In this paper we propose a “Discrete Duality Finite Volume” method (DDFV for short) for the diffuse interface modelling of incompressible two-phase 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 derive 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.
Mots clés : Cahn–Hilliard/Stokes model, dynamic boundary conditions, contact angle dynamics, finite volume method
@article{M2AN_2017__51_5_1691_0,
author = {Boyer, Franck and Nabet, Flore},
title = {A {DDFV} method for a {Cahn\ensuremath{-}Hilliard/Stokes} phase field model with dynamic boundary conditions},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1691--1731},
publisher = {EDP-Sciences},
volume = {51},
number = {5},
year = {2017},
doi = {10.1051/m2an/2016073},
mrnumber = {3731546},
zbl = {1391.35196},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2016073/}
}
TY - JOUR AU - Boyer, Franck AU - Nabet, Flore TI - A DDFV method for a Cahn−Hilliard/Stokes phase field model with dynamic boundary conditions JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1691 EP - 1731 VL - 51 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016073/ DO - 10.1051/m2an/2016073 LA - en ID - M2AN_2017__51_5_1691_0 ER -
%0 Journal Article %A Boyer, Franck %A Nabet, Flore %T A DDFV method for a Cahn−Hilliard/Stokes phase field model with dynamic boundary conditions %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1691-1731 %V 51 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016073/ %R 10.1051/m2an/2016073 %G en %F M2AN_2017__51_5_1691_0
Boyer, Franck; Nabet, Flore. A DDFV method for a Cahn−Hilliard/Stokes phase field model with dynamic boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1691-1731. doi : 10.1051/m2an/2016073. http://www.numdam.org/articles/10.1051/m2an/2016073/
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