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| HAL : hal-00368026, version 1 |
| DOI : 10.1016/j.cma.2009.12.014 |
| Fiche détaillée |  Récupérer au format |
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| Computer Methods in Applied Mechanics and Engineering 199, 23-24 (2010) 1491-1501 |
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| Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures |
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| Alexandre Ern 1Igor Mozolevski 2 |
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| (15/04/2010) |
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| We design and investigate a sequential discontinuous Galerkin method to approximate two-phase immiscible incompressible flows in heterogeneous porous media with discontinuous capillary pressures. The nonlinear interface conditions are enforced weakly through an adequate design of the penalties on interelement jumps of the pressure and the saturation. An accurate reconstruction of the total velocity is considered in the Raviart-Thomas(-Nedelec) finite element spaces, together with diffusivity-dependent weighted averages to cope with degeneracies in the saturation equation and with media heterogeneities. The proposed method is assessed on one-dimensional test cases exhibiting rough solutions, degeneracies, and capillary barriers. Stable and accurate solutions are obtained without limiters. |
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| 1 : | Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) |
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Ecole des Ponts ParisTech |
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| 2 : | Departamento de Matematica |
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Universidade Federal de Santa Catarina |
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| 3 : | Instituto de Matemática e Estatística (IME) |
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Universidade de São Paulo |
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| Domaine | : | Mathématiques/Analyse numérique |
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| hal-00368026, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00368026 | |
| oai:hal.archives-ouvertes.fr:hal-00368026 | |
| Contributeur : Alexandre Ern | |
| Soumis le : Vendredi 13 Mars 2009, 12:03:44 | |
| Dernière modification le : Mercredi 2 Novembre 2011, 17:23:28 | |
