Comptes Rendus
no. 9-10
Numerical Analysis
Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows

Presented by: Olivier Pironneau

Alexandre Ern1; Igor Mozolevski1, 2; L. Schuh3
1 Université Paris-Est, CERMICS, École des ponts, 6 & 8, avenue B. Pascal, 77455 Marne-la-Vallée cedex 2, France
2 Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900, Florianópolis-SC, Brasil
3 IME, Universidade de São Paulo, Rua do Matão, 1010, Cidade Universitária, 05508-090, São Paulo, SP, Brasil
Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 551-554.

We consider Discontinuous Galerkin approximations of two-phase, immiscible porous media flows in the global pressure/fractional flow formulation with capillary pressure. A sequential approach is used with a backward Euler step for the saturation equation, equal-order interpolation for the pressure and the saturation, and without any limiters. An accurate total velocity field is recovered from the global pressure equation to be used in the saturation equation. Numerical experiments show the advantages of the proposed reconstruction.

Nous considérons une méthode de Galerkine discontinue pour approcher les écoulements diphasiques non-miscibles en milieu poreux dans la formulation en pression globale. Une approche séquentielle est utilisée avec un schéma d'Euler implicite pour l'équation de la saturation, le même ordre polynomial pour la pression et la saturation, et en l'absence de limiteurs. Nous montrons comment reconstruire à partir de l'équation en pression une vitesse totale précise pour l'équation de la saturation. Des exemples numériques illustrent les avantages de l'approche proposée.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.02.011

Alexandre Ern 1; Igor Mozolevski 1, 2; L. Schuh 3

1 Université Paris-Est, CERMICS, École des ponts, 6 & 8, avenue B. Pascal, 77455 Marne-la-Vallée cedex 2, France
2 Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900, Florianópolis-SC, Brasil
3 IME, Universidade de São Paulo, Rua do Matão, 1010, Cidade Universitária, 05508-090, São Paulo, SP, Brasil 
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     title = {Accurate velocity reconstruction for {Discontinuous} {Galerkin} approximations of two-phase porous media flows},
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Alexandre Ern; Igor Mozolevski; L. Schuh. Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows. Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 551-554. doi : 10.1016/j.crma.2009.02.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.02.011/

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