Automatic simplification of Darcy's equations with pressure dependent permeability
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 6, p. 1797-1820

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.

DOI : https://doi.org/10.1051/m2an/2013089
Classification:  76S05,  65N35
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {47},
number = {6},
year = {2013},
pages = {1797-1820},
doi = {10.1051/m2an/2013089},
zbl = {1311.76128},
mrnumber = {3123377},
language = {en},
url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 6, pp. 1797-1820. doi : 10.1051/m2an/2013089. http://www.numdam.org/item/M2AN_2013__47_6_1797_0/

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