Quasi-K-Orthogonal Grid Generation for Quasi-Positive CVD-MPFA

Abstract

Summary A novel Quasi K-orthogonal grid generation method is presented, where the grid is designed to ensure that linear control-volume distributed multi-point flux approximation (CVD-MPFA) methods retain a discrete quasi positive approximation. The quasi K-orthogonal grid generation method improves grid quality and method stability with respect to flux approximation in the presence of strongly anisotropic full-tensor permeability fields. K-orthogonal grid generation is only possible for relatively low anisotropy ratios. Quasi K-orthogonal grid generation involves satisfying the K-orthogonal condition approximately, resulting in practical grids that place less demand on an approximation with respect to stability conditions, and therefore improve grid quality with respect to flux approximation in the presence of anisotropic permeability fields. The standard two-point flux approximation (TPFA) requires strict K-orthogonality for consistency, consequently CVD-MPFA schemes which are consistent on non k-orthogonal meshes are still required as the grids are only approximately K-orthogonal in such cases. The grid generation employed enables Delaunay grid generation principles to be employed in a locally transformed system according to local permeability tensor variation. The resulting method has great flexibility for handling complex geometries and can handle jumps in permeability tensor principal axes orientation and jumps in coefficients and details will be presented. Results are presented that demonstrate the benefit of the quasi K-orthogonal grid generator. Highly challenging cases involving strong full-tensor permeability fields are tested, where CVD-MPFA schemes exceed their stability limits and yield solutions with spurious oscillations when using conventional grids. In contrast when employing the new quasi K-orthogonal grids, the CVD-MPFA schemes yield well resolved solutions that are free of visible spurious oscillations.