C
C-----VERSION
C
C
C
C
C
1642 12MAY1987ULAPRW
****************************~**********~***********~**************
PRINT 1 LAYER ARRAY
******************************************************************
SPECIFICATIONS:
”
C
CHARACTER*4 TEXT
DIMENSIONBUF(NCOL,NRCW)rTEXT(4)
-----------_------------------------------------------------------
h------PRINT
A HEADER
IF(ILAY.LE.0)
GO TO 5
WRITE(IOUT,l) TEXT,ILAY,KSTP,KPER
1 FORMAT(lHl,lOX,4A4,' IN LAYER',I3,' AT END OF TIME STEP',I3,
1
' IN STRESS PERIOD',I3/llX,71('-'1)
C
C2---- MAKE SURE THE FORMATCODE (IP OR IPRN) IS
C2---- BETWEEN1 AND 12.
5 IP=IPRN
IF(IP.LT.l
.OR. IP.GT.12) IF'=12
THE UTILITY MODULEUCOLNOTO PRINT COLUMNNUMBERS.
IF(IP.EQ.l) CALL UCOLNO(lrNCOL,O,llrll,IOUT)
IF(IP.EQ.2) CALL UCOLNO(1,NCOL,O,9,14rIOUT)
IF(IP.GT.2 .AND. IP.LT.7) CALL UCOLNO(lrNCOL,3,15r8rIOUT)
IF(IP.GT.6 .AND. IP.LT.12) CALL UCOLN0(1,NCOL,3,20,6,10UT)
IF(IP.EQ.12) CALL UCOLNO(lrNCOL,O,10,12rIOUT)
:3 ------CALL
E4------LOOP THROUGHTHE ROWSPRINTINGEACH ONEIN ITS ENTIRETY.
DO 1000 I=lrNROW
GO T0(10,20,30,40,50,60,70,80,90,100,110,120~,
IP
:------------
FORMAT 11610.3
10 WRITE(IOUT,ll) I,(BUF(J,I)rJ=l,NCCL)
11 FORMAT~1HO,I3r2X,1PGlO.3,lO~lX,GlO.3~/~5X,ll~lX,GlO.3~~~
GO TO 1000
:------------
FORMAT9613.6
20 WRITE(IOUT,21) I,(BUF(J,I),J=l,NCOL)
21 FORMAT~1HO,I3,2X,1ffi13.6,8~1X,Gl3.6~/~5X,9~lX,Gl3.6~~~
GO TO 1000
C
C-----------FORMAT 15F7.1
30 WRITE(IOUT,31) I,(BUF(J,I)rJ=l,NCOL)
31 F0RMAT(1H0,13,1X,15(1X,F7.1)/0X,15~1X,F7.1~~~
GO TO 1000
14-19
C
C-----------FORMAT 15F7.2
40 WRITE(IOUT,41) I,(BUF(J,I)rJ=l,NCOL)
41 FORMAT(1HO,I3,1X,15(lX,F7.2)/(5X,l5~lX,F7.2~~~
GO TO 1000
C------------
FORMAT 15F7.3
50 WRITE(IOUT,Sl) I,(BUF(J,I),J=lrNCOL)
51 FORMAT(1HO,I3,1X,15(lX,F7.3)/(5X,l5~lX,F7.3~~~
GO TO 1000
C
C-----------FORMAT 15F7.4
60 WRITE(IOUT,61) I,(BUF(J,I)rJ=l,NCOL)
61 FORMAT(1HO,I3rlX,15(1X,F7.4)/(5X,l5~lX,F7.4~~~
GO TO 1000
:------------
FORMAT2OF5.0
70 WRITE(IOUT,71) I,(BUF(J,I),J=lrNCOL)
71 F0RMAT(1H0,13,1X,20(1X,F5.0)/0X,20~1X,F5.0~~~
GO TO 1000
C
C-----------FORMAT 20F5.1
80 WRITE(IOUT,81) I,(BUF(J,I)rJ=lrNCOL)
81 FORMAT(1HO,I3,1X,20(lX,F5.1)/(5X,2O~lX,F5.l~~~
GO TO 1000
C------------
FORMAT 20F5.2
90 WRITE(IOUT,91) I,(BUF(J,I)rJ=lrNCOL)
91 FORMAT(1HO,I3rlX~20(lX,F5.2)/(5X,2O~lX,F5.2~~~
GO TO 1000
C
C-----------FORMAT20F5.3
100 WRITE(IOUT,lOl) I,(BUF(J,I),J=l,NCOL)
101 FORMAT(1HO,I3rlX,20(lX,F5.3)/(5X,2O~lX,F5.3~~~
GO TO 1000
C
FORMAT20F5.4
C-----------110 WRITE(IOUT,lll) I,(BUF(J,I)rJ=l,NCOL)
111 FORMAT(1HO,I3,1X,20(1X,F5.4)/(5X120(1XIF5.4~~~
GO TO 1000
:-----------FORMAT 10611.4
120 WRITE(IOUT,121) I,(BUF(J,I)rJ=l,NCOL)
121 FORMAT~1HO,I3r2X,1PGll.4r9~lX,Gll.4~/~5X,lO~lX,Gll.4~~~
C
1000 CONTINUE
C
c5------RETURN
RETURN
END
14-20
List
Variable
of Variables
for
Module ULAPRW
Definition
Range
BUF
Module
Buffer
containing
data to be printed
I
Module
Index
for
ILAY
Module
Layer
number.
IOUT
Global
Primary
unit
IP
Module
Format
code.
IPRN
Module
Code for
J
Module
Index
KPER
Global
Stress
KSTP
Global
Time step
period.
NCOL
Global
Number of columns
NROW
Global
Number of rows in the
TEXT
Module
Label
or recorded.
rows.
the
for
number for
format
all
printed
output.
to be used when printing
IOUT = 6.
arrays.
columns.
period
counter.
Reset at the start
counter.
in the
to be printed
14-21
of each stress
grid.
grid.
or recorded
with
the array
data.
Narrative
for
Module UCOLNO prints
column
It
performs
numbers are printed.
1.
Calculate
of a line
the
Module UCOLNO
numbers at the top
its
functions
number of columns
(NTOT), and the
in the
number of lines
Jl
the
line.
and print
3.
Clear
the
4.
Determine
current
line
each line
buffer
the
first
(NLBL),
the width
all
of the
and 52 which
contain
(DO STEPS 3-6).
(BF) in which
(Jl)
order:
needed to print
numbers (NWRAP). Initialize
the fields
.,
first
and last column number on each print
Build
following
to be printed
column
2.
of a page when arrays
and last
the
(52)
line
is
column
built.
number for
the
line.
5.
Put the
from
the
array
tens
digit,
column numbers in the
The indices
DG.
and hundreds
6.
Print
the
7.
Print
a line
8.
RETURN.
digit,
line
buffer.
11, 12, and I3 point
respectively.
line.
of dots.
14-22
They are selected
to the
units
digit,
of
Flow Chart
for
Module UCOLNO
CALCULATE THE
NUMBER OF LINES
NEEDED TO PRINT
ALL O;J;tiEC;LUMN
F(
CLEAR THE BUFFER
IN WHICH THE LINE
IS ASSEMBLED
DETERMINE THE RANGE
OF COLUMN NUMBERS
WHICH GO IN THE LINE
THE CONTENTS
OF THE BUFFER
14-23
SUBRWTINE
lJCOLNO(NLBL1,NLBL2,NSPACEtNCPLrNDIGtIOUT)
-VERSION 1638 12MAY1987 UCOLNO
***********~**C****************************~~******~**************
OUTPUT COLUMN NlJmERS ABOVE A MATRIX PRINTOUT
NLBLl IS THE START COLUMN LABEL (NlJb8ER)
NLBLZ IS THE STOP COLUMN LABEL (NlJb8ER)
NSPACE IS NUMBER OF BLANK SPACES TO LEAVE AT START OF LINE
NCPL IS NlJb8ER OF COLUMN NUb8ERS PER LINE
NDIG IS NUb8ER OF CHARACTERS IN EACH COLUMN FIELD
IOUT IS OUTPUT CHANNEL
C
c
SPECIFICATIONS:
-----------------------------------------------------------------CHARACTER*4 DOT. SPACE, DG, BF
DIMENSION BF(130),DG(lO)
C
1
2
DATA ffi(l)rDG(2),ffi(3)rffi(4),DG(S),ffi(6).DG(7~,ffi~8~,ffi~9~,ffi~lO~/
‘0
‘,‘l
‘1’3
‘,‘4
‘r’5
‘*‘2
‘7
‘r’8
‘,‘9
‘/
DATA DOT,SPACE/‘.
I,’
‘/
‘,‘6
‘,
-----------------------------------------------------------------Cl------CALCULATE
# OF COLUMNS TO BE PRINTED (NLBL),
Cl------OF
A LINE (NTOT), NlJmER OF LINES (NWRAP).
WRITE(IOUT.l)
1 FORMAT
NLBL=NLBLZ-NLBLl+l
N=NLBL
IF(NLBL.GT.NCPL)
N=NCF’L
NTOT=NSPACE+N*NDIG
IF(NTOT.GT.130)
GO TO 50
MdRAP=(NLBL-l)/NCPL
t 1
Jl=NLBLl-NCPL
J2=NLBLl-1
C
C2------BUILD
AND PRINT EACH LINE
DO 40 ti=l,tWRAP
WIDTH
:3 ------CLEAR
THE BUFFER (8F).
DO 20 1=1.130
BF(I)=SPACE
20 CONTINUE
NBF=NSPACE
C
C4------DETERMINE
FIRST (Jl)
AND LAST (52) COLUMN I FOR THIS LINE.
Jl=Jl+NCPL
J2= JZ+NWL
IF(J2.GT.NLBL2)
J2=NLBL2
(Z------LOAD
THE COLUMN I’S INTO THE BUFFER,
DO 30 J=Jl,JZ
NBF=NBFtNDIG
12=J/lO
Il=J-12*10+1
BF(MF)=DG(Il)
IF(12.EQ.0)
GO TO 30
13=12/10
12=12-13+10+1
BF(hBF-l)=OG(I2)
IF(13.EQ.0)
GO TO 30
BF(F8F-2)=DG(I3+1)
30 CONTINUE
C
C6------PRINT
THE CONTENTS OF THE BUFFER (I.E.
PRINT THE LINE).
WRITE(IOUT,31)
(BF(I),I=l,NBF)
31 FOF&fAT(lX,130Al)
C
40 CONTINUE
:7 ------PRINT
A LINE OF DOTS (FOR ESTHETIC PUF(POSES ONLY).
50 NTOT=NTOTt5
IF(NTOT.GT.130)
NTOT=130
WRITE(IOUT,51)
(DOT,I=l,NTOT)
51 FORMAT( 1X, 130Al)
C
CI------RETURN
RETURN
END
14-24
List
Variable
of Variables
for
Module UCOLNO
Definition
Range
BF
Module
DIMENSION (130),
Buffer
in which
DG
Module
DIMENSION (lo),
DOT
Module
Field
containing
1
Module
Index
for
IOUT
Global
Primary
11
Module
Index
for
DG (units
12
Module
Index
for
DG (tens
13
Module
Index
for
DG (hundreds
J
Module
Index for
Jl
Module
First
52
Module
Last
N
Module
Number of column
NBF
Module
Index
NCPL
Module
Number of column numbers per line.
NDIG
Module
Number of characters
NLBL
Module
Number of column numbers to be printed.
NLBLl
Module
Start
NLBL2
Module
Stop column
NSPACE
Module
Number of blank
NTOT
Module
Total
NWRAP
Module
Number of lines
SPACE
Module
Field
Digits
a line
0 through
is assembled.
9.
a period.
BF.
unit
number for
all
output.
IOUT = 6.
digit).
digit).
digit).
column numbers.
column number on the
column number on the
for
printed
current
current
line.
line.
numbers.
BF.
in each column number field.
column number.
number.
spaces
at start
number of characters
containing
of line.
on a line.
needed in wrap format.
blanks.
14-25
Narrative
for
Module UZDREL
Module UEDREL reads values for a two-dimensional
real array.
First
it
Then, based on the contents
of the arrayreads an "array-control
record."
