Design of Coupled Finite Volume Schemes Minimizing the Grid Orientation Effect in Reservoir Simulation

In this paper, we present and compare two nine-point finite volume schemes to reduce the so-called grid orientation effect (GOE) which occurs in the simulation of unstable two phase flow in porous media. The first scheme is a more classical nine-point scheme with one tuning parameter whereas the second one, more original, uses two parameters (one per direction). A numerical test problem testify to the improvement brought by the new scheme.