Sequential implicit vertex approximate gradient discretization of incompressible two-phase Darcy flows with discontinuous capillary pressure

This work deals with sequential implicit schemes for incompressible and immiscible two-phase Darcy flows which are commonly used well understood in the case of spatially homogeneous capillary pressure functions. To our knowledge, stability this type splitting solving sequentially a equation followed by saturation has not been investigated so far discontinuous curves at different rock interfaces. It will be shown here to raise severe issues stabilization strategies work. fix ideas, spatial discretization is based on Vertex Approximate Gradient (VAG) scheme accounting unstructured polyhedral meshes combined an Hybrid Upwinding (HU) transport term upwind positive approximation gravity fluxes. The built from total velocity formulation flow model only differ way conservative VAG fluxes approximated. stability, accuracy computational cost studied tested oil migration test cases 1D, 2D 3D basins large range parameters drain barrier types. that usual fail capture right solutions highly contrasted types it can fixed maintaining locally coupling interfaces definition numerical investigation also extended widely finite volume Two-Point Flux Approximation discretization.