Finite Volume approximation of a two-phase two fluxes degenerate Cahn-Hilliard model

Cancès, Clément; Nabet, Flore

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1051/m2an/2021002

Title :

Finite Volume approximation of a two-phase two fluxes degenerate Cahn-Hilliard model

Author(s) :

Cancès, Clément [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Nabet, Flore [Auteur]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]

Journal title :

ESAIM: Mathematical Modelling and Numerical Analysis

Pages :

969--1003

Publisher :

EDP Sciences

Publication date :

2021

ISSN :

0764-583X

English keyword(s) :

two-phase flow
degenerate Cahn-Hilliard system
finite volumes
convergence

HAL domain(s) :

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

English abstract : [en]

We study a time implicit Finite Volume scheme for degenerate Cahn-Hilliard model proposed in [W. E and P. Palffy-Muhoray. Phys. Rev. E, 55:R3844R3846, 1997] and studied mathematically by the authors in [C. Cancès, D. ...
Show more >We study a time implicit Finite Volume scheme for degenerate Cahn-Hilliard model proposed in [W. E and P. Palffy-Muhoray. Phys. Rev. E, 55:R3844R3846, 1997] and studied mathematically by the authors in [C. Cancès, D. Matthes, and F. Nabet. Arch. Ration. Mech. Anal., 233(2):837-866, 2019]. The scheme is shown to preserve the key properties of the continuous model, namely mass conservation, positivity of the concentrations, the decay of the energy and the control of the entropy dissipation rate. This allows to establish the existence of a solution to the nonlinear algebraic system corresponding to the scheme. Further, we show thanks to compactness arguments that the approximate solution converges towards a weak solution of the continuous problems as the discretization parameters tend to 0. Numerical results illustrate the behavior of the numerical model.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

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

Collections :