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.

翻译：本文提出了一种可压缩流体流动中热传导的新模型。该模型在欧拉坐标系中基于Hamilton平稳作用原理建立，其中熵守恒作为欧拉-拉格朗日方程被恢复。研究表明，该控制方程组为双曲型，在添加适当的松弛项后，其渐近行为与可压缩热传导流体的欧拉方程一致。对Rankine-Hugoniot条件和Clausius-Duhem不等式的分析表明，接触间断无法存在，而膨胀波和压缩扇区可作为控制方程的解。我们通过一系列数值算例验证了上述特性。