通过汉密尔顿原理得出的传热欧拉双曲模型:分析和数值研究

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-02-07 DOI:10.1098/rspa.2023.0440
Firas Dhaouadi, Sergey Gavrilyuk
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引用次数: 0

摘要

在本文中,我们提出了一种新的可压缩流体流动传热模型。该模型源于欧拉坐标中的汉密尔顿静止作用原理,熵守恒恢复为欧拉-拉格朗日方程。提出了模型双曲性的充分标准。如果添加适当的松弛项,治理方程与可压缩导热流体的欧拉方程近似一致。针对状态方程的特定选择,对兰金-胡格尼奥特条件和克劳修斯-杜恒不等式进行了研究。研究结果特别表明,接触不连续不可能存在,而膨胀波和压缩风扇则是控制方程的可能解。一组数值测试案例证明了这些特性。
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An Eulerian hyperbolic model for heat transfer derived via Hamilton’s principle: analytical and numerical study
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.
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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