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arXiv · 2303.15817

Structure Preserving Finite Volume Approximation of Cross-Diffusion Systems Coupled by a Free Interface

Clément Cancès·Jean Cauvin-Vila·Claire Chainais-Hillairet·Virginie Ehrlacher
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Abstract

We propose a two-point flux approximation finite-volume scheme for the approximation of two cross-diffusion systems coupled by a free interface to account for vapor deposition. The moving interface is addressed with a cut-cell approach, where the mesh is locally deformed around the interface. The scheme preserves the structure of the continuous system, namely: mass conservation, nonnegativity, volume-filling constraints and decay of the free energy. Numerical results illustrate the properties of the scheme.

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Clément Cancès, Jean Cauvin-Vila, Claire Chainais-Hillairet, Virginie Ehrlacher. 2023-03-28. Structure Preserving Finite Volume Approximation of Cross-Diffusion Systems Coupled by a Free Interface. https://arxiv.org/abs/2303.15817

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