Are upwind techniques in multi-phase flow models necessary?

Abstract

Two alternatives of primary variables are compared for two-phase flow in heterogeneous media by solving fully established benchmarks. The first combination utilizes pressure of the wetting fluid and saturation of the non-wetting fluid as primary variables, while the second employs capillary pressure of the wetting fluid and pressure of the non-wetting fluid. While the standard Galerkin finite element method (SGFEM) is known to fail in the physical reproduction of two-phase flow in heterogeneous media (unless employing a fully upwind correction), the second scheme with capillary pressure as a primary variable without applying an upwind technique produces correct physical fluid behaviour in heterogeneous media, as observed from experiments.