Grid Orientation Effect in coupled Finite Volume Schemes

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

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 IFPEN - IFP Energies nouvelles
3 JAD - Laboratoire Jean Alexandre Dieudonné

The numerical simulation of two-phase flow in a porous medium may lead, when using structured grids, to the apparition of the so-called Grid Orientation Effect (GOE). We propose in this paper a procedure to eliminate this phenomenon, based on the use of new fluxes with a new stencil in the discrete version of the convection equation, without changing the discrete scheme for computing the pressure field. A mathematical study, based on a weak BV inequality using the new fluxes, shows the convergence of the modified scheme in a particular case. Finally, numerical results show the efficiency and the accuracy of the method.

Mots clés: oil reservoir simulation; grid orientation effect; scalar hyperbolic equations; weak BV inequality

Domaines: Analyse numérique [math.NA]

Robert Eymard, Cindy Guichard, Roland Masson. Grid Orientation Effect in coupled Finite Volume Schemes. 2011. ⟨hal-00623721v1⟩