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Automatic simplification of Darcy’s equations with pressure dependent permeability

Published online by Cambridge University Press:  07 October 2013

Etienne Ahusborde
Affiliation:
Laboratoire de Mathématiques et de leurs Applications (U.M.R. 5142 CNRS), Bâtiment IPRA, Université de Pau et des Pays de l’Adour, avenue de l’Université, B.P. 1155, 64013 Pau Cedex, France.. etienne.ahusborde@univ-pau.fr
Mejdi Azaïez
Affiliation:
Université de Bordeaux, I2M (UMR C.N.R.S. 5295), 33405 Talence, France.; azaiez@ipb.fr
Faker Ben Belgacem
Affiliation:
LMAC (E.A. 2222), Université de Technologie de Compiègne, B.P. 20529, 60205 Compiègne Cedex, France, and Université de Bordeaux, I2M (UMR C.N.R.S. 5295), 33405 Talence, France.; faker.ben-belgacem@utc.fr
Christine Bernardi
Affiliation:
Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France.; bernardi@ann.jussieu.fr
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Abstract

We consider the flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with mixed boundary conditions. Since the boundary pressure can present high variations, the permeability of the medium also depends on the pressure, so that the model is nonlinear. A posteriori estimates allow us to omit this dependence where the pressure does not vary too much. We perform the numerical analysis of a spectral element discretization of the simplified model. Finally we propose a strategy which leads to an automatic identification of the part of the domain where the simplified model can be used without increasing significantly the error.

Type
Research Article
Copyright
© EDP Sciences, SMAI 2013

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