Convergence of finite volume schemes for a degenerate convection–diffusion equation arising in flow in porous media Original Research Article

This paper develops discretizations using the finite volume method for a nonlinear, degenerate, convection–diffusion equation in multiple dimensions on unstructured grids. We will derive three families of numerical schemes. They are classified as explicit, implicit, and semi-implicit. A Godunov scheme is used for the convection term. It is shown that these finite volume schemes (FVS) satisfy a discrete maximum principle. We prove the convergence of these FVS. This is done by means of a priori estimates in L∞ and weak BV estimates under appropriate CFL conditions. Numerical results for oil recovery simulation are presented.