CE 475 INTRODUCTION TO GROUNDWATER MODELLING
Computer Laboratory Session No. 7
One-dimensional unsteady flow in a finite confined aquifer: Solution by explicit finite
difference:
t=0
h0
t>0
hL
T, S
L
Mathematical Model
Governing Differential Equation:
2 h
x2

S h
T t
(1)
Initial Condition:
hx, 0 h o
, 0 x  L
(2)
Boundary Condition:
h0, t  h o
,
t 0
(3)
hL, t  h L
,
t 0
(4)
Explicit Finite Difference Approximation

h ih1  h ik  Tt 2 h ik1 2h ik h ik1
Sx 

(5)
Solution
a) Solution by a computer program:
A computer program which solves this model using Eq. 5 is given as an
executable file. The source program is also provided. By running the program the
values of piezometric head at different nodes and at different times can be obtained.
b) Solution by a spreadsheet program:
The solution of the same problem can be achieved using a spreadsheet program
in a more flexible way. The spreadsheet file is provided.
Tasks to be performed:
Consider the following data:
ho = 16 m
hL = 11 m
T = 0.02 m2/min
S = 0.002
L = 100 m
x = 10 m
t = 5 min
a)
Run the computer program for these model parameters and print the results.
b)
Input the model parameters into the spreadsheet. Obtain the results and compare
them with the results of Fortran program.
c)
Plot the piezometric head as a function of time at one or more nodes.
d)
Plot the piezometric head as a function of distance at some selected times.
e)
Compare the numerical solution for late times with the steady-state analytical
solution.
To see the solution click here.