Abstract
AbstractWe consider an immiscible incompressible two-phase flow in a porous medium composed of two different rocks. The flows of oil and water are governed by the Darcy–Muskat law and a capillary pressure law, where the capillary pressure field may be discontinuous at the interface between the rocks. Using the concept of multi-valued phase pressures, we introduce a notion of weak solution for the flow, and prove the convergence of a finite volume approximation towards a weak solution.KeywordsFinite volumetwo phase flowdiscontinuous capillary pressures
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