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Ismael Herrera and Multilayered Aquifer Theory

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.

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Ismael Herrera and Multilayered Aquifer Theory

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  1. Ismael Herrera andMultilayered 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

  2. Early pioneers of groundwater Flow

  3. Henry Philibert Gaspard Darcy(1803-1858) Darcy’s Law (1856)

  4. Arsene Jules Emile JuvenalDupuit (1804-1866) Dupuit Approximation Steady state flow toward pumping well in unconfined and confined aquifers (1863)

  5. Philip Forchheimer(1852-1933) Laplace equation (1886)

  6. 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.

  7. Leaky aquifer theory

  8. Charles E. Jacob (?-1970) Jacob, C. E. (1946), Radial flow in a leaky artesian aquifer, Transactions, American Geophysical Union, 27(2), 198-205.

  9. 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), 95-100.

  10. Multilayered aquifer system

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

  12. I. Herrera (1969, 1970)

  13. 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.

  14. Mathematical formulation and numerical solution

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

  16. Neuman-Witherspoon Formulation

  17. (3 spatial + 1 temporal) = 4D

  18. Herrera Integro-Differential Formulation

  19. (2 Spatial + 1 Temporal) = 3D

  20. My acquaintance with Prof. Herrera

  21. Cheng & Ou (1989) Laplace Transform + FDM

  22. 2 Spatial Dimension = 2D

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

  24. 1 Spatial Dimension = 1D

  25. Green’s Function (Pumping Well Solution)

  26. Two Aquifer One Aquitard System

  27. Other collaborations and common research areas

  28. Trefftz Method “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 Walter Ritz (1878–1909) Erich Trefftz (1888-1937) Trefftz, E. (1926), EinGegenstückzumRitz’schenverfahren (A counterpart to Ritz method), in Verh d.2. Intern Kongr f TechnMech (Proc. 2nd Int. Congress Applied Mechanics), edited, pp. 131-137, Zurich.

  29. International Workshop on the TrefftzMethod 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: KatholiekeUniversiteit Leuven, Belgium, 2008. Trefftz/MFS 2011: National Sun Yat-sen University, Taiwan, 2011.

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