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

Author:

Dhaouadi Firas1ORCID,Gavrilyuk Sergey2

Affiliation:

1. Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento, Italy

2. Aix-Marseille University and CNRS UMR 7343 IUSTI, 5 rue Enrico Fermi, 13453 Marseille, France

Abstract

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. A sufficient criterion for the hyperbolicity of the model is formulated. The governing equations are 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 Clausius–Duhem inequality is performed for a specific choice of the equation of state. In particular, this 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.

Funder

Agence Nationale de la Recherche

Ministero dell'Istruzione, dell'Università e della Ricerca

Publisher

The Royal Society

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