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Article Dans Une Revue Interfaces and Free Boundaries Année : 2009

Two-phase flows involving capillary barriers in heterogeneous porous media

Résumé

We consider a simplified model of a two-phase flow through a heterogeneous porous medium, in which the convection is neglected. This leads to a nonlinear degenerate parabolic problem in a domain shared in an arbitrary finite number of homogeneous porous media. We introduce a new way to connect capillary pressures on the interfaces between the homogeneous domains, which leads to a general notion of solution. We then compare this notion of solution with an existing one, showing that it allows to deal with a larger class of problems. We prove the existence of such a solution in a general case, then we prove the existence and the uniqueness of a regular solution in the one-dimensional case for regular enough initial data.
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Dates et versions

hal-00464334 , version 1 (16-03-2010)

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Clément Cancès, Thierry Gallouët, Alessio Porretta. Two-phase flows involving capillary barriers in heterogeneous porous media. Interfaces and Free Boundaries, 2009, 11 (2), pp. 239-258. ⟨10.4171/IFB/210⟩. ⟨hal-00464334⟩
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