The array-control
record contains
control
record,
it may read array values.
four fields:
location
(LOCAT), constant
(CNSTNT), format (FMTIN), and
The LOCAT field
determines
where array values
printout
indicator
(IPRN).
it is the unit number from which
If LOCAT is positive,
will
come from.
array values will
be read in the format specified
in FMTIN.
If LOCAT is
negative,
the sign is reversed to give the unit number from which an
unformatted
record containing
the array values will
be read.
(Before the
array record is read, a record will
be read and ignored.
Thus output from
the module ULASAV can be read.)
If LOCAT is zero, all of the array values
will
be set equal to CNSTNT. When LOCAT is not zero and CNSTNT is not
zero, the array values will
be multiplied
by the value of CNSTNT. The
field
IPRN contains
a code number for a FORTRAN format to be used when
printing
the array.
Module UZDREL performs
1.
its
Read the array-control
2.
Use LOCAT to determine
GO TO STEPS 3, 4, OR 5.
3. If LOCAT equals
a message to that effect,
4.
format
then
tasks
in the
record
If LOCAT is greater
than
in FMTIN: GO TO STEP 6.
order:
(LOCAT, CNSTNT, FMTIN, and IPRN).
where the
zero , set all
and RETURN.
following
array
array
values
values
zero , read array
are coming from.
equal
values
to CNSTNT, print
according
to the
dummy record and
5. If LOCAT is less than zero, read an unformatted
read an unformatted
record containing
the array values.
GO TO STEP 6.
6.
7.
to print
8.
If
CNSTNT is not equal
to zero,
multiply
If IPRN is greater than or equal to zero,
the array values using IPRN as the format
RETURN.
14-26
array
values
call utility
code.
by CNSTNT.
module ULAPRW
Flow Chart
for
Module UZDREL-
Array Control
Record controls
the input of array values.
It contains
four fields:
LOCAT, CNSTNT, FMTIN, and
IPRN.
LOCAT is a code shawing where
array values will
come from.
READ THE ARRAY
CONTROL
RECORD
If LOCAT < 0, array values
will
be read from an
unformatted
record from a
unit number equal to -LOCAT.
If LOCAT = 0, array values
will
be set equal to CNSTNT.
LOCAT >O
If LOCAT > 0, array values
will
be read from the unit
number equal to LOCAT in the
format specified
in FMTIN.
a
CNSTNT is the constant
to which
all array values are set if
LOCAT is equal to zero, and
it is the constant
by which
all array values are rmltiplied
if LOCAT is not equal to zero.
FMTIN is the format in which
array values are read if LOCAT
is greater than zero.
READ AN
UNFORMATTED
DUMMY RECORD
FROM UNIT=
-LOCAT
READ ARRAY
VALUES IN
FORMAT FMTIN
FROM UNIT=
LOCAT
READ AN
UNFORMATTED
RECORD OF
ARRAY VALUES
FROM UNIT=
-LOCAT
IF CNSTNT IS
NOT ZERO,
MULTIPLY ARRAY
VALUES BY
CNSTNT
‘b
I
IPRN is a code showing the format
to be used if array values are
to be printed.
14-27
SET ALL
ARF&Vf+$ES
CNSTNT
PRINT A
MESSAGE TO
THAT EFFECT
1
SUBROUTINE U2DREL(A,ANAME,II,JJ,KtIN,IOUT)
C
C
C-----VERSION
1648 12MAY1987 U2DREL
**********+*************************************************~*****
c
ROUTINE TO INPUT 2-D REAL DATA MATRICES
C
A IS ARRAY TO INPUT
c
C
ANAME IS 24 CHARACTER DESCRIPTIONOF A
II IS NO. OF RCWS
JJ IS NO. OF CDLS
K IS LAYER NO. (USED WITH NAFE TO TITLE
C
c
IN IS INPUT UNIT
IOUT IS OUTPUT UNIT
******************************************************~***********
c
PRINTOUT UNLESS K IS 0)
SPECIFICATIONS:
------_---------------------------------------------------------CHARACTER*4 ANM
CHARACTER*20 FMTIN
DIMENSION A(JJ,II).ANAME(6)
-----------------------------------------------------------------:
Cl------READ
ARRAYCONTROL RECORD.
READ (IN,l)
LOCAT,CNSTNT,FMTIN,IPRN
1 FORMAT(IlO,F10.0,A20rI10)
LOCAT TO SEE WHERE ARRAY VALUES CDME FROM.
:2 ------USE
IFtLCCAT)
200,50,90
C
C3------IF
LOCAT=O MEN SET ML ARRAY VALUES EQUAL TO CNSTNT. RETURN
50 DO 80 I=lrII
DO 80 .l=l.JJ
80 A(J,I)=CNSTNT
IF(K.GT.0)
WRITE(IOUT,2)
ANM,CNSTNT,K
2 FORMAT(lH0,52X,6A4,’
=‘,G15.7.’
FOR LAYER’,I3)
IF(K.LE.0)
WRITE(IOUT,3)
ANAMEsCNSTNT
3 FORMAT(lHD.52X,6A4,’
=‘,G15.7)
RETURN
c
C4------IF
LOCAT>O THEN READ FORMATTED RECORDS USING FOMAT FMTIN.
90 IF(K.GT.0)
WRITE(IOUT,4)
ANM,K,LCCAT,FMTIN
4 FORMAT(lHO,///30X,6A4,’
FOR LAYER’,13,’
WILL BE READ ON UNIT’,
1
13,’ USING FOMAT: ‘,A20/3OX,96(‘-‘1)
IF(K.LE.0)
WRITE(IOUT,S)
ANM,LOCAT,FMTIN
5 FORMAT(lm),///30X,6A4,’
WILL BE READ ON UNIT’,
1
13.’ USING FOFMAT: ‘rAZ0/30X,83(‘-‘)I
DO 100 I=l,II
READ (LOCAT,FMTIN) (A(J,I),J=l,JJ)
100 CONTINUE
GO TO 300
C5------LOCAT<O
THEN READ UNFORMATTED RECORD CONTAINING ARRAYVALUES
200 LOCAT=-LOCAT
IF(K.GT.0)
WRITE(IOUT,201)
ANM,K.LOCAT
201 FORMAT(lHD,///30X,6A4,‘,
LAYER’,I3,
1
’ WILL BE READ UNFORMATTED ON UNIT’rI3/30X,73(‘-‘1)
IF(K.LE.0)
WRITE(IOUT,ZOP)
ANM,LCCAT
202 FORMT(ll-!Gr///30X.
1
’ WILL BE READ UNFORMATTED ON UNIT’,I3/30X,60(‘-‘1)
:5A ------READ
AN UNFORMATTED DUMMY RECORD FIRST.
READ( LOCAT)
READ( LOCAT) A
CNSTNT NOT ZERO THEN MULTIPLY .ARRAY VALUES BY CNSTNT.
:6 ------IF
300 IF(CNSTNT.EQ.0.)
GO TO 320
DO 310 I=lrII
DO 310 J=l.JJ
A(J,I)=A(j;IPCNSTNT
3 10 CONTINUE
:7 ------IF
PRINT CODE (IPRN) =>O THEN PRINT ARRAY VALUES.
320 IF(IFRN.LT.0)
RETURN
CALL ULAPRW(A,ANAtk,O,O,JJ,II,O,IPRN,IOUT)
RETURN
c
C&-----RETURN
END
14-28
List
Variable
of Variables
for
Module UEDREL
Definition
Range
A
Module
DIMENSION (JJ,II),
Input
ANAME
Module
Label
of the
CNSTNT
Module
Constant to which all array values are set if
LOCAT is equal to zero or by which all array
values are multiplied
if LOCAT is not equal
to zero.
FMTIN
Module
Format under which
I
Module
Index
II
Module
Number of rows.
IN
Module
Unit
IOUT
Global
Primary
IPRN
Module
Code for
J
Module
Index for
JJ
Module
Number of columns.
K
Module
Layer
LOCAT
Module
Location of values to fill
in the array.
< 0, read an unformatted
record containing
the
array values.
= 0, set all the array values equal to constant
(CNSTNT).
> 0, read the formatted
records containing
the
array values.
for
for
printout
array
array.
input
values
array.
will
be read.
rows.
number from which
be read.
unit
number for
format
the array
all
control
printed
record
output.
to be used when printing
will
IOUT = 6.
the arrays.
columns.
number.
14-29
Narrative
for
Module UZDINT
Module U2DINT reads values for a two-dimensional
integer
array.
First
Then,
based
on
the
contents
of
the
arrayit reads an "array-control
record."
The
array-control
record
contains
control
record,
it may read array values.
four fields:
location
(LOCAT), constant
(ICONST), format (FMTIN), and
The LOCAT field
determines
where array values
printout
indicator
(IPRN).
it
is
the
unit
number
from which
If
LOCAT
is
positive,
will
come from.
array values will
be read in the format specified
in FMTIN.
If LOCAT is
negative,
the sign is reversed to give the unit number from which an
(Before the
unformatted
record containing
the array values will
be read.
be read and ignored.
Thus output from
array record is read, a record will
the module ULASAV can be read.)
If LOCAT is zero, all of the array values
will
be set equal to ICONST. When LOCAT is not zero and ICONST is not
zero, the array values will
be multiplied
by the value of ICONST. The
field
IPRN (table
1) contains
a code number for a FORTRAN format to‘be
used when printing
the array.
Module U2DINT performs
1.
its
tasks
Read the array-control
in the
record
2. Use LOCAT to determine
3, 4, OR 5.
If
4.
then
in
LOCAT is greater
FMTIN.
than
zero,
values
read array
equal
values
to CNSTNT, print
according
to the
GO TO STEP 6.
If
ICONST is not equal to zero,
7.
If IPRN is greater than
IPRN as the format code.
8.
the
array
GO TO STEPS
is coming from.
5. If LOCAT is less than zero, read an unformatted
dummy record and
read an unformatted
record containing
the array values.
GO TO STEP 6.
6.
using
order:
(LOCAT, ICONST, FMTIN, and IPRN).
where the array
3. If LOCAT equals zero, set all
message to that effect,
and RETURN.
format
fo llowing
Call
utility
or equal
Print
each row in the array.
10.
Select
11.
RETURN.
the
to zero,
module UCOLNOto print
page.
9.
multiply
format
for
printing.
14-30
array
print
values
by ICONST.
the array
values
column numbers at the top of
a
Flow Chart
for
Module U2DINT
Array Control
Record controls
the input of array values.
It contains
four fields:
LOCAT, ICONST, FMTIN, and
IPRN.
LOCAT is a code showing where
array values will
come from.
READ THE ARRAY
CONTROL
RECORD
If LOCAT < 0, array values
will
be read from an
unformatted
record from a
unit number equal to -LOCAT.
If LOCAT = 0, array values
will
be set equal to ICONST.
If LOCAT > 0, array values
will
be read from the unit
number equal to LOCAT in the
format specified
in FMTIN.
ICONST is the constant
to which
all array values are set if
LOCAT is equal to zero, and it
is the constant
by which all
array values are multiplied
if LOCAT is not equal to zero.
FMTIN is the format in which
array values are read if LOCAT
is greater than zero.
READ AN
UNFORMATTED
DUMMY RECORD
FROM UNIT=
-LOCAT
\
READ ARRAY
VALUES IN
FORMAT FMTIN
FROM UNIT=
LOCAT
6
5A
READ AN
UNFORMATTED
RECORD OF
ARRAY VALUES
FROM UNIT=
-LOCAT
IF ICONST IS
NOT ZERO,
MULTIPLY ARRAY
VALUES BY
ICONST
I
IPRN is a code showing the format
to be used if array values are
to be printed.
IF IPRN=X.
PRINT
ARRAY VALUES
14-31
1
3A
PRINT A
MESSAGE TO
THAT EFFECT
SUBROUTINE U2DINT(IA,ANAME,II,JJrK,IN,IOUT)
C
: -----VERSION 1645 12MAY1987UZDINT
******************************************************************
ROUTINE TO INPUT Z-D INTEGER DATA MATRICES
:
IA IS ARRAY TO INPUT
C
ANAME IS 24 CHARACTERDESCRIPTION OF IA
II IS NO; OF RC#iS
:
JJ IS NO. OF COLS
C
K IS LAYER NO. (USED WITH NAME TO TITLE PRINTOUT UNLESS K IS 0)
C
IN IS INPUT UNIT
IOUT IS OUTPUT UNIT
:
****************************************~*************************
C
E
SPECIFICATIONS:
”
CHARACTER*4 ANAME
CHARACTER”20 FMTIN
DIMENSION IA(JJ,II),ANAME(6)
---------------------------------------------------------------
E
Cl--C
READ ARRAY CONTROL RECORD.
