Convergence of a Hyperbolic Thermodynamically Compatible Finite Volume scheme for the Euler equations
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| Format: | Preprint |
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2024
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| _version_ | 1866914172812394496 |
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| author | Dumbser, Michael Lukáčová-Medvid'ová, Mária Thomann, Andrea |
| author_facet | Dumbser, Michael Lukáčová-Medvid'ová, Mária Thomann, Andrea |
| contents | We study the convergence of a novel family of thermodynamically compatible schemes for hyperbolic systems (HTC schemes) in the framework of dissipative weak solutions, applied to the Euler equations of compressible gas dynamics. Two key novelties of our method are i) entropy is treated as one of the main field quantities and ii) the total energy conservation is a consequence of compatible discretization and application of the Abgrall flux. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_15730 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence of a Hyperbolic Thermodynamically Compatible Finite Volume scheme for the Euler equations Dumbser, Michael Lukáčová-Medvid'ová, Mária Thomann, Andrea Numerical Analysis We study the convergence of a novel family of thermodynamically compatible schemes for hyperbolic systems (HTC schemes) in the framework of dissipative weak solutions, applied to the Euler equations of compressible gas dynamics. Two key novelties of our method are i) entropy is treated as one of the main field quantities and ii) the total energy conservation is a consequence of compatible discretization and application of the Abgrall flux. |
| title | Convergence of a Hyperbolic Thermodynamically Compatible Finite Volume scheme for the Euler equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2412.15730 |