An Eulerian hyperbolic model for heat transfer derived via Hamilton's principle: analytical and numerical study
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910562057715712 |
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| author | Dhaouadi, Firas Gavrilyuk, Sergey |
| author_facet | Dhaouadi, Firas Gavrilyuk, Sergey |
| contents | In this paper, we present a new model for heat transfer in compressible fluid flows. The model is derived from Hamilton's principle of stationary action in Eulerian coordinates, in a setting where the entropy conservation is recovered as an Euler--Lagrange equation. The governing system is shown to be hyperbolic. It is asymptotically consistent with the Euler equations for compressible heat conducting fluids, provided the addition of suitable relaxation terms. A study of the Rankine--Hugoniot conditions and the Clausius--Duhem inequality reveals that contact discontinuities cannot exist while expansion waves and compression fans are possible solutions to the governing equations. Evidence of these properties is provided on a set of numerical test cases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_12229 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Eulerian hyperbolic model for heat transfer derived via Hamilton's principle: analytical and numerical study Dhaouadi, Firas Gavrilyuk, Sergey Analysis of PDEs Numerical Analysis Fluid Dynamics 35L65, 80A05, 80M12, 80-10, 65M08 In this paper, we present a new model for heat transfer in compressible fluid flows. The model is derived from Hamilton's principle of stationary action in Eulerian coordinates, in a setting where the entropy conservation is recovered as an Euler--Lagrange equation. The governing system is shown to be hyperbolic. It is asymptotically consistent with the Euler equations for compressible heat conducting fluids, provided the addition of suitable relaxation terms. A study of the Rankine--Hugoniot conditions and the Clausius--Duhem inequality reveals that contact discontinuities cannot exist while expansion waves and compression fans are possible solutions to the governing equations. Evidence of these properties is provided on a set of numerical test cases. |
| title | An Eulerian hyperbolic model for heat transfer derived via Hamilton's principle: analytical and numerical study |
| topic | Analysis of PDEs Numerical Analysis Fluid Dynamics 35L65, 80A05, 80M12, 80-10, 65M08 |
| url | https://arxiv.org/abs/2305.12229 |