READ (IN,11 LOCAT,ICONSTIFMTINIIF'RN
1 F0RMAT(110,110,A20,110)
c2----
USE LOCAT TO SEE WHEREARRAY VALUES COME FROM.
IFtLOCAT) 200,50,90
LOCAT=O THEN SET ALL ARRAY VALUES EQUAL TO ICONST. RETURN
:3 ------IF
50 DO 80 I=lrII
DO80 J=lrJJ
80 IA(J,I)=ICONST
IF(K.GT.0) WRITE(IOUT,2)ANAME,ICONST,K
2 FORMAT(lHO,52X,6A4r'
='rIlSr'
FOR LAYER'rI3)
IF(K.LE.0) WRITE(IOUT,3)ANAMEIICONST
3 FORMAT(lH0,52X,6A4,’
RETURN
=‘,I151
C
LOCAT>O THEN READ FORMATTEDRECORDSUSING FORMAT FMTIN.
c4 ------IF
90 IF(K.GT.0)
WRITE(IOUT,4)ANAMErK,LOCAT,FMTIN
4 FORMAT(lHOr///3OXr6A4,’
FOR LAYER’rI3,’
WILL BE READ ON UNIT’,
13,' USING FORMAT:'rA20/3OXr96('-'1)
1
IF(K.LE.0)
WRITE(IOUT,5) ANAME,LOCAT,FMTIN
5 FORMAT(lHOr///3OXr6A4,’
WILL BE READ ON UNIT',
13,' USINGFORMAT: ‘rA20/30X,83(‘-‘1)
1
DO 100 I=lrII
READ (LOCAT,FMTIN) (IA(J,I)rJ=lrJJ)
100 CONTINUE
GOTO 300
C
c5 ------LOCAT<
THEN READ UNFORMATTEDRECORDCONTAINING ARRAY VALUES
200 LOCAT=-LOCAT
IF(K.GT.0) WRITE(IOUT,201) ANAME,K,LOCAT
201 FORMAT(lHOr///3OXt6A4r'r LAYER'rI3,
' WILL BE READ UNFORMATTEDON UNIT'rI3/30X,73('-'1)
1
IF(K.LE.0)
WRITE(IOUT,202) ANAMEILOCAT
202 FORMAT(lHO,///30X,6A4,
1
’ WILL BE READ UNFORMATTEDON UNIT’rI3/30X,60(
C
14-32
‘-‘I
1
pjA---
READ AN UNFORMATTEDDUMMYRECORDFIRST.
READtLOCAT)
READtLOCAT) IA
C
C6--IF ICONST NOT ZERO THEN MULTIPLY ARRAY VALUES BY ICONST.
300 IF(ICONST.EQ.0)
GO TO 320
DO 310 I=l,II
DO310 J=lrJJ
IA(J,I)=IA(J,I)*ICONST
310 CONTINUE
C
C7------ IF PRINT CODE (IFRN) =>O MEN PRINT ARRAY VALUES.
320 IF(IPRN.LT.0)
RETURN
IF(IPRN.GT.5) IPRN=O
IPRN=IF'RN+l
C
c8------PRINT
COLUMNNUMBERSAT TOP OF PAGE.
IF(IPRN.EQ.l) CALL UCOLNO(1,JJ,O,1O,12rIOUT)
NL=125/IPRN/5*5
IF(IPRN.GT.1) CALL UCOLNO(1,JJr4,NLrIPRN,IOUT)
L-----P~~INT
EACH ROWIN THE ARRAY.
DO110 I=l,II
Lo- ----SELECT
THE FORMAT
GO T0(101,102,103,104,105,106),
C
C----------------FORMAT
IF’RN
10111
101 WRITE(IOUT,lOOl) I,(IA(J,I)rJ=lrJJ)
1001 FORMAT(1HO,I3,2X,Illr9(1X,I11)/(5X,1O(1X,I11)))
GO TO 110
C
6011
C----------------FOFAT
102 WRITE(IOUT,1002)I,(IA(J,I)rJ=l,JJ)
1002 FORMAT(1HO,I3rlX,60(lX,Il)/(5X,6O~lX,Il)~~
GOTO 110
C
4012
C----------------FORMAT
103 WRITE(IOUT,1003)I,(IA(J,I)rJ=lrJJ)
1003 FORMAT(1HO,I3rlX,40(1X,I2)/(5X,4O~lX,I2)~~
GOTO 110
C
C----------------FORMAT
104 WRITE(IOUT,1004)
3013
I,(IA(J,I),J=l,JJ)
1004 FORMAT(1HQrI3,lX,30(1X,I3)/(5X,30(1X,I3)))
GOTO 110
C
2514
C----------------FORMAT
105 WRITE(IOUT,1005)I,(IA(J,I),J=lrJJ)
1005 FORMAT(1HOrI3rlX,25(1X,I4)/(5X,25(1X,I4)))
GO TO 110
C
2015
C----------------FORMAT
106 WRITE(IOUT,1006)I,(IA(J,I),J=lrJJ)
1006 F0RMAT(1HO,13,1X,20(1X,15)/(5X,20(1X,15))1
110 CONTINUE
RETURN
C
Cll-----RETURN
END
14-33
List
Variable
of Variables
for
Module UZDINT
Definition
Range
ANAME
Module
Label
for
the printout
of input
FMTIN
Module
Format
I
Module
Index for
IA
Module
DIMENSION (JJ,II),
ICONST
Module
Constant to which all array values are set if
LOCAT is equal to zero or by which all array
values are multiplied
if LOCAT is not equal
to zero.
II
Module
Number of rows.
IN
Module
Unit
IOUT
Global
Primary
IPRN
Module
Code for
3
Module
Index
35
Module
Number of columns.
K
Module
Layer
LOCAT
Module
Location
of values to fill
in the array.
< 0, read an unformatted
record containing
the
array values.
= 0, set all the array values equal to constant
(CNSTNT).
> 0, read formatted
records containing
the array
values.
NL
Module
Number
under which the
array
array.
values
will
be read.
rows.
Input
number from which
be read.
unit
for
number for
format
array.
the
all
array-control
printed
record
output.
to be used when printing
will
IOUT = 6.
arrays.
columns.
number.
of
columns
14-34
per
line.
Narrative
Module UlDREL reads
reads
an "array-control
control
four
record,
fields:
printout
will
it
values
zero,
all
for
a one-dimensional
If
values.
of the array
values
value
of CNSTNT.
a FORTRAN format
The field
is the
to CNSTNT.
IPRN (table
its
tasks
values
values
number from which
be set equal
the array
contains
and
where array
unit
it
of the array-
(FMTIN),
in FMTIN.
to be used when printing
Module UlDREL performs
determines
First
record
specified
is not zero and CNSTNT is not zero,
the
it
format
will
contents
(CNSTNT), format
LOCAT is positive,
array.
The array-control
The LOCAT field
be read in the
real
based on the
(LOCAT), constant
(IPRN).
will
Module UlDREL
Then,
may read array
indicator
array
values
record."
location
come from.
for
will
2) contains
If
If
LOCAT is
LOCAT
be multiplied
by
a code number for
the array.
in the
following
1.
Read the array-control
record
2.
Use LOCAT to determine
where the array
3.
If
order:
(LOCAT, CNSTNT, FMTIN, and IPRN).
is coming from
(DO STEPS 3
OR 4).
print
LOCAT equals
a message to that
4.
format
If
zero,
set
effect.
LOCAT is greater
all
array
values
equal
to CNSTNT and
RETURN.
than zero,
read array
values
according
to the
in FMTIN.
5.
If
CNSTNT is
6.
If
IPRN is
7.
RETURN.
not equal
greater
than
to zero,
or equal
14-35
multiply
to zero,
the array
print
values
the array
by CNSTNT.
values.
Flow Chart
for
Module UlDREL
Array Control
Record controls
the input of array values.
It contains four fields:
LOCAT, CNSTNT, FMTIN, and
IPRN.
LOCAT is a code showing where
array values will
come from.
t
READ THE ARRAY
CONTROL RECORD
If LOCAT = 0, array values
will
be set equal to CNSTNT.
If LOCAT > 0, array values
will
be read from the unit
number equal to LOCAT in the
format specified
in FMTIN.
LOCAT >O
CNSTNT is the constant
to which
all array values are set if
LOCAT is equal to zero, and
it is the constant
by which
all array values are multiplied
if LOCAT is not equal to zero.
4
READ ARRAY
VALUES IN
FORMAT FMTIN
FRW\lT=
SET ALL
ARRAY VALUES
EcQNusA:NTp
FMTIN is the format in which
array values are read if LOCAT
is greater than zero.
3A
IPRN is a code showing the format
to be used if array values are
to be printed.
IF CNSTNT
MULTIPLY
IS
ARRAY
IF IPRN=X,
PRINT
ARRAYVALUES
14-36
PRINT
A
MESSAGE TO
THAT EFFECT
SUBROUTINE UlDREL(A,ANAME,JJ,IN,IOUT)
C
C
C-----VERSION 1643 12MAY1987UlDREL
******************~***********************************************
C
C
ROUTINE TO INPUT 1-D REAL DATA MATRICES
C
A IS ARRAY TO INPUT
C
ANAME IS 24 CHARACTERDESCRIPTION
OF A
C
JJ IS NO. OF ELEMENTS
C
IN IS INPUT UNIT
C
IOUT IS OUTPUT UNIT
***************************************************************~**
C
C
C
SPECIFICATIONS:
CHARACTER*4 ANAME
CHARACTER*20 FMTIN
DIMENSIONA(JJ),ANAME(6)
-----------_--------_____________L______-------------------------C
C
Cl---READ ARRAY CONTROL RECORD.
READ (IN, 1) LOCAT,CNSTNT, FMTIN,IPRN
1 FORMAT(I10,F10.O,A20,IlO)
C
c2----
USE LOCAT TO SEE WHERE ARRAY VALUES COME FROM.
IF(LOCAT.GT.0) GOTO 90
C
C3..----- IF LOCAT=O THEN SET ALL ARRAY VALUES EQUAL TO CNSTNT. RETURN
DO 80 J=lrJJ
80 A( J )=CNSTNT
WRITE(IOUT,3) ANAME,CNSTNT
3 FORMAT(lH0,52X,6A4,’
RETURN
C
c4 ------IF
=‘rG15.7)
LOCAT>O THEN READ FORMATTEDRECORDSUSING FORMAT FMTIN.
90 WRITE(IOUT,5) ANAME,LOCAT,FMTIN
5 FORMAT(lHO,///30X,6A4,' WILL BE READ ON UNIT'rI3,
1
’ USING FORMAT: ‘rA20/30X,79(‘-‘)/I
READ (LOCAT,FMTIN) (A(J),J=l,JJ)
C
C5------ IF CNSTNT NOT ZERO THEN MULTIPLYARRAY VALUES BY CNSTNT.
IF(CNSTNT.EQ.0.) GOTO 120
DO 100 J=l,JJ
100 A(J)=A(J)*CNSTNT
C
Cfj---IF PRINT CODE (IPRN) =>O THEN PRINT ARRAY VALUES.
120 IF(IPRN.LT.0) RETURN
WRITE(IOUT,lOOl) (A(J)rJ=l,JJ)
1001 FORMAT((lX,lPG12.5,9(1XIG12.5)))
RETURN
C
C7------CONTINUE
END
14-37
List
Variable
of Variables
for
Module UlDREL
Definition
Range
A
Module
DIMENSION (JJ),
ANAME
Module
Label
CNSTNT
Module
Constant to which all array values are set if
LOCAT is equal to zero or by which all array
values are multiplied
if LOCAT is not equal
to zero.
FiTIN
Module
Format
IN
Module
Unit
IOUT
Global
Primary
IPRN
Module
Code for the
arrays.
J
Module
Array
33
Module
Number of elements
LOCAT
Module
Location
of values to fill
in the array.
< 0, read an unformatted
record containing
the
array values.
