Incompressible immiscible multiphase flows in porous media: a variational approach
| Autor: | Thomas Gallouët, Léonard Monsaingeon, Clément Cancès |
|---|---|
| Přispěvatelé: | Reliable numerical approximations of dissipative systems (RAPSODI ), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Département de Mathématiques [Liège], Université de Liège, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), ANR-13-JS01-0007,GEOPOR,Approche géométrique pour les écoulements en milieux poreux: théorie et numérique(2013), ANR-12-MONU-0013,ISOTACE,Systemes d'Interactions, Transport Optimal, Applications a la simulation en Economie.(2012), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Capillary pressure
Motion (geometry) Space (mathematics) 01 natural sciences constrained par-abolic system 35A15 Physics::Fluid Dynamics Wasserstein gradient flows Mathematics - Analysis of PDEs 35K65 35A15 49K20 76S05 Phase (matter) Convergence (routing) FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics [SDU.STU.HY]Sciences of the Universe [physics]/Earth Sciences/Hydrology Mathematics - Optimization and Control Multiphase porous media flows 49K20 Mathematics Numerical Analysis Applied Mathematics 010102 general mathematics Mathematical analysis 35K65 minimizing movement scheme 010101 applied mathematics constrained parabolic system Optimization and Control (math.OC) Compressibility [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Balanced flow Porous medium Analysis Analysis of PDEs (math.AP) 76S05 |
| Zdroj: | Analysis & PDE Analysis & PDE, Mathematical Sciences Publishers, 2017, 10 (8), pp.1845-1876. ⟨10.2140/apde.2017.10.1845⟩ Analysis & PDE, 2017, 10 (8), pp.1845-1876. ⟨10.2140/apde.2017.10.1845⟩ Anal. PDE 10, no. 8 (2017), 1845-1876 |
| ISSN: | 2157-5045 1948-206X |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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