First-order greedy invariant-domain preserving approximation for hyperbolic problems: scalar conservation laws, and p-system
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917730606645248 |
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| author | Guermond, Jean-Luc Maier, Matthias Popov, Bojan Saavedra, Laura Tomas, Ignacio |
| author_facet | Guermond, Jean-Luc Maier, Matthias Popov, Bojan Saavedra, Laura Tomas, Ignacio |
| contents | The paper focuses on first-order invariant-domain preserving approximations of hyperbolic systems. We propose a new way to estimate the artificial viscosity that has to be added to make explicit, conservative, consistent numerical methods invariant-domain preserving and entropy inequality compliant. Instead of computing an upper bound on the maximum wave speed in Riemann problems, we estimate a minimum wave speed in the said Riemann problems such that the approximation satisfies predefined invariant-domain properties and predefined entropy inequalities. This technique eliminates non-essential fast waves from the construction of the artificial viscosity, while preserving pre-assigned invariant-domain properties and entropy inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01713 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | First-order greedy invariant-domain preserving approximation for hyperbolic problems: scalar conservation laws, and p-system Guermond, Jean-Luc Maier, Matthias Popov, Bojan Saavedra, Laura Tomas, Ignacio Numerical Analysis 35L65, 65M60, 65M12, 65N30 The paper focuses on first-order invariant-domain preserving approximations of hyperbolic systems. We propose a new way to estimate the artificial viscosity that has to be added to make explicit, conservative, consistent numerical methods invariant-domain preserving and entropy inequality compliant. Instead of computing an upper bound on the maximum wave speed in Riemann problems, we estimate a minimum wave speed in the said Riemann problems such that the approximation satisfies predefined invariant-domain properties and predefined entropy inequalities. This technique eliminates non-essential fast waves from the construction of the artificial viscosity, while preserving pre-assigned invariant-domain properties and entropy inequalities. |
| title | First-order greedy invariant-domain preserving approximation for hyperbolic problems: scalar conservation laws, and p-system |
| topic | Numerical Analysis 35L65, 65M60, 65M12, 65N30 |
| url | https://arxiv.org/abs/2310.01713 |