Mathematical and Numerical Study of an Industrial Scheme for Two-phase Flows in Porous Media under Gravity

AbstractIn this paper, we consider a dead-oil model where the capillary pressure is neglected. In a multidimensional space and for a phase-by-phase upstream weigthing cell-centered finite volume scheme, we prove the pressure estimates, the existence of solutions to the discrete equations and the stability of the saturation calculation. This is done in the explicit case as well as in the implicit case. Some numerical tests show the convergence of the scheme.