Total velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure

Abstract This work proposes a finite volume scheme for two-phase Darcy flow in heterogeneous porous media with different rock types. The fully implicit discretization is based on cell-centered, as well face-centered degrees of freedom order to capture accurately the nonlinear transmission conditions at type interfaces. These play major role dynamics. formulated natural physical unknowns, and notion global pressure only introduced analyze its stability convergence. It combines two-point flux approximation gradient normal fluxes Hybrid Upwinding transport terms. convergence weak solution established taking into account discontinuous capillary interfaces degeneracy phase mobilities. Numerical experiments show additional robustness proposed compared classical Phase Potential approach.