= 0, set all the array values equal to constant
(CNSTNT).
> 0, read the formatted
records containing
the
array values.
for
Input
printout
under which
array.
of the
the
array
number from which the
be read.
unit
number for
format
input
all
array.
values
array
will
control
printed
be read.
record
output.
to be used when printing
will
IOUT = 6.
the
index.
14-38
in the
array.
REFERENCES
Collins,
R. E., 1961, Flow of fluids
through
Reinhold Publishing
Corp., 270 p.
porous
Crichlow,
Henry B., 1977, Modern reservoir
engineering
Englewood Cliffs,
N.J., Prentice
Hall
approach;
materials;
New York,
- A simulation
Inc.,
354 p.
McDonald, M.G., and Harbaugh, A.W., 1984, A modular three-dimensional
finite-difference
ground-water
flow model:
U.S. Geological
Survey
Open-File
Report 83-875 , 528 p.
reservoir
Peaceman, Donald W., 1977, Fundamentals of numerical
New York, Elsevier
Scientific
Publishing
Company, 176 p.
Remson, Irwin,
Hornberger,
methods in subsurface
simulation;
George M. and Molz, Fred J., 1971, Numerical
hydrology;
New York, Wiley-Interscience,
389 p.
flow-numerical
Rushton, K. R., Redshaw S. C., 1979, Seepage and groundwater
analysis
by analog and digital
methods; New York, John Wiley and Sons
Trescott,
Peter C., 1975, Documentation
of finite-difference
model for
simulation
of three-dimensional
ground-water
flow: U.S. Geological
Survey Open-File
Report 75-438, 32 p.
Trescott,
Peter C. and Larson, S. P., 1976, Supplement to Open-File
Report
75-438, Documentation
of finite-difference
model of three-dimensional
ground-water
flow; U.S. Geological
Survey Open-File
Report 76-591, 21 p.
Trescott,
P. C., Pinder,
G. F., and Larson, S. P., 1976, Finitedifference
model for aquifer
simulation
in two dimensions
with
results
of numerical
experiments:
U.S. Geological
Survey Techniques
of Water-Resources
Investigations,
Book 7, Chapter Cl, 116 p.
Weinstein,
H. C., Stone, H. L., and Kwan, T. V., 1969, Iterative
procedure
for solution
of systems of parabolic
and elliptic
equations
in three
dimensions:
Indus. Engineering
Chemistry Fundamentals,
v. 8, no. 2,
p. 281-287.
14-39
APPENDIX A
PROGRAMPORTABILITY
Introduction
One of the major design requirements
for the model program was that it
should be portable.
A portable
program is one that can be run with a minimum
of modification
on most computers that are physically
capable of running a
program of its type.
The goal of portability
for the model program has been
attained
as evidenced by the fact that it has run successfully
in either
its
present form or the earlier
form (McDonald and Harbaugh, 1984) on computers
manufactured
by many companies including
mainframe computers,
minicomputers,
and microcomputers.
The following
discussion
explains
in more detail
the
concept of portability,
what was done to maximize portability
of the model
programs and circumstances
that might require
that the program be changed in
order to run successfully
on a particular
computer.
The
Impact of the Programming Language on Portability
The programming language is the most important
factor
that determines
program portability.
There are a variety
of programming languages available,
and for each language, there are numerous versions
which have resulted
from
the desire of vendors to improve the power of the language and to take
The most
advantage of the hardware features
of their
particular
computers.
commonly available
language suitable
to use for the model program is FORTRAN.
There are two versions
defined by the American National
Standards Institute
(ANSI) on which most commercial versions
are based, ANSI X3.9-1966 and ANSI
X3.9-1978.l
These versions
are commonly referred
to as FORTRAN66 and
FORTRAN77, respectively.
FORTRAN66 was selected
for the original
version of
the model because, at the time, it was far more widely supported than was
FORTRAN 77.
Now that the FORTRAN77 standard is more widely supported,
the
program has been converted
to this standard.
The program in this report
is nearly identical
to the original
program
except for the changes required
to make it comply with the FORTRAN77
standard.
These changes are minor and are described
by McDonald and Harbaugh
The conversion
was done solely
for the purpose of making the
(1984, p. 505).
program comply with the FORTRAN77 standard;
many of the features
that make
FORTRAN77 more powerful than FORTRAN66 were not used.
An effort
to make
more extensive
FORTRAN77 revisions
to the program is judged to be
uneconomical.
Such an effort
would not result
in significant
improvements in
program clarity
or efficiency.
I American National
Standards Institute,
Standards Institute,
X3.9-1966, 36 p.
American
American
National
National
Standards
Standards
Institute,
Institute,
1966,
FORTRAN: American
1978,
Programming
language
X3.9-1978, chs. 1-18.
A-l
National
FORTRAN:
Most commercial versions
of FORTRAN77 compilers
include
some extended
features
not defined as part of the FORTRAN 77 standard.
Such features
vary
The
widely among computer vendors and were not used in the model program.
program contains
only one exception
to complete compliance
to the FORTRAN77
This exception , which is explained
in
standard that the authors are aware of.
a following
section
(see The Impact of Allocating
Array Storage In a Single
is commonly allowed on computers and should not be a
Array on Portability),
Because the program closely
follows
the
major restriction
to portability.
FORTRAN77 standard,
the program should work on any computer supporting
this
language provided that the computer has adequate computational
power.
It is recognized
that some users may want the program converted
back into
the FORTRAN66 language because they have access only to older compilers.
Only a few changes are required
to convert the program back to FORTRAN66.
Information
about how to convert
is provided
in a following
section
(see
Conversion
to FORTRAN66).
The Impact
of Computational
Precision
on Portability
Variation
of precision
among computers causes some problems with program
portability.
Computational
precision
refers to the accuracy at which numbers
are calculated
and stored in the computer.
To prevent the imposition
of
constraints
on the computers on which FORTRAN is implemented,
the
computational
precision
was not defined as part of the standards.
The
accuracy of model results
are dependent on the computational
precision,
so
precision
must be considered
when moving the model program among computers.
The model program was developed on computers using 32 binary bits to
represent
single
precision
real numbers.
This gives from 6 to 7 decimal
digits
of precision
and includes
values that range in magnitude from
approximately
lo**-39
to 10**38.
Double precision
real numbers are
represented
by 64 binary bits and range in magnltude from approximately
lo**-10000
to 10**10000 with 14 to 15 decimal digits
of precision.
The head
array? HNEW, and some variables
in the solvers
are stored as double precision,
and accordingly
many calculations
in the solvers
are double precision.
This
was necessary for accuracy under some conditions.
The model program should
perform adequately
for most problems on computers that use 32 bits for single
precision
and 64 bits for double precision.
However, the required
precision
depends on the problem being simulated.
Thus, the user must ultimately
determine
if adequate precision
is being used for solving
a particular
problem.
There are some situations
for which there is a need to modify the program
to make all real number calculations
in double precision.
If using a computer
that represents
single
precision
real numbers with less than 32 bits,
then
double precision
is probably necessary for all real numbers and calculations.
Even on computers that represent
single
precision
numbers with 32 bits,
certain
problems are difficult
to solve without
making all real numbers and
calculations
double precision.
it is difficult
to predict
if a
Unfortunately,
specific
problem requires
all double precision.
Simulations
with very large
numbers of cells,
for example more than 50000, are more likely
to have
precision
problems than are smaller
simulations.
Simulations
in which there
are areas having significant
ground-water
flow and yet the heads in the
adjacent
model cells
in these areas are equal within
.Ol percent or less are
A-2
also more likely
to have precision
problems.
In addition,
precision
problems
depend on the preciseness
of the attempted solution.
In general,
the symptoms
of inadequate
precision
are either
a poor volumetric
flow balance or lack of
convergence
by the solver.
However, these same symptoms are more commonly
caused by bad input data or improper adjustment
of parameters that control
iteration.
Because precision
problems are in general fairly
unlikely
and use
of all double precision
results
in increased memory and computer time usages
conversion
to double precision
should probably be done as a last resort
in
order to solve convergence problems.
If the program is converted
to all
double precision,
almost twice the computer memory is required
for model data.
To convert all real numbers and calculations
to double precision,
do the
following:
1.
Declare all single
precision
real arrays and variables
as DOUBLE PRECISION
in the main program and in every subroutine.
This can be done by adding
the statement
IMPLICIT
DOUBLE PRECISION (A-H,O-Z)
to the beginning of the specifications
section
of every subroutine
and the
Alternately
main program.
, some compilers
have a special
command that
will
accomplish
this without
the need to modify the program itself.
2.
In’ the Basic
statement
Package Allocate
module (subroutine
BASlAL) change the
I SUM=ISUM+2*NRCL
to
ISUM=ISUM+NRCL
3.
Change the real intrinsic
functions
Specifically,
precision
equivalents.
DMAXl, and AMINl to DMINl.
in subroutine
change all
SSIPlI to their
double
occurrences
of AMAXl to
If using a computer on which significantly
more than 32 bits are used to
use of double
represent
single
precision
real numbers, then the partial
precision
data and calculations
as included
in the present model program may
be unnecessary.
The program should still
work on such computers without
modification,
but computational
time and memory would be saved if double
The program was designed so that changing to all
precision
were eliminated.
single
precision
would 'be easy.
For this reason* the use of double precision
intrinsic
functions
and constants
is avoided,
and all conversions
between real
and double precision
are done by implied type changes in assignment
statements.
If it is determined that the use of all single
precision
is
acceptable,
make the following
changes to the program:
1.
Delete
all
2.
In the Basic
statement
DOUBLE PRECISION specification
Package Allocate
module
ISUM=ISUMt2*NRCL
to
ISUM=ISUMtNRCL
A-3
Statements.
(subroutine
BASlAL)
change the
The model program
was developed
on computers
that
use 32 bits
for integer
This
is more than adequate
to represent
the range
numbers and calculations.
of integer
numbers that
are used in the program
under any conditions.
The
largest
integer
that
the computer
must be able to represent
is the dimensioned
size of the X array
in the main program.
Many FORTRAN compilers
allow
one to
specify
that
integers
be represented
by 16 bits,
which does not provide
enough
precision
for larger
model simulations.
That is, a 16 bit
integer
in a
typical
computer
can represent
numbers
in the range -32768
to 32767,
and an X
array
dimension
of 32767 is adequate
only
for simulations
that
have 2200 to
3000 cells,
depending
on what options
are used.
The Impact
of
Allocating
Array
Storage
in
a Single
Array
on Portability
Because
almost
all
model data are stored
in the X arrayI
which
is
dimensioned
in the main program , this
array
can be quite
large.
It is
generally
10 to 15 times
the size of the number of model cells.
Some
computers
require
that
special
compiler
options
be used when an array
exceeds
a specified
size.
Users are cautioned
to be aware of this
and use the
appropriate
options
as needed.
The result
of using the incorrect
option
can
sometimes
be that
the program
will
execute
without
producing
error
messages#
but answers
will
be incorrect.
All computers
limit
the amount of array
space that
a program
can use.
If
a user's
simulation
exceeds
this
limit,
the only options
may be to use a
different
computer
or make the simulation
smaller.
However,
some computers
make a distinction
between
total
amount of memory used for all
arrays
and the
total
used by a single
array.
That is, some computers
might
allow
4 arrays
each having
32000 elements,
but not allow
a single
array
consisting
of 128000
elements.
On such a computer,
it is quite
possible
that
one could
exceed the
size
limit
for a single
array
without
exceeding
the total
array
size
limit
because
nearly
all
model data are stored
in the single
X array.
If this
situation
occurs,
it is possible
to break the X array
into
smaller
pieces.
Although
this
can be done by modifying
only the main program*
the modification
is fairly
complex.
Such modification
requires
a knowledgeable
programmer
who
has a clear
understanding
of how model data are stored
within
the X array.
Before
making such a modification,
it would be prudent
to assess
how long the
desired
simulation
might
take to execute.
Generally,
computer
execution
speed
is more of a constraint
on maximum problem
size than is array
size.
The only known exception
to the use of the FORTRAN 77 standard
in the
model program
is that the da?a type of actual
subroutine
arguments does not
always
match the type of the corresponding
dummy arguments.
The standard
requires
the data type of actual
and dummy arguments
to match.
