A two-fluid hyperbolic model in a porous medium
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 6, p. 1319-1348

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.

DOI : https://doi.org/10.1051/m2an/2010033
Classification:  76S05,  76M12,  65M12,  76T10
Keywords: porous medium, well-balanced scheme, analytic solution, convergence rate, two-phase flow
@article{M2AN_2010__44_6_1319_0,
     author = {Girault, La\"etitia and H\'erard, Jean-Marc},
     title = {A two-fluid hyperbolic model in a porous medium},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {6},
     year = {2010},
     pages = {1319-1348},
     doi = {10.1051/m2an/2010033},
     zbl = {pre05835024},
     mrnumber = {2769060},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2010__44_6_1319_0}
}
Girault, Laëtitia; Hérard, Jean-Marc. A two-fluid hyperbolic model in a porous medium. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 6, pp. 1319-1348. doi : 10.1051/m2an/2010033. http://www.numdam.org/item/M2AN_2010__44_6_1319_0/

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