High Performance Computing linear algorithms for two-phase flow in porous media

Robert Eymard (1) , Cindy Guichard (2) , Roland Masson (3, 4)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 LJLL - Laboratoire Jacques-Louis Lions
3 COFFEE - COmplex Flows For Energy and Environment
4 LJAD - Laboratoire Jean Alexandre Dieudonné

We focus here on the difficult problem of linear solving, when considering implicit scheme for two-phase flow simulation in porous media. Indeed, this scheme leads to ill-conditioned linear systems, due to the different behaviors of the pressure unknown (which follows a diffusion equation) and the saturation unknown (mainly advected by the total volumic flow). This difficulty is enhanced by the parallel computing techniques, which reduce the choice of the possible preconditioners. We first present the framework of this study, and then we discuss different algorithms for linear solving. Finally, numerical results show the performances of these algorithms.

Domaines: Analyse numérique [math.NA]

Robert Eymard, Cindy Guichard, Roland Masson. High Performance Computing linear algorithms for two-phase flow in porous media. FVCA7 - The International Symposium of Finite Volumes for Complex Applications VII, Jun 2014, Berlin, Germany. ⟨10.1007/978-3-319-05591-6_55⟩. ⟨hal-00958131⟩