Title :

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

Author(s) :

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

Journal title :

ESAIM: Mathematical Modelling and Numerical Analysis

Pages :

1691-1731

Publisher :

EDP Sciences

Publication date :

2017-10-20

ISSN :

0764-583X

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL