Ismael Herrera and
Multilayered Aquifer Theory
By Alex Cheng, University of Mississippi
Simposio Ismael Herrera Avances en Modelación
Matemática en Ingeniería y Geosistemas
UNAM, Mexico, Miércoles 28 de septiembre
EARLY PIONEERS OF
GROUNDWATER FLOW
Henry Philibert Gaspard Darcy
(1803-1858)
Darcy’s Law
(1856)
Arsene Jules Emile Juvenal Dupuit
(1804-1866)
Dupuit Approximation
Steady state flow toward
pumping well in unconfined
and confined aquifers (1863)
Philip Forchheimer
(1852-1933)
Laplace equation
(1886)
Charles V. Theis
(1900-1987)
Theis, C. V. (1935), The relation between the lowering of the
piezometric surface and the rate and duration of discharge of a
well using ground water storage, Transactions-American
Geophysical Union, 16, 519-524.
LEAKY AQUIFER THEORY
Charles E. Jacob (?-1970)
Jacob, C. E. (1946), Radial flow in a leaky
artesian aquifer, Transactions, American
Geophysical Union, 27(2), 198-205.
Mahdi S. Hantush (1921–1984)
Hantush, M. S., and C. E. Jacob (1955), Nonsteady radial flow in an infinite leaky aquifer,
Transactions, American Geophysical Union,
36(1), 95-100.
MULTILAYERED AQUIFER SYSTEM
S.P. Neuman & P.A. Witherspoon (1969)
I. Herrera (1969, 1970)
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Herrera, I., and G. E. Figueroa (1969), A correspondence principle for theory of leaky aquifers,
Water Resources Research, 5(4), 900-904.
Herrera, I. (1970), Theory of multiple leaky aquifers, Water Resources Research, 6(1), 185-193.
Herrera, I., and L. Rodarte (1972), Computations using a simplified theory of multiple leaky
aquifers, Geofisica International, 12(2), 71-87.
Herrera, I., and L. Rodarte (1973), Integrodifferential equations for systems of leaky aquifers and
applications .1. Nature of approximate theories, Water Resources Research, 9(4), 995-1004.
Herrera, I. (1974), Integrodifferential equations for systems of leaky aquifers and applications .2.
Error analysis of approximate theories, Water Resources Research, 10(4), 811-820.
Herrera, I. (1976), A review of the integrodifferential equations appraoch to leaky aquifer
mechanics, Advances in Groundwater Hydrology, September, 29-47.
Herrera, I., and R. Yates (1977), Integrodifferential equations for systems of leaky aquifers and
applications .3. Numerical-methods of unlimited applicability, Water Resources Research, 13(4),
725-732.
Herrera, I., A. Minzoni, and E. Z. Flores (1978), Theory of flow in unconfined aquifers by
integrodifferential equations, Water Resources Research, 14(2), 291-297.
Herrera, I., J. P. Hennart, and R. YATE (1980), A critical discussion of numerical models for
muItiaquifer systems, Advances in Water Resources, 3, 159-163.
Hennart, J. P., R. Yates, and I. Herrera (1981), Extension of the integrodifferential approach to
inhomogeneous multi-aquifer systems, Water Resources Research, 17(4), 1044-1050.
Chen, B., and I. Herrera (1982), Numerical treatment of leaky aquifers in the short-time range,
Water Resources Research, 18(3), 557-562.
MATHEMATICAL FORMULATION
AND NUMERICAL SOLUTION
Solution Mesh for General Groundwater
Problem (3 Spatial + 1 Temporal = 4D)
Neuman-Witherspoon Formulation
(3 spatial + 1 temporal) = 4D
Herrera Integro-Differential
Formulation
(2 Spatial + 1 Temporal) = 3D
MY ACQUAINTANCE WITH
PROF. HERRERA
Cheng & Ou (1989) Laplace Transform +
FDM
2 Spatial Dimension = 2D
Cheng & Morohunfola (1993) Laplace
Transform + BEM (1 Spatial Dimension)
1 Spatial Dimension = 1D
Green’s Function
(Pumping Well Solution)
Two Aquifer One Aquitard System
OTHER COLLABORATIONS AND
COMMON RESEARCH AREAS
Trefftz Method
Walter Ritz
(1878–1909)
“Ritz’s idea was to use variational
method and trial functions to minimize a
functional, in order to find approximate
solutions of boundary value problems.
Typically, trial functions are polynomials
or elementary functions. Trefftz’s
contribution was to use the general
solutions of the partial differential
equation as trial functions.” Cheng &
Cheng (2005), History of BEM
Trefftz, E. (1926), Ein Gegenstück zum Ritz’schen
verfahren (A counterpart to Ritz method), in Verh d.2.
Intern Kongr f Techn Mech (Proc. 2nd Int. Congress
Applied Mechanics), edited, pp. 131-137, Zurich.
Erich Trefftz
(1888-1937)
International Workshop on the
Trefftz Method
First Workshop: Cracow, May 30-June 1,
1996.
Second Workshop: Sintra, Portugal,
September 1999.
Third Workshop: University of Exeter, UK,
16-18 September 2002.
Fourth Workshop: University of Zilina,
Slovakia, 23-26 August 2005.
Fifth Workshop: Katholieke Universiteit
Leuven, Belgium, 2008.
Trefftz/MFS 2011: National Sun Yat-sen
University, Taiwan, 2011.