Title :

Incompressible immiscible multiphase flows in porous media: a variational approach

Author(s) :

Cancès, Clément [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Gallouët, Thomas [Auteur]
Département de Mathématiques [Liège]
Monsaingeon, Leonard [Auteur]
Institut Élie Cartan de Lorraine [IECL]

Journal title :

Analysis & PDE

Pages :

1845–1876

Publisher :

Mathematical Sciences Publishers

Publication date :

2017

ISSN :

2157-5045

English keyword(s) :

Wasserstein gradient flows
Multiphase porous media flows
constrained par-abolic system
minimizing movement scheme

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Optimisation et contrôle [math.OC]
Planète et Univers [physics]/Sciences de la Terre/Hydrologie

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Approche géométrique pour les écoulements en milieux poreux: théorie et numérique
Systemes d'Interactions, Transport Optimal, Applications a la simulation en Economie.
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL