Discretization on quadrilateral grids with improved monotonicity properties

Multi-point flux approximation (MPFA) discretization methods have been applied in the oil industry since the mid 1990s. The discretizations are based on a control volume formulation and the finite difference structure makes general skew grids and unstructured grids feasible in a fully implicit formulation. MPFA methods are therefore suitable for flow problems in realistic reservoirs. Monotonicity issues are known to arise for high aspect ratios combined with skewness of computational grids for MPFA methods. In this paper, we improve the MPFA discretization techniques for general quadrilateral grids, such that the above difficulties are handled to give a more robust discretization of the governing equations for fluid flow in porous media. Comparisons to the MPFA O-method are made, and the suggested discretization is shown to be an improvement in regards to monotonicity. For smooth solutions, the method performs equally well as the O-method when the convergence is examined.