This only
happens
in the main program
where it calls
subroutines
using
actual
arguments
that
are elements
from the X array.
The X array
itself
is data type
real,
and
several
model arrays
stored
withi
X are either
integer
(arrays
IOFLG, IBOUND,
IRCH, IEVT, and LRCH) or double
precision
(array
HNEW).
For example,
actual
argument
X(LCIRCH)
in the main program
is passed to dummy argument
IRCH in
subroutine
RCHlRP.
X(LCIRCH)
is of type real,
and IRCH is of type integer.
This practice
has not been a problem
in the past.
Should this
become a
problem
on future
computers,
required
changes
will
be fairly
minor,
affecting
only the main program
and some of the Allocate
modules.
A-4
The Impact on Portability
of Preconnected
File
Units
FORTRAN77 provides 2 ways for a file
unit to become connected to
(associated
with) a file
-- preconnection
and the OPEN statement.
The model
program use preconnection.
This means that the computer's
operating
system
provides the connection
between files
and file
units prior to program
execution.
Often the user must issue commands to the system, which connect
the necessary files
and file
units,
prior to running the program.
The
Generally,
specific
method for doing this varies among.computers.
preconnection
is adequate, but it may be inconvenient
on some computers.
Modification
of the main program to use OPEN statements
is a simple task for a
programmer.
Conversion
to FORTRAN66
Because the model program uses only one feature
of FORTRAN 77 that is not
part of FORTRAN66, few changes are needed in order to make the program comply
with the FORTRAN66 standard.
All of the required
changes are a result
of
differences
in the way character
(alphanumeric)
data are handled by the two
versions
of FORTRAN. Any variables
or arrays holding character
data must be
declared to be the character
data type in a FORTRAN77 program; in a FORTRAN
The
66 program, character
data are stored in numeric variables
or arrays.
specific
changes that are required to make the model program comply with the
It is assumed that at least four
FORTRAN66 standard are shown below.
characters
can be stored in a single
precision
real variable
or array element.
1.
Delete all
program.
2.
In each of the array
change the statement
CHARACTER*4 statements
reading
throughout
utility
modules
all
subroutines
(UlDREL,
and the main
U2DREL, and U2DINT1,
CHARACTER*20 FMTIN
to
DIMENSION FMTIN(5)
3.
In each of the array reading utility
modules (UlDREL, U2DREL, and
change all occurrences
of W20V1 to 115A411. For example, change
1
' USING FORMAT: ',A20/3OX,79('-')/I
in subroutine
1
4.
U2DINT)r
UlDREL to
' USING FORMAT: ',5A4/30X,79('-')/I
To make the program strictly
comply with the FORTRAN66 standard,
it is
necessary to change character constants in DATA statements to Hollerith
constants.
However, most FORTRAN66 compilers
accept character
constants
specified
using FORTRAN77 notation
(using apostrophes).
Thus, it is
unlikely
that this change will
be required.
A-5
APPENDIX B
SPACE REQUIREMENTS IN THE X ARRAY
The outline
The formulas
given
the X-array
can be used to calculate.the
However,
problem.
program and let
as part
below gives
it
it
calculate
the
NODES is defined
I.
the size.
The total
even if
X array
is
approximately
on the options
each package.
X array
for
a
run the model
space required
is printed
is dimensioned
too
small.
10 to 15 times
the
number
In the
selected.
outline
number of nodes in the model.
BAS Package
A.
8*NODES + (NLAY - l)*NCOL*NROW + NROW+ NCOL + 4*NLAY
B.
Additionally,
add NODES if
start
BUFF is separate
head is saved
(ISTRT is not 0),
from RHS (IAPART is not 0)
BCF Package
A.
NLAY
B.
If
c.
For each layer
where LAYCON is one or three,
add 2*NCOL*NROW
D.
For each layer
where LAYCON is two or three,
add NCOL*NROW
E.
If a transient
simulation
a transient
simulation
LAYCON is two or three,
III.
for
of the
to simply
the X array
as NCOL*NROW*NLAY, the
and add NODES if
II.
size
easier
of nodes in the model depending
below,
exact
is generally
of the model printout
As a rough estimate,
space requirements
WEL Package --
(ISS is 0),
(ISS is 0),
add NODES
for
add NCOL*NROW
4*MXWELL
6-i
each layer
where
IV.
DRN Package --
5*MXDRAN
V.
RIV Package --
6*MXRIVR
VI.
EVT Package
A.
Option
1 --
3*NCOL*NROW
B.
Option
2 --
4*NCOL*NROW
GHB Package --
VII.
VIII.
5*MXBND
RCH Package
IX.
x.
A.
Options
B.
Option
2 --
SIP Package ---
SOR Package
Generally,
close
to the
hand,
it
is
is selected.
a factor
1 and 3 --
it
NCOL*NROW
2*NCOL*NROW
4*NODES + 4*MXITER + NPARM
(NLAY + 4)*NCOL*NLAY
is advisable
to have the X-array
amount of space needed for
inconvenient
Several
of two should
to redimension
load
+ 4WXITER
modules
with
be adequate.
B-2
a specific
problem.
the X array
the size
dimension
every
of the
relatively
On the
time
X array
other
a new option
differing
by
APPENDIX C
CONTINUATION OF A PREVIOUS RUN
There
is often
value
model runs.
This
continue
simulation.
the
allows
not have a special
to continue
disk
file,
subroutine
generated
option
that
reads
disk
files
the
not the total
budget
for
that
file
starting
of all
a series
simulation
time
output
budget
are always
for
runs,
it
C-l
report
does
is quite
simple
on a
heads for
the
the next
need for
run.
of reading
The
model-
reformatting.
set to zero at the start
only
but total
that
runs.
If
the totals
the model program
runs can be calculated
of each run.
or not to
is to be continued
runs is desired,
model runs,
short
of the
of continuation
Similarly,
single
in this
on a model run represents
of continuation
only
whether
heads (UZDREL) is capable
terms
several
of one run as input
run that
as starting
runs in a series
of continuation
times
the
of saved heads without
printed
runs,
making continuation
run can be added externally.
simulation
between
into
the model program
heads from the
budget
a series
for
by using
and specify
Because volumetric
model run,
Although
save the
long simulations
one to decide,
a simulation
Simply
next.
in breaking
one run,
a total
from each
keeps track
simulation
externally
of a
time
by adding
of
for
the
APPENDIX D
SAMPLE PROBLEM
This sample problem is intended to illustrate
input and output from
as shown in the accompanying
There are three simulated
layers,
the program.
illustration,
which are separated from each other by confining
layers.
Each layer is a square 75,000 feet on a side and is divided
by a grid into
15 rows and 15 columns which form squares 5,000 feet on a side.
Flow
within
the confining
layers
is not simulated,
but the effects
of the
confining
layers on flow between the active
layers are incorporated
in the
Flow into the system is infiltration
vertical
leakance (Vcont) terms.
flow out of the system is to buried drain tubes,
from precipitation;
discharging
wells,
and a lake which is represented
by a constant-head
boundary.
I
Recharge
to Layer 1
1234567
LAYER 1
UNCONFINE
LAYER 2
CONFINED
LAYER 3
CONFINED
Between layers 1 and 2 vertical hydraulic
conductiwty diwded by thickness
= 2X10-~
Between layers 2 and 3 vertical hydraulic
conductivity divided by thickness
= 1X10-%
D-l
q
3X104 ft/s
Setting
starting
heads equal to 0.0, the program was run to get a
steady-state
solution.
The Strongly
Implicit
Procedure was used to solve
the system of difference
equations:
the error criterion
was set at 0.001
feet,
the acceleration
parameter was set to 1.0, and the maximum number
of iterations
was set equal to 50. A seed of 0.001 was specified
for use
in calculating
the iteration
parameters;
31 iterations
were needed to close.
List
Q = 5 ft3/s
Layer
of Wells
List
for
Conductance
Row
each well
Column
Layer
Row
of Drains
= 1 ftz/s
Column
Elevation
3
5
11
1
8
2
0.0
2
4
6
1
8
3
0.0
2
6
12
1
8
4
10.0
1
9
8
1
8
5
20.0
1
9
10
1
8
6
30.0
1
9
12
1
8
7
50.0
1
9
14
1
8
8
70.0
1
11
8
1
8
9
90.0
1
11
10
1
8
10
100.0
1
11
12
1
11
14
1
13
8
1
13
10
1
13
12
1
13
14
D-2
Input
Data for
Sample Problem
Note that input item names are included
in many of the data records shown
below.
These are Included for Identification
purposes.
These names are
ignored by the model program when it reads the data because they are placed
columns beyond those used to hold model data.
in
Input for FORTRAN unit 1 -- Basic Package:
SAMPLE---- 3 LAYERS, 15 ROWS, 15 COLUMNS; STEADY STATE; CONSTANT HEADS COLUMN1,
LAYERS 1 AND 2; RECHARGE,.WELLS AND DRAINS
1
15
15
1
3
11 12 13 0 0 0 0 18 19 0 0 00
0
0
IAPART, ISTRT
IBOUND3
1
l(1513)
1 1 1 1 1 1
-1 1 1 1 10 1111
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1
-1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 : 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1
-1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 : 1 1 1 1
3
IBOUND1
l(1513)
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1
1
1 1 1 1 1 1 1
-1
-1 : : : 1 1 1 1 1 1 1 : 1 : 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
IBOUND0
1
999.99
HEAD-l
0.
0
HEAD-Z
0.
0
HEAD-3
0.
0
PERLEN,NSTP,TSMULT
1
1.
86400.
D-3
Input
for
1
FORTRAN unit
0
11 -- Block-Centered
ISS, IBCFBD
Flow Package:
100
0
0
0
0
0
0
0
:
Input
for
cLc,
Input
Input
1
1
0
1.
5000.
5000.
.OOl
-150.
2.E-8
.Ol
l,E-8
.02
FORTRAN unft
0
18 -- Recharge Package:
NRCHOP,IRCHBD
INRECH
RECH-1
3.E-8
for FORTRAN unit
50
5
1.
.OOl
Implicit
19 -- Strongly
MXITER, NPARM
0
.OOl
for
13 -- Drain Package:
MXDRAI, IDRNBD
NDRAIN
2
0.
3
0.
4
10.
5
20.
6
30.
7
50.
8
70.
9
90.
10
100.
9
9
1
1
1
1
1
1
1
1
1
Input
TRPY
DELR
DELC
HY-1
BOT-1
VHY/THICK-1
T-2
T-3
VHY/THICK-2
FORTRAN unit
0
for
15
15
3
8.
8
8
8
8
8
8
8
8
FORTRAN unit
0
5
12 -- Well Package:
MXWELL,IWELBD
ITMP (NWELLS)
11
-5.
f
1
:
9
1;
8
1;:
-5.
:
1
1
1
1
1
1
1
1
1
ii
9
11
11
11
11
13
13
13
13
:;
14
8
10
12
14
8
10
12
14
1;:
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
D-4
Procedure
Package:
1 ACCLrERR, IPCALC, WSEED
l.EOO
l.EOO
l.EOO
l.EOO
l.EOO
l.EOO
l.EOO
l.EOO
i.EOO
Sample Problem
Output
Note that it should not be expected that the outputs from running the same
problem on different
computers will
exactly
match.
Small variations
in output
can be caused by differences
in the way real numbers are stored and
calculated.
Storage and calculation
of real numbers depend on the specific
computer hardware , the FORTRANcompiler , and the math library
that is loaded
with the compiled program.
Output variations
among computers also depend on
the size of the problem, the number of iterations
required
for solution,
and
the precision
used when printing
results.
In this sample problem, most values
should not vary from one computer to another.
Those few values that vary
should generally
vary only in the least significant
digit;
however, the budget
term llIN-OUT1lr because it is the difference
of two nearly identical
numbers,
may vary by as much as a factor
of 3 from one computer to another.
U.S.
GEOLOGICAL
SURVEY
MOWLAR
FINITE-DIFFERENCE
15 CCLU~S;
STEADY STATE;
SAMPLE----3
LAYERS, 15 REM,
15 Rws
15 alLUrnS
7 I AYERS
1 STRESS FERIODt&IN SIMJLATION
MODEL TIME UNIT IS SECONDS
_ _...-.._
I/O UNITS:
ELEMENT OF
I/O
IUNIT:
UNIT:
GROUND-WATER MODEL
PACKAGE, VERSION 1. 9/l/87 INPUT READ FROM UNIT
ARRAYS RHS AND BUFF WILL SHARE MEMORY.
