# 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

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topGirault, 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 -

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