Coupling Darcy and Stokes equations for porous media with cracks

Christine Bernardi; Frédéric Hecht; Olivier Pironneau

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 39, Issue: 1, page 7-35
  • ISSN: 0764-583X

Abstract

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In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization and derive a priori and a posteriori error estimates. We present some numerical experiments that are in good agreement with the analysis.

How to cite

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Bernardi, Christine, Hecht, Frédéric, and Pironneau, Olivier. "Coupling Darcy and Stokes equations for porous media with cracks." ESAIM: Mathematical Modelling and Numerical Analysis 39.1 (2010): 7-35. <http://eudml.org/doc/194260>.

@article{Bernardi2010,
abstract = { In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization and derive a priori and a posteriori error estimates. We present some numerical experiments that are in good agreement with the analysis. },
author = {Bernardi, Christine, Hecht, Frédéric, Pironneau, Olivier},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Darcy and Stokes equations; finite elements; error estimates.; finite element discretization; error estimates; interface pressure continuity},
language = {eng},
month = {3},
number = {1},
pages = {7-35},
publisher = {EDP Sciences},
title = {Coupling Darcy and Stokes equations for porous media with cracks},
url = {http://eudml.org/doc/194260},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Bernardi, Christine
AU - Hecht, Frédéric
AU - Pironneau, Olivier
TI - Coupling Darcy and Stokes equations for porous media with cracks
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 1
SP - 7
EP - 35
AB - In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization and derive a priori and a posteriori error estimates. We present some numerical experiments that are in good agreement with the analysis.
LA - eng
KW - Darcy and Stokes equations; finite elements; error estimates.; finite element discretization; error estimates; interface pressure continuity
UR - http://eudml.org/doc/194260
ER -

References

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