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Incompressible
immiscible multiphase flows in porous media: a variational
approach
Clément Cancès, Thomas O. Gallouët and Léonard Monsaingeon |
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Vol. 10 (2017), No. 8, 1845–1876
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Abstract |
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We describe the competitive motion of 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, 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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Keywords
multiphase porous media flows, Wasserstein gradient flows,
constrained parabolic system, minimizing movement scheme
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Mathematical Subject Classification 2010
Primary: 35K65, 35A15, 49K20, 76S05
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Milestones
Received: 13 July 2016
Revised: 23 May 2017
Accepted: 29 June 2017
Published: 18 August 2017
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Authors |
| Clément Cancès | |
| Team RAPSODI Inria Lille – Nord Europe Lille France |
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| Thomas O. Gallouët | |
| Département de Mathématiques Université de Liège Liège Belgium |
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| Léonard Monsaingeon | |
| Institut Élie Cartan de
Lorraine Université de Lorraine Nancy France |
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