Structure preserving finite volume approximation of cross-diffusion systems coupled by a free interface. (English) Zbl 1530.65103
Franck, Emmanuel (ed.) et al., Finite volumes for complex applications X – Volume 1. Elliptic and parabolic problems. FVCA 10, Strasbourg, France, October 30 – November 3, 2023. Invited contributions. Cham: Springer. Springer Proc. Math. Stat. 432, 205-213 (2023).
Authors’ abstract: In this proceedings paper for the FVCA10 conference, held in Strasbourg in fall 2023, the authors 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 one-dimensional 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.
For the entire collection see [Zbl 1529.65004].
For the entire collection see [Zbl 1529.65004].
Reviewer: Victor Michel-Dansac (Strasbourg)
MSC:
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 65N08 | Finite volume methods for boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 76A20 | Thin fluid films |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
cross-diffusion system; cut-cell method; finite volume scheme; free energy dissipation; moving interface; vapor depositionReferences:
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