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arXiv · 1005.5634

Two-phase flows involving capillary barriers in heterogeneous porous media

Clément Cancès·Thierry Gallouet·Alessio Porretta
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Abstract

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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Clément Cancès, Thierry Gallouet, Alessio Porretta. 2010-05-31. Two-phase flows involving capillary barriers in heterogeneous porous media. https://doi.org/10.4171/ifb%2F210

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