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.
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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.
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