Title :

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

Author(s) :

Bailo, Rafael [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Carrillo, José [Auteur]
Department of Mathematics [Imperial College London]
Kalliadasis, Serafim [Auteur]
Perez, Sergio [Auteur]
Department of Mathematics [Imperial College London]

Journal title :

Communications in Computational Physics

Pages :

713-748

Publisher :

Global Science Press

Publication date :

2023-06

ISSN :

1815-2406

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL