A space-time extension of a conservative two-fluid cut-cell method for moving diffusion problems

Fuente: arXiv
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Main Authors: Libat, Louis, Selçuk, Can, Chénier, Eric, Chenadec, Vincent Le
Format: Preprint
Published: 2025
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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
id 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