Improving the robustness of the control volume finite element method with application to multiphase porous media flow

Control volume finite element methods (CVFEM) have been proposed to simulate flow in heterogeneous porous media because they are better able to capture complex geometries using unstructured meshes. However, producing good quality meshes in such models is non-trivial and may sometimes be impossible, especially when all or parts of the domains have very large aspect ratio. A novel CVFEM is proposed here that uses a control volume representation for pressure and yields significant improvements in the quality of the pressure matrix. The method is initially evaluated and then applied to a series of test cases using unstructured (triangular/tetrahedral) meshes, and numerical results are in good agreement with semi-analytically obtained solutions. The convergence of the pressure matrix is then studied using complex, heterogeneous example problems. The results demonstrate that the new formulation yields a pressure matrix than can be solved efficiently even on highly distorted, tetrahedral meshes in models of heterogeneous porous media with large permeability contrasts. The new approach allows effective application of CVFEM in such models. This article is protected by copyright. All rights reserved