A two-fluid hyperbolic model in a porous medium

Laëtitia Girault; Jean-Marc Hérard

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 6, page 1319-1348
  • ISSN: 0764-583X

Abstract

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The paper is devoted to the computation of two-phase flows in a porous medium when applying the two-fluid approach. The basic formulation is presented first, together with the main properties of the model. A few basic analytic solutions are then provided, some of them corresponding to solutions of the one-dimensional Riemann problem. Three distinct Finite-Volume schemes are then introduced. The first two schemes, which rely on the Rusanov scheme, are shown to give wrong approximations in some cases involving sharp porous profiles. The third one, which is an extension of a scheme proposed by Kröner and Thanh [SIAM J. Numer. Anal. 43 (2006) 796–824] for the computation of single phase flows in varying cross section ducts, provides fair results in all situations. Properties of schemes and numerical results are presented. Analytic tests enable to compute the L1 norm of the error.

How to cite

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Girault, Laëtitia, and Hérard, Jean-Marc. "A two-fluid hyperbolic model in a porous medium." ESAIM: Mathematical Modelling and Numerical Analysis 44.6 (2010): 1319-1348. <http://eudml.org/doc/250832>.

@article{Girault2010,
abstract = { The paper is devoted to the computation of two-phase flows in a porous medium when applying the two-fluid approach. The basic formulation is presented first, together with the main properties of the model. A few basic analytic solutions are then provided, some of them corresponding to solutions of the one-dimensional Riemann problem. Three distinct Finite-Volume schemes are then introduced. The first two schemes, which rely on the Rusanov scheme, are shown to give wrong approximations in some cases involving sharp porous profiles. The third one, which is an extension of a scheme proposed by Kröner and Thanh [SIAM J. Numer. Anal. 43 (2006) 796–824] for the computation of single phase flows in varying cross section ducts, provides fair results in all situations. Properties of schemes and numerical results are presented. Analytic tests enable to compute the L1 norm of the error. },
author = {Girault, Laëtitia, Hérard, Jean-Marc},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Porous medium; well-balanced scheme; analytic solution; convergence rate; two-phase flow.; porous medium; two-phase flow},
language = {eng},
month = {10},
number = {6},
pages = {1319-1348},
publisher = {EDP Sciences},
title = {A two-fluid hyperbolic model in a porous medium},
url = {http://eudml.org/doc/250832},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Girault, Laëtitia
AU - Hérard, Jean-Marc
TI - A two-fluid hyperbolic model in a porous medium
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/10//
PB - EDP Sciences
VL - 44
IS - 6
SP - 1319
EP - 1348
AB - The paper is devoted to the computation of two-phase flows in a porous medium when applying the two-fluid approach. The basic formulation is presented first, together with the main properties of the model. A few basic analytic solutions are then provided, some of them corresponding to solutions of the one-dimensional Riemann problem. Three distinct Finite-Volume schemes are then introduced. The first two schemes, which rely on the Rusanov scheme, are shown to give wrong approximations in some cases involving sharp porous profiles. The third one, which is an extension of a scheme proposed by Kröner and Thanh [SIAM J. Numer. Anal. 43 (2006) 796–824] for the computation of single phase flows in varying cross section ducts, provides fair results in all situations. Properties of schemes and numerical results are presented. Analytic tests enable to compute the L1 norm of the error.
LA - eng
KW - Porous medium; well-balanced scheme; analytic solution; convergence rate; two-phase flow.; porous medium; two-phase flow
UR - http://eudml.org/doc/250832
ER -

References

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