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: firstname.lastname@example.org
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
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