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 (1997) R3844–R3846] and studied mathematically by the authors in [C. Cancès, D. Matthes and F. Nabet, Arch. Ration. Mech. Anal. 233 (2019) 837–866]. 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.
Keywords: two-phase flow, degenerate Cahn–Hilliard system, finite volumes, convergence
@article{M2AN_2021__55_3_969_0,
author = {Canc\`es, Cl\'ement and Nabet, Flore},
title = {Finite {Volume} approximation of a two-phase two fluxes degenerate {Cahn{\textendash}Hilliard} model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {969--1003},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {3},
doi = {10.1051/m2an/2021002},
mrnumber = {4253167},
zbl = {1492.65250},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021002/}
}
TY - JOUR AU - Cancès, Clément AU - Nabet, Flore TI - Finite Volume approximation of a two-phase two fluxes degenerate Cahn–Hilliard model JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 969 EP - 1003 VL - 55 IS - 3 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021002/ DO - 10.1051/m2an/2021002 LA - en ID - M2AN_2021__55_3_969_0 ER -
%0 Journal Article %A Cancès, Clément %A Nabet, Flore %T Finite Volume approximation of a two-phase two fluxes degenerate Cahn–Hilliard model %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 969-1003 %V 55 %N 3 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021002/ %R 10.1051/m2an/2021002 %G en %F M2AN_2021__55_3_969_0
Cancès, Clément; Nabet, Flore. Finite Volume approximation of a two-phase two fluxes degenerate Cahn–Hilliard model. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 3, pp. 969-1003. doi: 10.1051/m2an/2021002
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