Titre :

A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow

Auteur(s) :

Cancès, Clément [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Matthes, Daniel [Auteur]
Technische Universität Munchen - Technical University Munich - Université Technique de Munich [TUM]
Nabet, Flore [Auteur]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]

Titre de la revue :

Archive for Rational Mechanics and Analysis

Pagination :

837–866

Éditeur :

Springer Verlag

Date de publication :

2019

ISSN :

0003-9527

Mot(s)-clé(s) en anglais :

Multiphase flow
constrained Wasserstein gradient flow
Cahn-Hilliard type system

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

Résumé en anglais : [en]

We study a non-local version of the Cahn-Hilliard dynamics for phase separation in a two-component incompressible and immiscible mixture with linear mobilities. In difference to the celebrated local model with nonlinear ...
Lire la suite >We study a non-local version of the Cahn-Hilliard dynamics for phase separation in a two-component incompressible and immiscible mixture with linear mobilities. In difference to the celebrated local model with nonlinear mobility, it is only assumed that the divergences of the two fluxes --- but not necessarily the fluxes themselves --- annihilate each other. Our main result is a rigorous proof of existence of weak solutions. The starting point is the formal representation of the dynamics as a constrained gradient flow in the Wasserstein metric. We then show that time-discrete approximations by means of the incremental minimizing movement scheme converge to a weak solution in the limit. Further, we compare the non-local model to the classical Cahn-Hilliard model in numerical experiments. Our results illustrate the significant speed-up in the decay of the free energy due to the higher degree of freedom for the velocity fields.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Approche géométrique pour les écoulements en milieux poreux: théorie et numérique
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL