Back to Search
Start Over
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
- Publication Year :
- 2021
-
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.
Details
- Database :
- OAIster
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.on1269549851
- Document Type :
- Electronic Resource
- Full Text :
- https://doi.org/10.4208.cicp.OA-2023-0049