Anisotropy favoring triangulation CVD(MPFA) finite-volume approximations

A family of flux-continuous, control-volume distributed multi-point flux approximation schemes CVD (MPFA) have been developed for solving the general geometry-permeability tensor pressure equation on structured and unstructured grids (Comput. Geo. 1998; 2: 259-290, Comput. Geo. 2002; 6: 433-452). The locally conservative schemes are applicable to the diagonal and 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 quantified by a quadrature parameterization. Improved numerical convergence for the family of CVD(MPFA) schemes for specified quadrature points has been observed for lower anisotropy ratios for both structured and unstructured grids in two dimensions. However, for strong full-tensor anisotropy fields the quadrilateral schemes can induce strong spurious oscillations in the numerical solution. This paper motivates and demonstrates the benefit of using anisotropy favoring triangulation for treating such cases. Test examples involving strong full-tensor anisotropy fields are presented in 2-D and 3-D, which show that the family of schemes on anisotropy favoring triangulation (prisms in 3-D) yield well-resolved pressure fields with little or no spurious oscillations. Copyright (C) 2010 John Wiley & Sons, Ltd.