Unconditional Bound-Preserving and Energy-Dissipating Finite-Volume Schemes for the Cahn-Hilliard Equation

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.

Author Details

Rafael Bailo

José A. Carrillo

Serafim Kalliadasis

Sergio P. Perez