Upstream Differencing for Multiphase Flow in Reservoir Simulation

Abstract

Upstream differencing for multiphase flow in reservoir simulation is analyzed. The associated numerical flux is shown to be well defined, monotone, Lipschitz–continuous, and consistent. In the case of a two-phase flow the corresponding numerical scheme is convergent and the numerical flux is compared to that of Godunov and Engquist–Osher. Finally, a simple way to obtain a higher-order scheme is outlined.