The domain-of-dependence stabilization for cut-cell meshes is fully discretely stable
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917462668214272 |
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| author | Petri, Louis Birke, Gunnar Engwer, Christian Ranocha, Hendrik |
| author_facet | Petri, Louis Birke, Gunnar Engwer, Christian Ranocha, Hendrik |
| contents | We present a fully discrete stability analysis of the domain-of-dependence stabilization for hyperbolic problems. The method aims to address issues caused by small cut cells by redistributing mass around the neighborhood of a small cut cell at a semi-discrete level. Our analysis is conducted for the linear advection model problem in one spatial dimension. We demonstrate that fully discrete stability can be achieved under a time step restriction that does not depend on the arbitrarily small cells, using an operator norm estimate. Additionally, this analysis offers a detailed understanding of the stability mechanism and highlights some challenges associated with higher-order polynomials. We also propose a way to mitigate these issues to derive a feasible CFL-like condition. The analytical findings, as well as the proposed solution are verified numerically in one- and two-dimensional simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05372 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The domain-of-dependence stabilization for cut-cell meshes is fully discretely stable Petri, Louis Birke, Gunnar Engwer, Christian Ranocha, Hendrik Numerical Analysis 65M12, 65M20, 65M60 We present a fully discrete stability analysis of the domain-of-dependence stabilization for hyperbolic problems. The method aims to address issues caused by small cut cells by redistributing mass around the neighborhood of a small cut cell at a semi-discrete level. Our analysis is conducted for the linear advection model problem in one spatial dimension. We demonstrate that fully discrete stability can be achieved under a time step restriction that does not depend on the arbitrarily small cells, using an operator norm estimate. Additionally, this analysis offers a detailed understanding of the stability mechanism and highlights some challenges associated with higher-order polynomials. We also propose a way to mitigate these issues to derive a feasible CFL-like condition. The analytical findings, as well as the proposed solution are verified numerically in one- and two-dimensional simulations. |
| title | The domain-of-dependence stabilization for cut-cell meshes is fully discretely stable |
| topic | Numerical Analysis 65M12, 65M20, 65M60 |
| url | https://arxiv.org/abs/2508.05372 |