A space-time extension of a conservative two-fluid cut-cell method for moving diffusion problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912796726263808 |
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| 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 space-time extension of a conservative Cartesian cut-cell finite-volume method for two-phase diffusion problems with prescribed interface motion. The formulation follows a two-fluid approach: one scalar field is solved in each phase with discontinuous material properties, coupled by sharp interface conditions enforcing flux continuity and jump laws. To handle moving boundaries on a fixed Cartesian grid, the discrete balance is written over phase-restricted space-time control volumes, whose geometric moments (swept volumes and apertures) are used as weights in the finite-volume operators. This construction naturally accounts for the creation and destruction of cut cells (fresh/dead-cell events) and yields strict discrete conservation. The resulting scheme retains the algebraic structure of the static cut-cell formulation while incorporating motion through local geometric weights and interface coupling operators. A series of verification and validation tests in two and three dimensions demonstrate super-linear accuracy in space, robust behavior under repeated topology changes and conservation across strong coefficient jumps and moving interfaces. The proposed space-time cut-cell framework provides a conservative building block for multiphase transport in evolving geometries and a foundation for future free-boundary extensions such as Stefan-type phase change. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_23358 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A space-time extension of a conservative two-fluid cut-cell method for moving diffusion problems Libat, Louis Selçuk, Can Chénier, Eric Chenadec, Vincent Le Computational Physics Numerical Analysis We present a space-time extension of a conservative Cartesian cut-cell finite-volume method for two-phase diffusion problems with prescribed interface motion. The formulation follows a two-fluid approach: one scalar field is solved in each phase with discontinuous material properties, coupled by sharp interface conditions enforcing flux continuity and jump laws. To handle moving boundaries on a fixed Cartesian grid, the discrete balance is written over phase-restricted space-time control volumes, whose geometric moments (swept volumes and apertures) are used as weights in the finite-volume operators. This construction naturally accounts for the creation and destruction of cut cells (fresh/dead-cell events) and yields strict discrete conservation. The resulting scheme retains the algebraic structure of the static cut-cell formulation while incorporating motion through local geometric weights and interface coupling operators. A series of verification and validation tests in two and three dimensions demonstrate super-linear accuracy in space, robust behavior under repeated topology changes and conservation across strong coefficient jumps and moving interfaces. The proposed space-time cut-cell framework provides a conservative building block for multiphase transport in evolving geometries and a foundation for future free-boundary extensions such as Stefan-type phase change. |
| title | A space-time extension of a conservative two-fluid cut-cell method for moving diffusion problems |
| topic | Computational Physics Numerical Analysis |
| url | https://arxiv.org/abs/2512.23358 |