@Article{CiCP-34-3,
author = {Rafael, Bailo and José, Carrillo, A. and Serafim, Kalliadasis and Sergio, Perez, P.},
title = {Unconditional Bound-Preserving and Energy-Dissipating Finite-Volume Schemes for the Cahn-Hilliard Equation},
journal = {Communications in Computational Physics},
year = {2023},
volume = {34},
number = {3},
pages = {713--748},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0049},
url = {https://global-sci.com/article/79379/unconditional-bound-preserving-and-energy-dissipating-finite-volume-schemes-for-the-cahn-hilliard-equation}
}