A two-phase two-fluxes degenerate Cahn-Hilliard ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow
Author(s) :
Cancès, Clément [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
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]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
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]
Journal title :
Archive for Rational Mechanics and Analysis
Pages :
837–866
Publisher :
Springer Verlag
Publication date :
2019
ISSN :
0003-9527
English keyword(s) :
Multiphase flow
constrained Wasserstein gradient flow
Cahn-Hilliard type system
constrained Wasserstein gradient flow
Cahn-Hilliard type system
HAL domain(s) :
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Analyse numérique [math.NA]
English abstract : [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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Popular science :
Non
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