An Eulerian hyperbolic model for heat transfer derived via Hamilton's principle: analytical and numerical study

Autor:	Dhaouadi, Firas, Gavrilyuk, Sergey
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematics - Numerical Analysis Physics - Fluid Dynamics 35L65 80A05 80M12 80-10 65M08
Zdroj:	Proceedings of the Royal Society Volume 480, Issue 2283 (2024)
Druh dokumentu:	Working Paper
DOI:	10.1098/rspa.2023.0440
Popis:	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. Comment: 27 pages, 9 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.12229 Zobrazit plný text záznamu View this record from Arxiv