An existence result related to two-phase flows with dynamical capillary pressure

C. Cancès, C. Choquet, Y. Fan, I.S. Pop

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Abstract

We consider a nonlinear degenerate pseudo-parabolic equation arising in the modeling of immiscible two-phase flows within porous media when the dynamic capillary pressure Pc = p(s) + T¿ts is a function of both the saturation s and its time derivative ¿ts. We show the existence of a weak solution to the problem using the compactness of a sequence of regularizations of the problem.
Original languageEnglish
Title of host publicationProceedings of the 4th International Conference on Approximation Methods and Numerical Modeling in Environment and Natural Resources (MAMERN'11, Saidia, Morocco, May 23-26, 2011)
Place of PublicationGranada
PublisherUniversidad de Granada
Pages1-4
Publication statusPublished - 2011

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Cancès, C., Choquet, C., Fan, Y., & Pop, I. S. (2011). An existence result related to two-phase flows with dynamical capillary pressure. In Proceedings of the 4th International Conference on Approximation Methods and Numerical Modeling in Environment and Natural Resources (MAMERN'11, Saidia, Morocco, May 23-26, 2011) (pp. 1-4). Granada: Universidad de Granada.