Publications
Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation
Rafael Bailo · José Antonio Carrillo · Serafim Kalliadasis · Sergio P. Perez
Communications in Computational Physics, 34 (3), 2023.
Communications in Computational Physics, 34 (3), 2023.
@Article{BCK2023,
title={Unconditional bound-preserving and energy-dissipating finite-volume schemes for the {C}ahn-{H}illiard equation},
author={Bailo, Rafael and Carrillo, José Antonio and Kalliadasis, Serafim and Perez, Sergio P.},
journal={Commun. Comput. Phys.},
year={2023},
doi={10.4208/cicp.OA-2023-0049},
volume={34},
number={3},
archivePrefix={arXiv},
arXivId={2105.05351},
eprint={2105.05351},
}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.
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.