Modeling multiphase flow with dynamic capillary pressure in heterogeneous media

Speaker(s)

Małgorzata Peszyńska

Affiliation

Oregon State University

Date

March 25, 2010, 12:30 p.m.

Room

room 4060

Seminar

Seminar of Mathematical Physics Equations Group

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Richards equation is a simplified one-equation model for two-phase flow of air and water in porous media. From mathematical point of view it is a egenerate nonlinear parabolic equation in which the elliptic part is
associated with the capillary pressure term. Since this term has degeneracies, the analysis and numerical approximation of Richards equation re complicated due to the presence of sharp fronts and appearance/
disappearance of fluid phases. In the talk we discuss an extension of the capillary pressure model by the dynamic terms; this extension was originally roposed by hydrologists, and it changes the type of the equation to seudo-parabolic. We are also interested in the influence of heterogeneous and multiscale data on the solutions for which we derive a homogenized model.

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