Finite element discretization of Darcy's equations with pressure dependent porosity

Handle URI:
http://hdl.handle.net/10754/598328
Title:
Finite element discretization of Darcy's equations with pressure dependent porosity
Authors:
Girault, Vivette; Murat, François; Salgado, Abner
Abstract:
We 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.
Citation:
Girault 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.
Publisher:
EDP Sciences
Journal:
ESAIM: Mathematical Modelling and Numerical Analysis
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
23-Feb-2010
DOI:
10.1051/m2an/2010019
Type:
Article
ISSN:
0764-583X; 1290-3841
Sponsors:
The 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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorGirault, Vivetteen
dc.contributor.authorMurat, Françoisen
dc.contributor.authorSalgado, Abneren
dc.date.accessioned2016-02-25T13:18:48Zen
dc.date.available2016-02-25T13:18:48Zen
dc.date.issued2010-02-23en
dc.identifier.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.en
dc.identifier.issn0764-583Xen
dc.identifier.issn1290-3841en
dc.identifier.doi10.1051/m2an/2010019en
dc.identifier.urihttp://hdl.handle.net/10754/598328en
dc.description.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.en
dc.description.sponsorshipThe 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.en
dc.publisherEDP Sciencesen
dc.subjectDarcy equationsen
dc.subjectFinite elementsen
dc.subjectPorous media flowsen
dc.titleFinite element discretization of Darcy's equations with pressure dependent porosityen
dc.typeArticleen
dc.identifier.journalESAIM: Mathematical Modelling and Numerical Analysisen
dc.contributor.institutionUniversite Pierre et Marie Curie, Paris, Franceen
dc.contributor.institutionCNRS Centre National de la Recherche Scientifique, Paris, Franceen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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