Enriched multi-point flux approximation for general grids

It is well known that the two-point flux approximation, a numerical scheme used in most commercial reservoir simulators, has O(1) error when grids are not K-orthogonal. In the last decade, the multi-point flux approximations have been developed as a remedy. However, non-physical oscillations can appear when the anisotropy is really strong. We found out the oscillations are closely related to the poor approximation of pressure gradient in the flux computation. s paper, we propose the control volume enriched multi-point flux approximation (EMPFA) for general diffusion problems on polygonal and polyhedral meshes. Non-physical oscillations are not observed for realistic and strongly anisotropic heterogeneous material properties described by a full tensor. Exact linear solutions are recovered for grids with non-planar interfaces, and a first and second order convergence are achieved for the flux and scalar unknowns, respectively.