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2017 Incompressible immiscible multiphase flows in porous media: a variational approach
Clément Cancès, Thomas O. Gallouët, Léonard Monsaingeon
Anal. PDE 10(8): 1845-1876 (2017). DOI: 10.2140/apde.2017.10.1845

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 nonnegative measures with prescribed masses, endowed with some tensorial Wasserstein distance. We show the convergence of the approximation obtained by a minimization scheme á la R. Jordan, D. Kinderlehrer and F. Otto (SIAM J. Math. Anal. 29:1 (1998) 1–17). This allows us to obtain a new existence result for a physically well-established system of PDEs consisting of 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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Clément Cancès. Thomas O. Gallouët. Léonard Monsaingeon. "Incompressible immiscible multiphase flows in porous media: a variational approach." Anal. PDE 10 (8) 1845 - 1876, 2017. https://doi.org/10.2140/apde.2017.10.1845

Information

Received: 13 July 2016; Revised: 23 May 2017; Accepted: 29 June 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1370.35230
MathSciNet: MR3694008
Digital Object Identifier: 10.2140/apde.2017.10.1845

Subjects:
Primary: 35A15 , 35K65 , 49K20 , 76S05

Keywords: constrained parabolic system , minimizing movement scheme , multiphase porous media flows , Wasserstein gradient flows

Rights: Copyright © 2017 Mathematical Sciences Publishers

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