Geodesic
Two-phase flows involving capillary barriers in heterogeneous porous media
Clément Cancès1 orcid ; Thierry Gallouët1 ; Alessio Porretta2
1Université de Provence, Marseille, France
2Università di Roma, Italy
Interfaces and free boundaries, Tome 11 (2009) no. 2, pp. 239-258

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DOI

We consider a simplified model of a two-phase flow through a heterogeneous porous medium, in which convection is neglected. This leads to a nonlinear degenerate parabolic problem in a domain divided into 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 one to deal with a larger class of problems. We prove the existence of such a solution in a general case, and the existence and uniqueness of a regular solution in the one-dimensional case for initial data regular enough.
DOI : 10.4171/ifb/210
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Flows in porous media, capillarity, nonlinear PDE of parabolic type

Clément Cancès  1   ; Thierry Gallouët  1   ; Alessio Porretta  2

1 Université de Provence, Marseille, France
2 Università di Roma, Italy 
Clément Cancès; Thierry Gallouët; Alessio Porretta. Two-phase flows involving capillary barriers in heterogeneous porous media. Interfaces and free boundaries, Tome 11 (2009) no. 2, pp. 239-258. doi: 10.4171/ifb/210
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     pages = {239--258},
     year = {2009},
     volume = {11},
     number = {2},
     doi = {10.4171/ifb/210},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/210/}
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