A Three-Dimensional Symmetric Positive Definite Control-Volume Distributed Multi-Point Flux Approximation for Flow Computation on Tetrahedral Grids

Abstract

A three-dimensional symmetric positive definite (SPD) cell-centred control-volume distributed multi-point flux approximation (CVD-MPFA) is presented for porous media flow simulation on tetrahedral grids. The scheme depends on a single degree of freedom per control-volume and is derived in physical space where the continuous fluxes are resolved directly along the face normals of the tetrahedra. We believe this is the first and possibly only general three-dimensional full-tensor finite-volume scheme that is flux- continuous and SPD in physical space, while depending on a single degree of freedom per control-volume. The equivalent general two-dimensional CVD-MPFA scheme that is SPD in physical space is presented in (Friis et al., 2008).