Incompressible immiscible multiphase flows in porous media: a variational approach - ANR - Agence nationale de la recherche Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2016

Incompressible immiscible multiphase flows in porous media: a variational approach

Résumé

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.
Fichier principal
Vignette du fichier
multiphase.pdf (419.92 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

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

Identifiants

Citer

Clément Cancès, Thomas Gallouët, Leonard Monsaingeon. Incompressible immiscible multiphase flows in porous media: a variational approach. 2016. ⟨hal-01345438v1⟩

Collections

X CMLS X-CMLS
650 Consultations
298 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More