A Convergent Finite Volume Scheme for Two-Phase Flows in Porous Media with Discontinuous Capillary Pressure Field *

Clément Cancès (1) , K Brenner (2) , D. Hilhorst (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We 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.

Mots clés: two phase flow; Finite volume; discontinuous capillary pressures

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Clément Cancès, K Brenner, D. Hilhorst. A Convergent Finite Volume Scheme for Two-Phase Flows in Porous Media with Discontinuous Capillary Pressure Field *. FVCA 6 - International Symposium Finite Volumes for Complex Applications , 2011, Prague, Czech Republic. ⟨hal-01713549⟩