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 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.

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Cited by in corpus (3)

• An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model
• A nonlocal-to-local approach to aggregation-diffusion equations
• Degenerate Cahn-Hilliard systems: From nonlocal to local