Solution of plane seepage problems for a multivalued seepage law when there is a point source

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作者：
Badriyev, I.B.
Zadvornov, O.A.
Ismagilov, L.N.
Skvortsov, E.V.
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Journal of Applied Mathematics and Mechanics | 2009年 / 73卷 / 04期
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The steady seepage of an incompressible fluid in a uniform porous medium; occupying an arbitrary bounded two-dimensional region; when there is a point source present is considered. Part of the boundary of the region is free; while the remaining part is impermeable for the fluid. It is assumed that the function defining the seepage law is multivalued and has a linear increase at infinity. A generalized formulation of the problem is proposed in the form of a variational inequality of the second kind. An approximate solution of the problem is obtained by an iterative splitting method; which enables approximate values of both the solution itself (the pressure) and its gradient to be found. Analytic expressions describing the boundaries of the region where the modulus of the pressure gradient takes a constant value are obtained for model problems of a line of bore holes. Numerical experiments are carried out for model problems; which confirm the effectiveness of the proposed method. Good agreement is observed between the results of calculations obtained analytically and by approximate methods. © 2009 Elsevier Ltd. All rights reserved;
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页码：434 / 442
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