A general analytical solution for steady flow in heterogeneous porous media. Issue 6 (11th June 2015)

• Record Type: Journal Article
• Authors: Craig, J. R.
• Is Part Of: Water resources research. Volume 51:Issue 6(2015:Jun.)
• Page Start: 4184
• Page End: 4197
• Publication Date: 2015-06-11
• Subjects: Hydrology -- Periodicals; 333.91
• DOI: 10.1002/2014WR016449
• Languages: English
• ISSNs: 0043-1397

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>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.</p> </abstract>