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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

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EARLY PIONEERS OF GROUNDWATER FLOW

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Henry Philibert Gaspard Darcy ( ) Darcys Law (1856)

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Arsene Jules Emile Juvenal Dupuit ( ) Steady state flow toward pumping well in unconfined and confined aquifers (1863) Dupuit Approximation

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Philip Forchheimer ( ) Laplace equation (1886)

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Charles V. Theis ( ) 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,

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LEAKY AQUIFER THEORY

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Charles E. Jacob (?-1970) Jacob, C. E. (1946), Radial flow in a leaky artesian aquifer, Transactions, American Geophysical Union, 27(2),

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Mahdi S. Hantush (1921–1984) Hantush, M. S., and C. E. Jacob (1955), Non- steady radial flow in an infinite leaky aquifer, Transactions, American Geophysical Union, 36(1),

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MULTILAYERED AQUIFER SYSTEM

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S.P. Neuman & P.A. Witherspoon (1969)

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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), Herrera, I. (1970), Theory of multiple leaky aquifers, Water Resources Research, 6(1), Herrera, I., and L. Rodarte (1972), Computations using a simplified theory of multiple leaky aquifers, Geofisica International, 12(2), 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), Herrera, I. (1974), Integrodifferential equations for systems of leaky aquifers and applications.2. Error analysis of approximate theories, Water Resources Research, 10(4), Herrera, I. (1976), A review of the integrodifferential equations appraoch to leaky aquifer mechanics, Advances in Groundwater Hydrology, September, 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), Herrera, I., A. Minzoni, and E. Z. Flores (1978), Theory of flow in unconfined aquifers by integrodifferential equations, Water Resources Research, 14(2), Herrera, I., J. P. Hennart, and R. YATE (1980), A critical discussion of numerical models for muItiaquifer systems, Advances in Water Resources, 3, Hennart, J. P., R. Yates, and I. Herrera (1981), Extension of the integrodifferential approach to inhomogeneous multi-aquifer systems, Water Resources Research, 17(4), Chen, B., and I. Herrera (1982), Numerical treatment of leaky aquifers in the short-time range, Water Resources Research, 18(3),

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MATHEMATICAL FORMULATION AND NUMERICAL SOLUTION

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Solution Mesh for General Groundwater Problem (3 Spatial + 1 Temporal = 4D)

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Neuman-Witherspoon Formulation

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(3 spatial + 1 temporal) = 4D

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Herrera Integro-Differential Formulation

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(2 Spatial + 1 Temporal) = 3D

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MY ACQUAINTANCE WITH PROF. HERRERA

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Cheng & Ou (1989) Laplace Transform + FDM

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2 Spatial Dimension = 2D

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Cheng & Morohunfola (1993) Laplace Transform + BEM (1 Spatial Dimension)

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1 Spatial Dimension = 1D

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Greens Function (Pumping Well Solution)

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Two Aquifer One Aquitard System

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OTHER COLLABORATIONS AND COMMON RESEARCH AREAS

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Trefftz Method Walter Ritz (1878–1909) Erich Trefftz ( ) Trefftz, E. (1926), Ein Gegenstück zum Ritzschen verfahren (A counterpart to Ritz method), in Verh d.2. Intern Kongr f Techn Mech (Proc. 2nd Int. Congress Applied Mechanics), edited, pp , Zurich. Ritzs 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. Trefftzs contribution was to use the general solutions of the partial differential equation as trial functions. Cheng & Cheng (2005), History of BEM

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International Workshop on the Trefftz Method First Workshop: Cracow, May 30-June 1, Second Workshop: Sintra, Portugal, September Third Workshop: University of Exeter, UK, September Fourth Workshop: University of Zilina, Slovakia, August Fifth Workshop: Katholieke Universiteit Leuven, Belgium, Trefftz/MFS 2011: National Sun Yat-sen University, Taiwan, 2011.

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