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

2023/03/28 by Cancès, Clément, Cauvin-Vila, Jean, Chainais-Hillairet, Claire +1
#Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2303.15817

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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