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.
Mots-clés : Darcy's equations, spectral elements, a posteriori analysis
@article{M2AN_2013__47_6_1797_0,
author = {Ahusborde, Etienne and Aza{\"\i}ez, Mejdi and Ben Belgacem, Faker and Bernardi, Christine},
title = {Automatic simplification of {Darcy's} equations with pressure dependent permeability},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1797--1820},
publisher = {EDP-Sciences},
volume = {47},
number = {6},
year = {2013},
doi = {10.1051/m2an/2013089},
mrnumber = {3123377},
zbl = {1311.76128},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2013089/}
}
TY - JOUR AU - Ahusborde, Etienne AU - Azaïez, Mejdi AU - Ben Belgacem, Faker AU - Bernardi, Christine TI - Automatic simplification of Darcy's equations with pressure dependent permeability JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 1797 EP - 1820 VL - 47 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2013089/ DO - 10.1051/m2an/2013089 LA - en ID - M2AN_2013__47_6_1797_0 ER -
%0 Journal Article %A Ahusborde, Etienne %A Azaïez, Mejdi %A Ben Belgacem, Faker %A Bernardi, Christine %T Automatic simplification of Darcy's equations with pressure dependent permeability %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 1797-1820 %V 47 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2013089/ %R 10.1051/m2an/2013089 %G en %F M2AN_2013__47_6_1797_0
Ahusborde, Etienne; Azaïez, Mejdi; Ben Belgacem, Faker; Bernardi, Christine. Automatic simplification of Darcy's equations with pressure dependent permeability. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 6, pp. 1797-1820. doi : 10.1051/m2an/2013089. http://www.numdam.org/articles/10.1051/m2an/2013089/
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