Higher‐resolution hyperbolic‐coupled‐elliptic flux‐continuous CVD schemes on structured and unstructured grids in 2‐D

Higher‐order convection schemes have been developed for the essentially hyperbolic systems of reservoir simulation and can significantly enhance solution quality. Locally conservative full‐tensor flux‐continuous finite‐volume schemes have also been developed for the porous medium pressure equation with general geometry and permeability tensors on structured and unstructured grids. These schemes remove O (1) errors induced by standard methods, and are now recognized as an essential component of any numerical method designed for reservoir simulation and modelling flow in porous media. In this paper, novel higher‐resolution hyperbolic conservation law schemes, designed for convective flux approximation on unstructured grids are coupled with general full‐tensor continuous Darcy flux approximations. The schemes are developed for multi‐phase flow in porous media. Benefits in terms of improved front resolution are demonstrated. Comparisons with current methods including the control‐volume finite element (CVFE) method highlight the advantages of the new formulation for flow resolution in reservoir simulation.