START HEAD WILL NOT BE SAVED -- DRAWCCWN CANNOT BE CALCULATED
5892 ELEMENTS IN X ARRAY ARE USED BY BAS
30000
5892 ELEMENTS OF X ARRAY USED CUT OF
BCFl --
BLOCK-CENTERED FLOW PACKAGE,
STEADY-STATE
SIMULATION
LAYER AGUIFER TYPE
----------_-_------
WELl
1
AND 2;
VERSION
1, 9/l/67
INWT
1
READ FRCM UNIT
11
1
0
:
3
LAYERS
1 2 3 4 5 6 7 6 9 10 11 12 13 14 15 16 17 16 19 20 21 22 23 24
11 12 13 0 0 0 0 18 19 0 0 0 0 0 0 0 0 0 D 0 0 0 0 0
BASl -- BASICMDDEL
453
6345
1,
CONSTANT HEADS WLUMV
0
ELEMENTS IN X ARRAY ARE USED BY BCF
30000
ELEMENTS OF X ARRAY USED CUT OF
WELL PACKAGE, VERSION 1. 9/l/87 INPUTREADFROM
12
15 WELLS
60 ELEMENTS IN X ARRAY ARE USED FOR WELLS
30000
6405 ELEMENTS OF X ARRAY USED OUT OF
-
MAX1t.MOF
PACKAGE, VERSION 1, 9/l/67 INPUTREAD FROM
9 DRAINS
45 ELEFENTS IN X ARRAY ARE USED FOR DRAINS
30000
6450 ELEtSZNTS OF X ARRAY USED OUT OF
DRNl --
DRAIN
MAXIWMOF
Ktil -- RECHARGE PACKAGE, VERSION
OPTION1 -- RECHARGE TO TOP LAYER
225
6675
1,
9/l/67
INPUTREAD
UNIT 13
FROM UNIT
16
ELEMENTS OF X ARRAY USED FOR RECHARGE
30000
ELEMENTS OF X ARRAY USED OUT OF
SIP1 -- STRONGLY IMPLICIT FRMTDURE SaLUTION PACKAGE,
MAXIMUM OF 50 ITERATIONS
ALLCWED FOR CLOSURE
5 ITERATIONPARAMETERS
2905 ELEMENTS IN X ARRAY ARE USED BY SIP
30000
9580 ELEMENTS OF X ARRAY USED CUT OF
VERSION 1.
D-5
9/l/87
INPUT
READ FROM UNIT
19
RECHARGE,
WELLS AND DRAINS
S/WI&---3
LAYERS.
15 RCWS. 15 COLUMNSJ STEADY STATE;
CONSTANT HEADS COLUM.4
1, LAYERS 1 AND 2; RECHARGE, WELLS AND DRAINS
BCUNDARYARRAY FOR LAYER 1 WILL BE READ ON UNIT
1 USING FOIMAT: (1513)
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
.....................................................................
1
-1
11111111111111
2
-1
11111111111111
3
-1
11111111111111
4
-1
11111111111111
5
-1
11111111111111
6
-1
11111111111111
7
-1
1
B
-1
11111111111111
1
1
1
1
1
1
1
I
1
1
1
1
1
9
-1
11111111111111
10
-1
I
1
I
1
1
1
1
1
1
1
1
1
1
1
11
-1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
12
-1
1
1
1
1
1
1
11111111
13
-1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
14
-1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
15
-1
11111111111111
BOUNDARYARRAY FOR LAYER 2 WILL BE READ ON UNIT
----__----------------------------------------------------------------------------------------
1
234567
8
9 10 11 12 13 14 15
.....................................................................
1
-1
11111111111111
2
-1
11111111111111
3
-1
11111111111111
4
-1
11111111111111
5
-1
11111111111111
6
-1
11111111111111
7
-1
11111111111111
8
-1
11111111111111
9
-1
11111111111111
10
-1
1
1
1
11
-1
1
1
1
12
-1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
13
-1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
14
-1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
15
-1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
D-6
1 USING FOMT:
(1513)
BOUNDARY ARRAY =
AQUIFER
HEAD WILL
BE SET TO
999.99
AT ML
NO-FLW
ME
FoLLWIffi
UJTFUT
COMES AT ME
HEAD =
READ =
0.0000000Et00
FOR LAYER
2
HEAD =
O.DDDOOOOEtOO
FOR LAYER
3
END OF EACH STRESS PERIOD:
ANISOTROPY
DELR =
5000.000
DELC =
5000 .OOO
VERT HYD CCND /THICKNESS
TRANSMIS.
VERT HYD CCND /THICKNESS
SCUTION
=
ALONG RCWS =
TRANSMIS.
l.OOODOO
=
BOTTOM =
=
ALONG RCW =
0.9999999E-03
FOR LAYER
1
-150.0000
FOR LAYER
1
0.2OOOOOOE-07
FOR LAYER
1
0.1000000E-01
FOR LAYER
2
0.1000000E-07
FOR LAYER
2
0.2ODOOOOE-01
FOR LAYER
3
BY THE STRONGLY IMPLICIT
MAXIfdJM
ITERATIONS
ALLWED FOR CLOSURE
ACCELERATION PARMTER
HEAD CHANGE CRITERION FOR CLOSURE
SIP HEAD CHANGE PRINTOUT INTERVAL
0.0000DD0Et0D
CALCULATED
D.B22172OE+OD
FROM SPECIFIED
0.9683772EtOO
1
INITIAL
HYD. COND. ALONG ROWS =
PARMETERS
FOR LAYER
0.0000000E+00
INITIAL
CCLUMY TO RW
5 ITERATION
3
NODES (IBWNO=O).
INITIAL
DEFAULT OUTPUT WNTRaL -TOTAL VCLLMETRIC BUDGE1
HEAD
1 FOR LAYER
WEED
= D.DDlOODOO
0.9943766EtOO
D-7
:
D.9990000EtOO
=
=
=
=
PROCEDURE
50
1 .OODO
O.lOOOOE-02
1
STRESS PERIoo No.
1s LENGrn =
_-_____-I------_----------------NlmERoFT1LE
MILTIFLIER
INITIAL
TIM
STEPS =
66400.00
1
FOR DELT =
1.000
STEP SUE =
06400.00
15 WELLS
3
:
STRESSRATE WELLNO.
-------------------11
-5 .oooo
1
2
6
9
9
12
6
0
10
-5 .oooo
-5.0000
-5 .oooo
-5 .oooo
:
4
5
09
ii
14
8
-i .oooo
-5.0000
-5 .oooo
-5 .oooo
-5.0000
-5 .oooo
-5 .oooo
-5 .owo
-5 .oooo
-5.0000
ii7
0
9
LAYER
Ran
1
1
:
:
ca.
::
:
::
1
:
:i
14
8
:i
1
:3
:z
14
::
::
::
9 DRAINS
LAYER
RCU
mw--m---m-m-.
cu.
---
REVATIOW
-1-------s
8
2
o.wow+oo
1
o.oowE+w
1
10.00
x
8
:
1
:
x
DRAIN NO.
1.060
1
i.ow
1.000
I.000
l.OW
1.000
1.000
1.000
1.000
20.66
30.00
50.00
10.00
90.00
x
8
:
-MX
loo.0
RECHRGE- 0.3000000E-07
31 ITERATIONS
FORTILL STEP 1 IN STRESS
FERIOO 1
UWMJMHEADCHANGE
FOREMY ITERATIONI
HEAD CW'JdGELAYER,RCM,COL
HEADCIMGE
----______---___----Iu--l----------12.48
-22.41
( 3, 5, 11)
2.482
( 1, 9, 14) 1.430
0.5503
( 3. 8, 7) 0.4821
LAVERRCU,OOL HEMOE
( 1,
(
(
1, 15)
3, 10, 13)
2, 6, 9)
13.39
6.214
0.4711
LAYER,R(W,COL HEADCMNGE LAYER.R(W,!XL HEADCHANGE LAYER,RW,CDL
_----_--------------____I_______________--------------( 3, 1, 14)
48.21
( 1, 1, 15) 35.90
( 3, 1, 13)
( 1, 12, 14) 7.411
( 3, 11, 14)
13.66
( 1. 15. 15)
f 3, 5, 10)
2.019
( 1, 11, 14) 2.302
( 3. 5, 13)
( 1, 14. 14) 0.3141
( 3, 13, 14) 0.3321
( 1, 15, 15)
( 3, llr 10) 0.7911E-01 ( 1, 14, 14) 0.85OOE-01 ( 3, 7, 14)
0.1108
(
O.%SE-02
0.4169E-02
0.2426E-03
(
(
1. 13, 12) 0.7059E-01 ( 3, 12, 11) 0.2819
1, 13, 12) 0.15&E-01 ( 2, 11s 11) 0.1777E-01
1, 13. 141 0.2555E-02 ( 3, 14, 15) 0.9771E-02 (
(
I,
13. 12)
D-8
1. 14. 14) O.l082E-01 ( 3. 13. 14) O.l03OE-01 ( 1. 15. 15)
MAD IN LAYER 1 AT END OF TIHE STEP
1 IN STRESS PERIOD 1
4
6
7
1
3
5
8
9
10
11
14
13
13
15
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....
1
2
O.OOOOEtOO
117.4
24.94
121.3
59.26
126.4
11.02
121.4
82.52
91.91
100.0
106.9
112.6
43.10
122.7
57.98
124.9
70.17
80.57
90.12
98.40
105.3
111.0
55.43
122.1
66.78
123.4
76.21
86.51
95.20
102.2
107.6
0.00OOEt00
115.7
119.6
O.OOOOEtOO
112.0
23.45
116.1
41.30
O.OOOOEtOO
21.92
110.7
38.61
114.9
51.75
81.34
90.75
91.64
102.5
117.9
61.79
119.4
68.03
106.1
5
0.0oo0Et00
91.29
19.73
103.1
34.92
108.8
41.32
112.5
57.69
114.3
66.74
11.09
85.76
92.22
96.15
6
O.OOOOEtOO
93.03
16.51
94.23
29.50
40.90
166.4
51.30
108.4
61.21
71.19
79.85
86.41
90.82
102.1
0.0000Et00
68.60
21.10
96.43
31.21
99.02
41.40
51.84
63.08
72.68
19.95
84.92
91.66
3.483
85.00
6.832
89.21
16.25
91.12
26.30
94.33
36.97
52.59
64.31
72.52
77.25
O.OOOOEtOO
73.93
10.54
13.79
19.11
28.12
80.17
36.92
86.49
45.21
52.95
55.36
65.15
66.07
80.84
O.OOOOEtOO
70.39
14.62
12.44
25.86
76.72
35.38
78.26
43.49
50.11
54.93
57.55
62.95
65.55
O.OOOOEtOO
66.43
17.11
29.96
72.22
40.01
71.04
47.78
77.62
53.24
55.81
53.33
60.27
59.29
65.45
12
0.00O0Et00
67.12
18.68
68.50
32.56
12.29
43.01
73.46
50.81
76.85
55.92
58.33
58.47
61.93
63.18
13
o.ooooEtoo
67.22
19.67
34.24
53.01
76.48
59.91
56.75
62.59
60.91
71.90
45.14
70.35
58.04
65.75
20.27
73.18
35.21
75.84
46.48
77.03
54.61
79.09
60.08
63.17
64.52
67.25
60.79
20.56
16.22
35.78
78.22
47.16
79.66
55.48
80.82
61.26
65.02
67.52
69.94
72.01
3
4
7
8
O.OOOOEtOO
81.99
9
10
11
14
O.OOOOEtOO
71.64
15
O.OOOOEtOO
14.29
24.45
44.01
124.3
11.55
119.6
126.1
101.8
81.79
D-9
HEAD IN LAYER 2 AT END OF TIE
-----------------------------------------------------------------------
STEP
1 IN STRESS PERIOD
1
6
7
10
5
0
9
1
2
3
15
11
12
13
1:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....
