Titre :

A DDFV method for a Cahn-Hilliard/Stokes phase field model with dynamic boundary conditions

Auteur(s) :

Boyer, Franck [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Nabet, Flore [Auteur]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Reliable numerical approximations of dissipative systems [RAPSODI]

Titre de la revue :

ESAIM: Mathematical Modelling and Numerical Analysis

Pagination :

1691-1731

Éditeur :

Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP

Date de publication :

2017-10-20

ISSN :

2822-7840

Mot(s)-clé(s) en anglais :

finite volume method
contact angle dynamics
dynamic boundary conditions
Cahn-Hilliard/Stokes model

Discipline(s) HAL :

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

Résumé en anglais : [en]

In this paper we propose a "Discrete Duality Finite Volume" method (DDFV for short) for the diffuse interface modelling of incompressible flows. This numerical method is, conservative, robust and is able to handle general ...
Lire la suite >In this paper we propose a "Discrete Duality Finite Volume" method (DDFV for short) for the diffuse interface modelling of incompressible flows. This numerical method is, conservative, robust and is able to handle general geometries and meshes. The model we study couples the Cahn-Hilliard equation and the unsteady Stokes equation and is endowed with particular nonlinear boundary conditions called dynamic boundary conditions. To implement the scheme for this model we have to define new discrete consistent DDFV operators that allows an energy stable coupling between both discrete equations. We are thus able to obtain the existence of a family of solutions satisfying a suitable energy inequality, even in the case where a first order time-splitting method between the two subsystems is used. We illustrate various properties of such a model with some numerical results.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL