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Finite element discretization of Darcy's equationswith pressure dependent porosity

Published online by Cambridge University Press:  23 February 2010

Vivette Girault ,
François Murat  and
Abner Salgado
Vivette Girault
Affiliation:
UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France. girault@ann.jussieu.fr
François Murat
Affiliation:
CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France. murat@ann.jussieu.fr
Abner Salgado
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA. abnersg@math.tamu.edu
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Abstract

We consider the flow of a viscous incompressible fluid through a rigidhomogeneous porous medium. The permeability of the medium dependson the pressure, so that the model is nonlinear. We propose a finiteelement discretization of this problem and, in the case where thedependence on the pressure is bounded from above and below, we proveits convergence to the solution and propose an algorithm to solvethe discrete system. In the case where the dependenceon the pressure is exponential, we propose a splittingscheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods.


Keywords

Porous media flowsDarcy equationsfinite elements
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 6 , November 2010 , pp. 1155 - 1191
Copyright
© EDP Sciences, SMAI, 2010

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