1
O.OOOOE+OO
117.2
2
O.OOOOE+OO
115.5
43.73
124.1
59.02
71.61
127.3
82.32
91.72
99.06
106.7
112.5
126.2
42.83
122.6
57.74
124.8
69.95
80.36
89.93
98.22
105.1
110.8
119.4
24.66
121.1
24.17
125.9
3
0.0000Et00
111.8
23.17
116.0
41.03
119.5
55.19
121.9
66.53
123.2
75.77
86.29
95.02
102.0
107.4
4
O.OOOOE+OO
105.4
21.65
110.4
38.34
114.8
51.50
117.7
61.35
119.2
60.17
80.90
90.55
97.45
102.3
5
O.OOOOEtOO
91.09
19.48
102.1
34.65
108.6
47.07
112.4
57.44
114.2
66.30
76.85
85.57
92.00
95.41
6
O,OOOOE+OO
92.06
16.27
29.24
101.7
40.65
106.2
51.07
108.3
60.98
70.98
79.65
86.28
90.54
86.23
11.38
91.24
20.95
96.22
31.05
99.65
41.25
101.6
51.70
62.90
72.48
79.16
84.73
8.330
17.58
91.59
27.58
94.17
38.25
52.94
64.19
72.34
77.12
7
O.OOOOE+OO
88.35
8
9
10
O.OOOOE+OO
81.81
O.OOOOE+OO
73.61
0.0000Et00
70.24
11
O.OOOOE+OO
12
O.OOOOE+OO
13
66.37
66.98
O.OOOOE+OO
67.16
14
0.0000Et00
15
O.OOOOEtOO
71.48
74.11
4.209
84.86
89.10
74.40
80.77
18.96
27.98
60.84
36.79
86.38
45.16
52.66
56.13
65.08
66.79
14.40
25.61
76.57
35.15
78.20
43.27
81.64
49.91
54.76
57.48
62.79
65.49
66.18
29.70
72.16
39.78
71.75
41.56
77.51
53.05
55.68
54.09
60.20
60.04
18.43
68.44
32.31
72.15
42.85
50.60
76.69
55.13
58.16
58.41
61.78
63.12
13.40
19.42
66.48
33.98
71.84
44.91
71.06
52.80
76.37
57.85
59.78
57.50
62.53
61.65
20.02
73.06
35.02
75.68
46.26
76.91
54.41
78.93
59.88
62.99
64.39
67.08
68.66
20.30
76.04
35.52
78.04
46.94
79.49
55.28
80.65
61.07
64.84
67.34
69.76
71.04
10.38
72.37
16.87
D-10
HEAD IN LAYER 3 AT END OF TIRE STEP 1 Itj STRESS PERIOD 1
2
12
1
11
3
13
. . . . . . ..*..................................
1
2
3
4
5
82.06
91.40
99.63
106.5
112.3
69.66
125.7
00.07
09.60
97.99
104.9
110.6
54.07
121.7
66.20
75.28
05.90
94.77
101.7
107.2
37.90
114.5
51.17
117.5
60.05
62.69
00.41
90.20
97.19
101.9
19.10
100.7
34.30
100.2
46.75
57.10
114.0
65.80
76.54
85.30
91.67
94.17
112.1
1.176
15.99
50.76
60.67
70.70
79.30
06.01
90.12
88.55
20.91
101.2
40.33
90.60
106.0
100.0
0.0273
07.90
11.21
90.77
20.79
95.94
30.88
41.09
101.4
51.55
62.67
72.22
79.50
04.46
99.41
0.4331
81.58
5.131
10.19
00.00
19.27
91.44
29.19
93.95
39.04
53.40
64.07
72.11
76.95
04.60
0.7543
73.01
10.22
75.31
10.02
27.04
52.70
57.03
65.02
67.64
01.64
36.66
86.24
45.06
80.72
14.13
72.33
25.29
76.39
34.05
78.15
42.99
49.65
54.54
57.44
62.61
65.44
81.43
47.28
77.30
52.79
55.53
55.01
60.16
60.94
55.47
57.94
50.37
61.60
63.00
1.000
117.0
24.34
43.36
50.70
71.33
120.9
123.9
126.0
127.1
1.764
115.3
23.85
42.46
122.4
57.42
124.6
1.691
111.5
22.86
115.7
40.67
119.3
1.570
104.1
21.35
110.0
1.415
77.46
6
7
0
9
10
1.039
70.05
11
12
13
14
119.2
123.0
119.0
1.224
16.59
29.37
39.47
66.33
67.06
72.13
72.60
1.341
66.80
18.15
60.41
31.97
71.97
42.54
73.36
50.32
1.415
67.12
19.14
33.65
71.80
44.61
59.63
50.39
62.40
62.54
71.90
52.53
76.24
57.60
67.35
19.73
72.91
34.60
75.47
45.96
76.77
54.13
70.71
59.63
62.76
64.24
66.87
68.52
20.01
35.18
77.01
46.63
55.00
00.42
60.01
64.59
67.11
69.52
71.61
1.460
71.27
15
6
9
7
0
10
4
14
1:
..................................................................................
1.401
73.07
75.02
79.27
76.49
D-11
VOLIJKTRIC
BUDGET FOR ENTIRE MODEL AT END OF TIK
--_------___________--------------------------------------------------------CUMULATIVE
------------------
VCCWS
STEP
LB*3
1 IN STRESS PERIOD
RATES FOR MIS
------------------------
IN:
---
TOTAL
=
=
=
=
=
IN =
OUT:
---STORAGE
CONSTANT HEAD
WELLS
DRAINS
RECHARGE
O.OOODOE+OD
O.OODCJOE+OO
0.00000E+00
0.00000E+00
O.l3608E+OB
STORAGE
CONSTANT HEAD
WELLS
DRAINS
RECHARGE
O.l3608E+08
TOTAL
=
=
=
=
=
IN =
L”9/7
0.00D00Et00
0.43265E+07
0.648OOEt07
0.28DllEtO7
0.00000Et00
STORAGE
CONSTANT HEAD
WELLS
DRAINS
RECHARBE
TOTAL OUT =
0.13608EtO8
TOTAL
CUT =
IN -
UJT =
PERCENT DISCREPANCY
184.00
=
0.00
PERCENT DISCREPANCY
SUNMARY AT END OF TINE STEP 1 IN STRESS PERIOD
1
SECONDS
MINUTES
HOURS
--------------------------------------------------------------------------86400.0
86400.0
86400.0
0 .OOOOOEtOO
O.OOOOOEtOO
0 .OOOOOEtOO
0.00000Et00
157.50
157.50
OUT:
---=
=
=
=
=
IN - CUT =
TIE
STEP LENGTH
STRESS PERIOD TIME
TOTAL SIWLATION
TIME
STEP
IN:
---
STORAGE
CONSTANT HEAD
WELLS
DRAINS
RECHARGE
TIE
TIHE
1
1440.00
1440.00
1440.00
24 .OOOO
24.0000
24.0000
D-12
DAYS
YEARS
1 .ooooo
1 .ooooo
1 .ooooo
0.273785E-02
0.273785E-02
0.273785E-02
=
=
=
=
=
=
0.00000Et00
50.075
75 .ooo
32.420
O.OOOOOEtOO
157.49
O.ZlZlOE-02
0.00
APPENDIX E
ABBREVIATED INPUT INSTRUCTIONS
These input instructions
are intended as a quick reference
for the
experienced
user.
Most explanations
that are contained
in the complete
input instructions
given in package documentation
have been omitted.
The
format of input fields
is given only for those records that contain fields
that are not 10 characters
wide.
Each input item, for which format is not
given, is identified
as either
a record or an array.
For records,
the
fields
contained
in the record are named. For arrays,
only the array name
is given.
Input fields
which contain
codes or flags are described.
All
other field
and array descriptions
have been dropped.
Array
Input
The real two-dimensional
array reader (UZDREL), the integer
two-dimensional
array reader (UZDINT), and the real one-dimensional
array reader (UlDREL)
read one array-control
record and, optionally,
a data array in a format
specified
on the array-control
record.
FOR REAL ARRAY READER (UZDREL or UlDREL)
LOCAT
CNSTNT
Data:
F10.0
110
Format:
FOR INTEGER ARRAY READER (U2DINT)
LOCAT
ICONST
Data:
110
110
Format:
FMTIN
5A4
IPRN
FMTIN
IPRN
5A4
110
110
IPRN--is
a flag indicating
that the array being read should be printed
and
a code for indicating
the format that should be used.
It is used only
if LOCAT is not equal to zero.
The format codes are different
for each
of the three modules.
IPRN is set to zero when the specified
value
If IPRN is less than zero,
exceeds those defined in the chart below.
the array will
not be printed.
IPRN
0
U2DREL
:
3
4
z
7
8
9
10
11
12
LOCAT--indicates
If LOCAT
If LOCAT
If LOCAT
the
< 0,
= 0,
> 0,
U2DINT
10611.4
10111
11610.3
9613.6
15F7.1
15F7.2
15F7.3
15F7.4
2OF5.0
20F5.1
20F5.2
20F5.3
20F5.4
10611.4
6011
4012
3013
2514
2015
UlDREL
10612.5
location
of the data which will
be put in the array.
unit number for unformatted
records.
all elements are set equal to CNSTNT or ICONST.
unit number for formatted
records.
E-l
Basic
Package Input
Input for the Basic (BAS) Package except for output control
the
in the main program.
If necessary,
unit 1 as specified
for BAS input can be changed to meet the requirements
of a
Input for the output control
option is read from
computer.
specified
in IUNIT(12).
FOR EACH SIMULATION
1. Record:
2. Record:
3. Record:
4. Data:
Format:
(BCF
HEADNG(32)
HEADNG (continued)
NROW
NPER
ITMUNI
NCOL
NLAY
IUNIT(24)
2413
WEL DRN RIV EVT xxx GHB RCH SIP xxx SIR
1
5.
6.
Record:
Array:
7.
8.
Record:
Array:
FOR EACH STRESS PERIOD
9. Data:
is read from
unit number
particular
the unit number
2
3
4
5
6
7
IAPART I STRT
IBOUND(NCOL,NROW)
(One array for each layer
HNOFLO
Shead(NCOL,NROW)
(One array for each layer
PERLEN
8
9
10
in the
grid)
in the
grid)
oc)
11 12
NSTP TSMULT
ITMUNI--is
the time unit of model data.
3 - hours
0 - undefined
4 - days
1 - seconds
5 - years
2 - minutes
Consistent
length and time units must be used for
The user
may choose
one length
unit
and one time
all
unit
model data.
to
be used
to specify
all input data.
IUNIT--is
a 24-element
table of input units for use by all major options.
IAPART--indicates
whether array BUFF is separate from array RHS.
If IAPART = 0, the arrays BUFF and RHS occupy the same space.
This
This option should be used
option conserves space.
unless some other package explicitly
says otherwise.
If IAPART f 0, the arrays BUFF and RHS occupy different
space.
ISTRT--indicates
whether starting
heads are to be saved.
heads are not saved.
If ISTRT = 0, starting
If ISTRT f 0, starting
heads are saved.
IBOUND--is the boundary array.
If IBOUND(I,J,K) < 0, cell 1,J ,K has a constant head.
If IBOUND(I ,J ,K) = 0, cell I,J,K is inactive.
If IBOUND(I,J,K) ) 0, cell I,J,K is active.
HNOFLO--is the value of head to be assigned to all inactive
cells.
m-is
head at the start
of the simulation.
PERLEN--is the length of a stress period.
NSTP--is the number of time steps in a stress
period.
fSMULT--is
the multiplier
for the length of successive
time steps.
E-2
Output
Control
Input
Input to Output Control
is read from the unit specified
in IUNIT(12).
All
printer
output goes to unit 6 as specified
in the main program.
If necessary,
the unit number for printer
output can be changed to meet the requirements
of a particular
computer.
FOR EACH SIMULATION
1. Record:
FOR EACH TIME STEP
2. Record:
IHEDFM
:
(Record
3 is
IHEDFM--is
IDDNFM--is
re,"d Ci:eiprodr
IDDNFM
I HEDUN
INCODE IHDDFL IBUDFL ICBCFL
Hdpr
Ddpr
NLAY times,
dependHy:i on ~~~"value
a code for
a code for
I DDNUN
of INCODE.)
the format in which heads will
be printed.
the format in which drawdowns will
be printed.
