MPFA and anisotropic diffusion
P. Kotzonis (University of Oxford, UK)
The classical two-point flux finite volume scheme and the multi-point flux O-method for solving the anisotropic diffusion equation are discussed. These schemes are widely used in the oil industry for simulating underground hydrocarbon flow. Full tensor anisotropy effects caused by non orthogonal simulation grids are observed in the two-point flux case - we observe “grid-steering” effects due to the inconsistency of the scheme. By contrast, the multi-point flux approximation is shown to be second order accurate and stable on any rectangular grid and for any anisotropy ratio. Positivity issues of the arising MPFA system matrix are also addressed.