A family of multi-point flux approximation schemes for general element types in two and three dimensions with convergence performance

A family of flux-continuous, locally conservative, control-volume-distributed multi-point flux approximation (CVD-MPFA) schemes has been developed for solving the general geometry-permeability tensor pressure equation on structured and unstructured grids. These schemes are applicable to the full-tensor pressure equation with generally discontinuous coefficients and remove the O(1) errors introduced by standard reservoir simulation schemes when applied to full-tensor flow approximation. The family of flux-continuous schemes is characterized by a quadrature parameterization. Improved numerical convergence for the family of CVD-MPFA schemes using the quadrature parameterization has been observed for structured and unstructured grids in two dimensions. The CVD-MPFA family cell-vertex formulation is extended to classical general element types in 3-D including prisms, pyramids, hexahedra and tetrahedra. A numerical convergence study of the CVD-MPFA schemes on general unstructured grids comprising of triangular elements in 2-D and prismatic, pyramidal, hexahedral and tetrahedral shape elements in 3-D is presented. Copyright (c) 2011 John Wiley & Sons, Ltd.