A mixed Finite Element - Finite Volume formulation of the Black-Oil model

In this paper a sequential coupling of mixed finite element and shock-capturing finite volume techniques is proposed, in order to numerically solve the system of partial differential equations arising from the Black-Oil model. The Brezzi-Douglas-Marini space of degree one (BDM1) is used to approximate 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 scheme, here extended to triangle-based unstructured grids. Numerical results on 1-D and 2-D test cases prove the effectiveness and the robustness of the coupling, which seems particularly suited to handling high heterogeneities and at the same time accurately resolving steep gradients without spurious oscillations