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A general analytical solution for steady flow in heterogeneous porous media
Author(s) -
Craig J. R.
Publication year - 2015
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2014wr016449
Subject(s) - polynomial , laplace transform , flow (mathematics) , mathematics , porous medium , mathematical analysis , matrix polynomial , calculus (dental) , porosity , geometry , engineering , geotechnical engineering , medicine , dentistry
A novel analytical solution approach for problems of steady flow in two‐dimensional heterogeneous porous media is presented, where the hydraulic conductivity may be represented as an arbitrary polynomial in space. The solution approach uses Wirtinger calculus and the Bers‐Vekua theory of elliptical functions. The final form of the solution comprises an arbitrary complex polynomial solution to the Laplace equation and additional nonholomorphic terms which are determined directly from the coefficients of this polynomial. The arbitrary polynomial coefficients may be chosen to satisfy general flow conditions along system boundaries. The approach is also extended to singular flow, such as that induced by pumping wells. The solution is demonstrated to be effectively exact for a number of test cases; the problems are solved to machine precision.