We consider an immiscible incompressible two-phase flow in a porous medium composed of two different rocks so that the capillary pressure field is discontinuous at the interface between the rocks. This leads us to apply a concept of multi-valued phase pressures and a notion of weak solution for the flow which have been introduced in [Cancés \& Pierre, {\em SIAM J. Math. Anal}, 44(2):966--992, 2012]. We discretize the problem by means of a numerical algorithm which reduces to a standard finite volume scheme in each rock and prove the convergence of the approximate solution to a weak solution of the two-phase flow problem. The numerical experiments show in particular that this scheme permits to reproduce the oil trapping phenomenon.
@article{hal-00675681,
author = {Brenner, Konstantin and Canc\`es, Cl\'ement and Hilhorst, Danielle},
title = {Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure},
journal = {HAL},
volume = {2013},
number = {0},
year = {2013},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00675681}
}
Brenner, Konstantin; Cancès, Clément; Hilhorst, Danielle. Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure. HAL, Tome 2013 (2013) no. 0, . http://gdmltest.u-ga.fr/item/hal-00675681/