Issue |
ESAIM: M2AN
Volume 47, Number 6, November-December 2013
|
|
---|---|---|
Page(s) | 1797 - 1820 | |
DOI | https://doi.org/10.1051/m2an/2013089 | |
Published online | 07 October 2013 |
Automatic simplification of Darcy’s equations with pressure dependent permeability
1 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
2 Université de Bordeaux, I2M (UMR
C.N.R.S. 5295), 33405
Talence,
France.
azaiez@ipb.fr
3 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
4 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
Received:
19
October
2011
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.
Mathematics Subject Classification: 76S05 / 65N35
Key words: Darcy’s equations / spectral elements / a posteriori analysis
© EDP Sciences, SMAI 2013
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