Volume 55, Number 3, May-June 2021
|Page(s)||969 - 1003|
|Published online||05 May 2021|
Finite Volume approximation of a two-phase two fluxes degenerate Cahn–Hilliard model
Inria, Univ. Lille, CNRS, UMR 8524 – Laboratoire Paul Painlevé, 59000 Lille, France
2 CMAP, École polytechnique, CNRS, I.P. Paris, 91128 Palaiseau, France
* Corresponding author: email@example.com
Accepted: 15 January 2021
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.
Mathematics Subject Classification: 65M12 / 65M08 / 76T99 / 35K52 / 35K65
Key words: two-phase flow / degenerate Cahn–Hilliard system / finite volumes / convergence
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.