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Journal Articles Analysis & PDE Year : 2017

Incompressible immiscible multiphase flows in porous media: a variational approach

Abstract

We describe the competitive motion of (N + 1) incompressible immiscible phases within a porous medium as the gradient flow of a singular energy in the space of non-negative measures with prescribed mass endowed with some tensorial Wasserstein distance. We show the convergence of the approximation obtained by a minimization schemè a la [R. Jordan, D. Kinder-lehrer & F. Otto, SIAM J. Math. Anal, 29(1):1–17, 1998]. This allow to obtain a new existence result for a physically well-established system of PDEs consisting in the Darcy-Muskat law for each phase, N capillary pressure relations, and a constraint on the volume occupied by the fluid. Our study does not require the introduction of any global or complementary pressure.
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Dates and versions

hal-01345438 , version 1 (13-07-2016)
hal-01345438 , version 2 (27-01-2017)

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Clément Cancès, Thomas Gallouët, Leonard Monsaingeon. Incompressible immiscible multiphase flows in porous media: a variational approach. Analysis & PDE, 2017, 10 (8), pp.1845-1876. ⟨10.2140/apde.2017.10.1845⟩. ⟨hal-01345438v2⟩
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