Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version)

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IssuesArchive of Issues2009-4pp.434-442

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Total articles in the database: 5078
In Russian (ΟΜΜ): 4279
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I.B. Badriyev, O.A. Zadvornov, L.N. Ismagilov, and E.V. Skvortsov, "Solution of plane seepage problems for a multivalued seepage law when there is a point source," J. Appl. Math. Mech. 73 (4), 434-442 (2009)
Year 2009 Volume 73 Issue 4 Pages 434-442
Title Solution of plane seepage problems for a multivalued seepage law when there is a point source
Author(s) I.B. Badriyev (Kazan, Russia,
O.A. Zadvornov (Kazan, Russia)
L.N. Ismagilov (Kazan, Russia)
E.V. Skvortsov (Kazan, Russia)
Abstract 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.
Received 11 March 2008
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