Maximal dissipation and shallow water flow -- the dam-break problem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912429360807936 |
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| author | Daw, Dalal Nedeljkov, Marko Ružičić, Sanja |
| author_facet | Daw, Dalal Nedeljkov, Marko Ružičić, Sanja |
| contents | The shallow water system with a bed jump describes a fluid flow over a dam, represented by a simple step function with the Riemann initial data is such that the vacuum is on the right-hand side. The main question is whether the fluid will stay on the left-hand side of the dam. After approximating the step function space derivative with a fixed shadow wave, solutions to that problem stay bounded. A proper connection between waves on both sides of the dam, and a unique solution afterward is found by using the maximal dissipation principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal dissipation and shallow water flow -- the dam-break problem Daw, Dalal Nedeljkov, Marko Ružičić, Sanja Analysis of PDEs 35L65, 35L67, 35G35, 76L05 The shallow water system with a bed jump describes a fluid flow over a dam, represented by a simple step function with the Riemann initial data is such that the vacuum is on the right-hand side. The main question is whether the fluid will stay on the left-hand side of the dam. After approximating the step function space derivative with a fixed shadow wave, solutions to that problem stay bounded. A proper connection between waves on both sides of the dam, and a unique solution afterward is found by using the maximal dissipation principle. |
| title | Maximal dissipation and shallow water flow -- the dam-break problem |
| topic | Analysis of PDEs 35L65, 35L67, 35G35, 76L05 |
| url | https://arxiv.org/abs/2502.08329 |