Quasi-K-Orthogonal Grid Generation

Abstract

Abstract Quasi K-orthogonal grid generation is presented, to improve 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 low anisotropy ratios. Quasi K-orthogonal grid generation involves satisfying the K-orthogonal condition approximately, resulting in 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 method 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 a quasi K-orthogonal grid. Highly challenging cases involving strong full-tensor permeability fields where control-volume distributed multi-point flux approximation (CVD-MPFA) schemes exceed their stability limits and yield solutions with spurious oscillations when using conventional grids, are solved using the new grid generation method. CVD-MPFA schemes are still required as the grids are only approximately K-orthogonal in such cases, however the schemes retain a discrete maximum principle on the new quasi-K-orthogonal grids and yield well resolved solutions that are free of spurious oscillations. While the two-point flux approximation (TPFA) requires strict K-orthogonality, results using both CVD-MPFA and TPFA will be presented. New Quasi K-orthogonal grid generation methods are presented that satisfy the K-orthogonal condition approximately, resulting in practical grids that restore a discrete maximum principle (stability) for the CVD-MPFA schemes when applied to cases involving general full-tensor permeability fields. Results are presented for a variety of test cases that confirm the validity of the grids.