Finite element discretization of Darcy's equations with pressure dependent porosity

Vivette Girault; François Murat; Abner Salgado

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 6, page 1155-1191
  • ISSN: 0764-583X

Abstract

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We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods.


How to cite

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Girault, Vivette, Murat, François, and Salgado, Abner. "Finite element discretization of Darcy's equations with pressure dependent porosity." ESAIM: Mathematical Modelling and Numerical Analysis 44.6 (2010): 1155-1191. <http://eudml.org/doc/250842>.

@article{Girault2010,
abstract = { We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods.
},
author = {Girault, Vivette, Murat, François, Salgado, Abner},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Porous media flows; Darcy equations; finite elements; exponential porosity; bounded porosity; convergence; splitting scheme},
language = {eng},
month = {10},
number = {6},
pages = {1155-1191},
publisher = {EDP Sciences},
title = {Finite element discretization of Darcy's equations with pressure dependent porosity},
url = {http://eudml.org/doc/250842},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Girault, Vivette
AU - Murat, François
AU - Salgado, Abner
TI - Finite element discretization of Darcy's equations with pressure dependent porosity
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/10//
PB - EDP Sciences
VL - 44
IS - 6
SP - 1155
EP - 1191
AB - We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods.

LA - eng
KW - Porous media flows; Darcy equations; finite elements; exponential porosity; bounded porosity; convergence; splitting scheme
UR - http://eudml.org/doc/250842
ER -

References

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