Automatic simplification of Darcy’s equations with pressure dependent permeability

Etienne Ahusborde; Mejdi Azaïez; Faker Ben Belgacem; Christine Bernardi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 6, page 1797-1820
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Ahusborde, Etienne, et al. "Automatic simplification of Darcy’s equations with pressure dependent permeability." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.6 (2013): 1797-1820. <http://eudml.org/doc/273225>.

@article{Ahusborde2013,
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.},
author = {Ahusborde, Etienne, Azaïez, Mejdi, Ben Belgacem, Faker, Bernardi, Christine},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Darcy’s equations; spectral elements; a posteriori analysis; Darcy's equations},
language = {eng},
number = {6},
pages = {1797-1820},
publisher = {EDP-Sciences},
title = {Automatic simplification of Darcy’s equations with pressure dependent permeability},
url = {http://eudml.org/doc/273225},
volume = {47},
year = {2013},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 6
SP - 1797
EP - 1820
AB - 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.
LA - eng
KW - Darcy’s equations; spectral elements; a posteriori analysis; Darcy's equations
UR - http://eudml.org/doc/273225
ER -

References

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