A high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916936370094080 |
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| author | Guermond, Jean-Luc Maier, Matthias Tovar, Eric |
| author_facet | Guermond, Jean-Luc Maier, Matthias Tovar, Eric |
| contents | We introduce a high-order space-time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP) and well-balanced with respect to rest states. The employed time-stepping technique is a novel explicit Runge-Kutta (ERK) approach which is an extension of the class of ERK-IDP methods introduced by Ern and Guermond (SIAM J. Sci. Comput. 44(5), A3366--A3392, 2022) for systems of non-linear conservation equations. The resulting method is then numerically illustrated through verification and validation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_17123 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations Guermond, Jean-Luc Maier, Matthias Tovar, Eric Numerical Analysis 65M60, 65M12, 35L50, 35L65, 76M10 We introduce a high-order space-time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP) and well-balanced with respect to rest states. The employed time-stepping technique is a novel explicit Runge-Kutta (ERK) approach which is an extension of the class of ERK-IDP methods introduced by Ern and Guermond (SIAM J. Sci. Comput. 44(5), A3366--A3392, 2022) for systems of non-linear conservation equations. The resulting method is then numerically illustrated through verification and validation. |
| title | A high-order explicit Runge-Kutta approximation technique for the Shallow Water Equations |
| topic | Numerical Analysis 65M60, 65M12, 35L50, 35L65, 76M10 |
| url | https://arxiv.org/abs/2403.17123 |