Non-Upwind Versus Upwind Schemes for Hyperbolic Conservation Laws in Porous Media

Abstract Standard reservoir simulation schemes employ upstream weighting approximations of the multi-phase/multi-component convective fluxes. The upstream definition depends upon the direction of the local phase velocities. This paper presents novel convective flow approximation schemes in a non-upwind finite volume framework, which avoids both upwinding and characteristic decomposition, leading to a fundamental simplification of current methods. Stable lower order and higher order monotonicity preserving non-upwind approximations are developed. The schemes are locally conservative and the formulation is consistent in IMPES mode (or sequentially implicit mode), with respect to sign change in wave velocity and mass balance. Comparisons between velocity upwinding and the non-upwind schemes are presented for gravity segregated flow problems where waves undergo sign changes.