Finite element discretization of Darcy's equations with pressure dependent porosity
KAUST Grant NumberKUS-C1-016-04
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AbstractWe consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme 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. © 2010 EDP Sciences, SMAI.
CitationGirault V, Murat F, Salgado A (2010) Finite element discretization of Darcy’s equations with pressure dependent porosity. ESAIM: Mathematical Modelling and Numerical Analysis 44: 1155–1191. Available: http://dx.doi.org/10.1051/m2an/2010019.
SponsorsThe third author is partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). Part of this work was done while the third author was visiting the Laboratoire Jacques-Louis Lions under the Study Abroad Non-Degree Reciprocal Educational Exchange Program between TAMU and UPMC. His stay was financed by the Master of the Mathematics Department of the Universite Pierre et Marie Curie (Paris VI). The authors would like to thank Prof. K.R. Rajagopal for proposing this model and suggesting to work on it.