 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10482 |
| In Russian (ΟΜΜ): | | 9683
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 73, Issue 4 / 2009 | Next article >> |
| 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, ildar.badriev@ksu.ru)
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 |
| Link to Fulltext |
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