A note on the central-upwind scheme for nonlocal conservation laws
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917256407023616 |
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| author | Friedrich, Jan Rathan, Samala Sudha, Sanjibanee |
| author_facet | Friedrich, Jan Rathan, Samala Sudha, Sanjibanee |
| contents | The central-upwind flux is a widely used numerical flux function for local conservation laws. It has been investigated by Kurganov and Polizzi (2009) for a specific nonlocal conservation law and can be derived from a fully-discrete second-order scheme. Here, we derive this fully-discrete scheme in detail with a particular focus on the occurring nonlocal terms. In addition, we derive the central-upwind flux for a class of nonlocal conservation laws and use an estimate on the nonlocal speed which fixes the nonlocality at the cell interfaces. We prove that the resulting first-order numerical scheme converges to the correct solution. Under additional assumptions on the analytical flux we present a similar result for a second-order central-upwind scheme. Numerical examples compare the central-upwind schemes to Godunov-type schemes and the fully-discrete scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01344 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the central-upwind scheme for nonlocal conservation laws Friedrich, Jan Rathan, Samala Sudha, Sanjibanee Numerical Analysis 35L65, 65M08, 65M12 The central-upwind flux is a widely used numerical flux function for local conservation laws. It has been investigated by Kurganov and Polizzi (2009) for a specific nonlocal conservation law and can be derived from a fully-discrete second-order scheme. Here, we derive this fully-discrete scheme in detail with a particular focus on the occurring nonlocal terms. In addition, we derive the central-upwind flux for a class of nonlocal conservation laws and use an estimate on the nonlocal speed which fixes the nonlocality at the cell interfaces. We prove that the resulting first-order numerical scheme converges to the correct solution. Under additional assumptions on the analytical flux we present a similar result for a second-order central-upwind scheme. Numerical examples compare the central-upwind schemes to Godunov-type schemes and the fully-discrete scheme. |
| title | A note on the central-upwind scheme for nonlocal conservation laws |
| topic | Numerical Analysis 35L65, 65M08, 65M12 |
| url | https://arxiv.org/abs/2512.01344 |