A Cartesian Cut-Cell Two-Fluid Method for Two-Phase Diffusion Problems
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917187057352704 |
|---|---|
| author | Libat, Louis Selçuk, Can Chénier, Eric Chenadec, Vincent Le |
| author_facet | Libat, Louis Selçuk, Can Chénier, Eric Chenadec, Vincent Le |
| contents | We present a Cartesian cut-cell finite-volume method for sharp-interface two-phase diffusion problems in static geometries. The formulation follows a two-fluid approach: independent diffusion equations are discretized in each phase on a fixed Cartesian grid, while the phases are coupled through embedded interface conditions enforcing continuity of diffusive flux and a general jump law. Cut cells are treated by integrating the governing equations over phase-restricted control volumes and surfaces, yielding discrete divergence and gradient operators that are locally conservative within each phase. Interface coupling is achieved by introducing a small set of interfacial unknowns per cut cell on the embedded boundary; the resulting algebraic system involves only bulk and interfacial averages. A key feature of the method is the use of a reduced set of geometric information based solely on low-order moments (trimmed volumes, apertures and interface measures/centroids), allowing robust implementation without constructing explicitly cut-cell polytopes. The method supports steady (Poisson) and unsteady (diffusion) regimes and incorporates Dirichlet, Neumann, Robin boundary conditions and general jumps. We validate the scheme on one-, two- and three-dimensional single-phase and two-phase benchmarks, including curved embedded boundaries, Robin conditions and strong property/jump contrasts. The results demonstrate a superlinear convergence behavior, sharp enforcement of interfacial laws and excellent conservation properties. Extensions to moving interfaces and Stefan-type free-boundary problems are natural perspectives of this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Cartesian Cut-Cell Two-Fluid Method for Two-Phase Diffusion Problems Libat, Louis Selçuk, Can Chénier, Eric Chenadec, Vincent Le Numerical Analysis Computational Physics Fluid Dynamics We present a Cartesian cut-cell finite-volume method for sharp-interface two-phase diffusion problems in static geometries. The formulation follows a two-fluid approach: independent diffusion equations are discretized in each phase on a fixed Cartesian grid, while the phases are coupled through embedded interface conditions enforcing continuity of diffusive flux and a general jump law. Cut cells are treated by integrating the governing equations over phase-restricted control volumes and surfaces, yielding discrete divergence and gradient operators that are locally conservative within each phase. Interface coupling is achieved by introducing a small set of interfacial unknowns per cut cell on the embedded boundary; the resulting algebraic system involves only bulk and interfacial averages. A key feature of the method is the use of a reduced set of geometric information based solely on low-order moments (trimmed volumes, apertures and interface measures/centroids), allowing robust implementation without constructing explicitly cut-cell polytopes. The method supports steady (Poisson) and unsteady (diffusion) regimes and incorporates Dirichlet, Neumann, Robin boundary conditions and general jumps. We validate the scheme on one-, two- and three-dimensional single-phase and two-phase benchmarks, including curved embedded boundaries, Robin conditions and strong property/jump contrasts. The results demonstrate a superlinear convergence behavior, sharp enforcement of interfacial laws and excellent conservation properties. Extensions to moving interfaces and Stefan-type free-boundary problems are natural perspectives of this framework. |
| title | A Cartesian Cut-Cell Two-Fluid Method for Two-Phase Diffusion Problems |
| topic | Numerical Analysis Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2512.19407 |