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Automatic simplification of Darcy’s equations with pressuredependent permeability

Published online by Cambridge University Press:  07 October 2013

Etienne Ahusborde ,
Mejdi Azaïez ,
Faker Ben Belgacem  and
Christine Bernardi
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 porousmedium provided with mixed boundary conditions. Since the boundary pressure can presenthigh variations, the permeability of the medium also depends on the pressure, so that themodel is nonlinear. A posteriori estimates allow us to omit thisdependence where the pressure does not vary too much. We perform the numerical analysis ofa spectral element discretization of the simplified model. Finally we propose a strategywhich leads to an automatic identification of the part of the domain where the simplifiedmodel can be used without increasing significantly the error.

Keywords

Darcy’s equationsspectral elementsa posteriori analysis

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 6 , November 2013 , pp. 1797 - 1820
Copyright
© EDP Sciences, SMAI 2013

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