Unconditional Bound-Preserving and Energy-Dissipating Finite-Volume Schemes for the Cahn-Hilliard Equation
Year: 2023
Author: Rafael Bailo, José A. Carrillo, Serafim Kalliadasis, Sergio P. Perez
Communications in Computational Physics, Vol. 34 (2023), Iss. 3 : pp. 713–748
Abstract
We propose finite-volume schemes for the Cahn-Hilliard equation which unconditionally and discretely preserve the boundedness of the phase field and the dissipation of the free energy. Our numerical framework is applicable to a variety of free-energy potentials, including Ginzburg-Landau and Flory-Huggins, to general wetting boundary conditions, and to degenerate mobilities. Its central thrust is the upwind methodology, which we combine with a semi-implicit formulation for the free-energy terms based on the classical convex-splitting approach. The extension of the schemes to an arbitrary number of dimensions is straightforward thanks to their dimensionally split nature, which allows to efficiently solve higher-dimensional problems with a simple parallelisation. The numerical schemes are validated and tested through a variety of examples, in different dimensions, and with various contact angles between droplets and substrates.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0049
Communications in Computational Physics, Vol. 34 (2023), Iss. 3 : pp. 713–748
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 36
Keywords: Cahn-Hilliard equation diffuse interface theory gradient flow finite-volume method bound preservation energy dissipation.
Author Details
-
Competing effects in fourth‐order aggregation–diffusion equations
Antonio Carrillo, José | Esposito, Antonio | Falcó, Carles | Fernández‐Jiménez, AlejandroProceedings of the London Mathematical Society, Vol. 129 (2024), Iss. 2
https://doi.org/10.1112/plms.12623 [Citations: 0] -
A Structure-Preserving, Upwind-SAV Scheme for the Degenerate Cahn–Hilliard Equation with Applications to Simulating Surface Diffusion
Huang, Qiong-Ao | Jiang, Wei | Yang, Jerry Zhijian | Yuan, ChengJournal of Scientific Computing, Vol. 97 (2023), Iss. 3
https://doi.org/10.1007/s10915-023-02380-6 [Citations: 7] -
A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation
Lyons, Rainey | Muntean, Adrian | Nika, GrigorComptes Rendus. Mécanique, Vol. 352 (2024), Iss. G1 P.239
https://doi.org/10.5802/crmeca.265 [Citations: 0] -
A Simple and Efficient Convex Optimization Based Bound-Preserving High Order Accurate Limiter for Cahn–Hilliard–Navier–Stokes System
Liu, Chen | Riviere, Beatrice | Shen, Jie | Zhang, XiangxiongSIAM Journal on Scientific Computing, Vol. 46 (2024), Iss. 3 P.A1923
https://doi.org/10.1137/23M1587853 [Citations: 8] -
On the phase field based model for the crystalline transition and nucleation within the Lagrange multiplier framework
Xia, Qing | Yang, Junxiang | Kim, Junseok | Li, YibaoJournal of Computational Physics, Vol. 513 (2024), Iss. P.113158
https://doi.org/10.1016/j.jcp.2024.113158 [Citations: 14]