Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Communications in Computational Physics Year : 2023

Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation

Abstract

We propose finite-volume schemes for the Cahn-Hilliard equation that unconditionally and discretely satisfy the boundedness of the phase field and the free-energy dissipation. Our numerical framework is applicable to a variety of free-energy potentials including the Ginzburg-Landau and Flory-Huggins, general wetting boundary conditions and degenerate mobilities. Its central thrust is the finite-volume upwind methodology, which we combine with a semi-implicit formulation based on the classical convex-splitting approach for the free-energy terms. Extension to an arbitrary number of dimensions is straightforward thanks to their cost-saving dimensional-splitting nature, which allows to efficiently solve higher-dimensional simulations with a simple parallelization. The numerical schemes are validated and tested in a variety of prototypical configurations with different numbers of dimensions and a rich variety of contact angles between droplets and substrates.

Dates and versions

hal-03541875 , version 1 (24-01-2022)

Identifiers

Cite

Rafael Bailo, José Carrillo, Serafim Kalliadasis, Sergio Perez. Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation. Communications in Computational Physics, 2023, 34 (3), pp.713-748. ⟨10.4208/cicp.OA-2023-0049⟩. ⟨hal-03541875⟩
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