A mixed finite element-finite volume formulation of the Black-Oil model

In this paper a sequential coupling of mixed finite element and shock-captu ring finite volume techniques is proposed, in order to numerically solve th e system of partial differential equations arising from the Black-Oil model . The Brezzi-Douglas-Marini space of degree one (BDM1) is used to approxima te the Darcy's velocity in the parabolic-type pressure equation, while the system of mass conservation laws is solved by a higher order Godunov-type s cheme, here extended to triangle-based unstructured grids. Numerical result s on 1-D and 2-D test cases prove the effectiveness and the robustness of t he coupling, which seems particularly suited to handling high heterogeneiti es and at the same time accurately resolving steep gradients without spurio us oscillations.