7 - (2DF5.0)
0 - (10611.4)
8 - (20F5.1)
1 - (11610.3)
9 - (20F5.2)
2 - (9613.6)
positive--wrap
10 - (20F5.3)
3 - (15F7.1)
4 - (15F7.2)
11 - (20F5.4)
negative--strip
12 - (10611.4)
5 - (15F7.3)
6 - (15F7.4)
IHEDUN--is the unit number on which heads will
be saved.
IDDNUN--is the unit number on which drawdowns will
be saved.
m--is
the head/drawdown ouput code.
If INCODE < 0, layer-by-layer
specifications
from the last time steps
Input item 3 is not read.
are used.
If INCODE = 0, all layers are treated
the same way.
Input item 3
will
consist
of one record.
IOFLG array will
be read.
If INCODE > 0, input item 3 will
consist
of one record for each layer.
IHDDFL--is a head and drawdown output flag.
heads nor drawdowns will
be printed
or saved.
If IHDDFL = 0, neither
If IHDDFL f 0, heads and drawdowns will be printed
or saved.
IBUDFL--is
a budget print
flag.
volumetric
budget will
not be printed.
If IBUDFL = 0, overall
If IBUDFL # 0, overall
volumetric
budget will
be printed.
ICBCFL--is
a cell-by-cell
flow-term
flag.
flow terms are not saved or printed.
If ICBCFL = 0, cell-by-cell
If ICBCFL # 0, cell-by-cell
flow terms are printed
or recorded on disk
depending on flags set in the component of flow packages,
.
IWELCB, IRCHCB, etc.
Hdpr--is
the output flab';;;
head printout.
If Hdpr = 0, head is not printed
for the corresponding
layer.
If Hdpr f 0, head is printed
for the corresponding
layer.
Ddpr--is
the output flag for drawdown printout.
for the corresponding
layer.
If Ddpr = 0, drawdown is not printed
If Ddpr f 0, drawdown is printed for the corresponding
layer.
Hdsv--is
the output flag for head save.
layer.
If Hdsv = 0, head is not saved for the corresponding
If Hdsv f 0, head is saved for the corresponding
layer.
Ddsv--is
the output flag for drawdown save.
layer.
If Ddsv = 0, drawdown is not saved for the corresponding
If Ddsv # 0, drawdown is saved for the corresponding
layer.
E-3
Block-Centered
Input
for
the BCF Package is
Flow Packaae Inout
read from the
unit
specified
in
IUNIT(1).
FOR EACH SIMULATION
IBCFCB
1. Record: ISS
LAYCON(NLAY)
(maximum of 80 layers)
Data:
2.
Format: 4012
(If there are 40 or fewer layers,
use one record.)
3.
4.
5.
Array:
Array:
Array:
All of the arrays (items
arrays for layer 2, etc.
TRPY(NLAY)
DELR(NCOL)
DELC(NROW)
6-12)
for
layer
1 are read first;
then
all
of the
IF THE SIMULATION IS TRANSIENT
sfl(NCOL NROW)
Array:
IF THE LAYER %PE CODE (LAYCON) Ii ZERO OR TWO
Tran(NCOL NROW)
Array:
IF THE LAYER GPE CODE (LAYCON) IS’ONE 0~ THREE
HY(NCOL,NROW)
8. Array:
9. Array:
BOT(NCOL,NROW)
IF THIS IS NOT THE BOTTOMLAYER
10. Array:
Vcont(NCOL,NROW)
IF THE SIMULATION IS TRANSIENT AND THE LAYER TYPE CODE (LAYCON) is TWO OR THREE
sfZ(NCOL,NROW)
11. Array:
IF THE LAYER TYPE CODE IS TWO OR THREE
12. Array:
TOP(NCOL,NROW)
ISS--is
If
the
steady-state
flag.
ISS f 0, the simulation
ISS = 0, the simulation
is steady state.
is transient.
IBCFCB--is a flag and a unit number.
If IBCFCB > 0, cell-by-cell
flow terms will
be recorded if ICBCFL
(see Output Control)
is set.
If IBCFCB = 0, cell-by-cell
flow terms will
not be printed
or recorded.
If IBCFCB < 0, print flow for constant-head
cells
if ICBCFL is set.
LAYCON--is the layer type table:
0 - confined,
1 - unconfined,
(T constant),
and 3 - confined/unconfined.
2- confined/unconfined
TRPY--is an anisotropy
factor
for each layer:
T or K along a column to T or
K along a row.
DELR--is the cell width along rows.
DELC--is the cell width along columns.
sfl--is
the primary storage factor.
En--is
the transmissivity
along rows.
ms
the hydraulic
conductivity
along rows.
m--is
the elevation
of the aquifer
bottom.
Gnt--is
the vertical
hydraulic
conductivity
divided
by the thickness
from
a layer to the layer beneath it.
sf2--is
the secondary storage factor.
m--is
the elevation
of the aquifer
top.
If
E-4
River
Input
IUNIT(4).
to the
River
(RIV)
Package Input
Package is
read from the
unit
specified
in
FOR EACH SIMULATION
I
Record: MXRIVR IRIVCB
FOR EACH STRE& PERIOD
2. Record: ITMP
Rbot
3.
Record: Layer
Row
Cond
Column Stage
(Input
item 3 normally
consists
of one record for each
river
reach.
If ITMP is negative
or zero, item 3 is not
read.)
IRIVCB--is
a flag and a unit number.
If IRIVCB > 0, cell-by-cell
flow terms will
be recorded.
If IRIVCB = 0, cell-by-cell
flow terms will
not be printed
or
recorded.
If IRIVCB < 0, river
leakage will
be printed
if ICBCFL is set.
ITMP--is a flag and a counter.
If ITMP < 0, river data from the last stress period will
be reused.
If ITMP 2
0,
ITMP
will
be
the
number
of
reaches
active
during
the
current
stress period.
Recharge
Input to the Recharge
IUNIT(8).
Package Input
(RCH) Package is
read from the
unit
specified
in
FOR EACH SIMULATION
Record: NRCHOP IRCHCB
FOR EACH STRE;J; PERIOD
2. Record: INRECH
INIRCH
Array:
RECH(NCOL NROW)
IF THE RECHAR;; OPTION IS EQUAL TO'2
4. Array:
IRCH(NCOL,NROW)
NRCHOP--is the
1 2 3 IRCHCB--is
If
If
INRECH--is
If
If
INIRCH--is
recharge option code.
Recharge is only to the top grid layer.
Vertical
distribution
of recharge is specified
in
Recharge is applied to the highest active
cell in
vertical
column.
a flag and a unit number.
IRCHCB > 0, unit number for cell-by-cell
flow terms.
IRCHCB 2 0, cell-by-cell
flow terms will
not be printed
recorded.
the RECH read flag.
INRECH < 0, recharge fluxes
from the preceding
stress
used.
INRECH L 0, an array of recharge fluxes,
RECH (Lt-l),
similar
to
INRECH.
E-5
array
each
IRCH.
or
period
is
read.
are
Well
Input
for
the Well
Package Input
(WEL) Package is
read from the
unit
specified
in
IUMIT(2).
FOR EACH SIMULATION
1. Record:
FOR EACH STRESS PERIOD
2. Record:
3. Record:
(Input
well.
MXWELL IWELCB
ITMP
Row
Column
Layer
item 3 normally
consists
of one reco:d
If ITMP is negative or zero, item 3 is
for each
not read.)
MXWELL--is
IWELCB--is
the maximum number of wells used at any time.
a flag and a unit number.
If IWELCB > 0, unit number for cell-by-cell
flow terms.
flow terms will
not be printed
or
If IWELCB = 0, cell-by-cell
recorded.
If IWELCB < 0, well recharge will be printed whenever ICBCFL is set.
ITMP--is a flag and a counter.
If ITMP < 0, well data from the last stress period will be reused.
If ITMP 2 0, ITMP will be the number of wells active during the
current
stress period.
Drain
Input
IUNIT( 3).
to the Drain
Package Input
(DRN) Package is
read from the
unit
specified
in
FOR EACH SIMULATION
IDRNCB
MXDRN
1. Record:
FOR EACH STRESS PERIOD
2. Record:
ITMP
Cond
Elevation
3. Record:
Layer
Row
co1
(Input item 3 normally consists
of one record for each drain.
If ITMP is negative
or zero, item 3 will
not be read.)
MXDRN--is the maximum
IDRNCB--is a flag and
If IDRNCB > 0,
If IDRNCB = 0,
number of drain cells
active
at one time.
a unit number.
unit number for cell-by-cell
flow terms.
cell-by-cell
flow terms will
not be printed
or
recorded.
If IDRNCB < 0, drain leakage for each cell will be printed whenever
ICBCFL is set.
ITMP--is a flag and a counter.
If ITMP < 0, drain data from the last stress period will be reused.
If ITMP 10,
ITMP will
be the number of drains active
during the current
stress period.
E-6
Evapotranspiration
Input
to the Evapotranspiration
specified
in IUNIT
(EVT) Package is
read from the
unit
(5).
FOR EACH SIMULATION
NEVTOP
1. Record:
FOR EACH STRESS
2. Record:
3. Array:
4. Array:
5. Array:
Package Input
PERIOD
I NSURF
SURF
EVTR
EXDP
IEVTCB
I NEXDP
I NEVTR
INIEVT
IF THE ET OPTION IS EQUAL TO TWO
6.
Array:
IEVT
NEVTOP--is the evapotranspiration
(ET) option code.
1 - ET is calculated
only for cells
in the top grid layer.
column is specified
by the
2 - The cell for each vertical
user in array IEVT.
IEVTCB--is
If
If
INSURF--is
If
If
a flag
and a unit
number.
number for cell-by-cell
IEVTCB 5 0, cell-by-cell
flow terms will
recorded.
IEVTCB > 0, unit
flow terms.
not be printed
or
the ET surface
(SURF) read flag.
INSURF 10,
an array containing
the ET surface elevation
will
be
read.
INSURF < 0, the ET surface from the preceding
stress
period will
be reused.
INEVTR--is
similar
to INSURF.
INEXDP--is
similar
to
INIEVT--is
similar
to INSURF.
INSURF.
E-7
General-Head
Input for
specified
the General-Head
in IUNIT(7).
Boundary
Boundary
Package Input
(GHB) Package is
read from the
unit
FOR EACH SIMULATION
IGHBCB
MXBND
1. Record:
FOR EACH STRESS PERIOD
Boundary
Record:
ITMP
2.
Cond
Head
Column
Row
3. Record:
Layer
(Input
item 3 normally
consists
of one record for each GHB.
If ITMP is negative or zero, item 3 is not read.)
MXBND--is the maximum
IGHBCB--is a flag and
If IGHBCB > 0,
If IGHBCB = 0,
number of general-head
boundary cells
at one time.
a unit number.
unit number for cell-by-cell
flow terms.
cell-by-cell
flow terms will
not be printed
or
recorded.
If IGHBCB < 0, boundary leakage for each cell will be printed
whenever ICBCFL is set.
ITMP--is
a flag and a counter.
If ITMP < 0, GHB data from the preceding stress period will be reused.
‘If ITMP 2 0, ITMP is the number of general-head
boundaries
during the
current
stress period.
Strongly
Implicit
Input to the Strongly
Implicit
unit specified
in IUNIT(9).
FOR EACH SIMULATION
MXITER
1. Record:
ACCL
2. Record:
Procedure
(SIP)
Procedure
NPARM
HCLOSE
Package Input
Package is
I PCALC
read from the
WSEED
IPRSIP
IPCALC--is
a flag indicating
where the iteration
parameter seed will
come from.
0 - the seed will
be entered by the user.
at the start
of the simulation
from
l- the seed will be calculated
problem parameters.
IPRSIP--is
the printout
interval
for SIP.
Slice-Successive
Overrelaxation
Input to the Slice-Successive
Overrelaxation
the unit specified
in IUNIT(11).
FOR EACH SIMULATION
1. Record:
2. Record:
MXITER
ACCL
HCLOSE
IPRSOR--is
interval
for
the
printout
SOR.
E-8
Q U.S. GOVERNMENT
PRINTING
OFFICE:
1988-2
0 1
-9
8 5
! 8 3 9 6 1
Package Input
(SOR) Package is
I PRSOR
read from