从非平衡热力学的单发电机支架形式出发的相对论流体力学

IF 4.3 3区 工程技术 Q1 MECHANICS Journal of Non-Equilibrium Thermodynamics Pub Date : 2023-12-05 DOI:10.1515/jnet-2023-0068
Vlasis G. Mavrantzas
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引用次数: 0

摘要

我们采用Beris和Edwards的非平衡热力学的广义支架形式,推导出具有粘度、膨胀粘度和导热性的不完美流体的洛伦兹协变时间演化方程。密切关注Öttinger提出的分析(物理学A, 259, 1998,24 - 42;对于同样的问题,但对于一般形式,我们在流体动力变量集合中包括一个协变矢量,它起着广义热力的作用,以及一个与速度梯度张量密切相关的协变张量。在我们这里的工作中,我们首先推导出非相对论性方程,然后通过将热变量提升到一个四向量,将机械力变量提升到一个四乘四张量,并通过用能量动量张量的时间分量表示系统的哈密顿量来获得相对论性方程。对于泊松和耗散支架,我们假设与非相对论情况下相同的一般结构,但耗散支架中描述摩擦对热和粘性效应的现象学系数被适当约束,从而使得到的动力方程显着为洛伦兹协变。最终的相对论方程与Öttinger导出的方程相同,但目前的方法似乎更普遍,因为人们可以考虑描述摩擦的现象学系数的其他形式,以确保洛伦兹协方差。
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Relativistic hydrodynamics from the single-generator bracket formalism of nonequilibrium thermodynamics
We employ the generalized bracket formalism of nonequilibrium thermodynamics by Beris and Edwards to derive Lorentz-covariant time-evolution equations for an imperfect fluid with viscosity, dilatational viscosity, and thermal conductivity. Following closely the analysis presented by Öttinger (Physica A, 259, 1998, 24–42; Physica A, 254, 1998, 433–450) to the same problem but for the GENERIC formalism, we include in the set of hydrodynamic variables a covariant vector playing the role of a generalized thermal force and a covariant tensor closely related to the velocity gradient tensor. In our work here, we derive first the nonrelativistic equations and then we proceed to obtain the relativistic ones by elevating the thermal variable to a four-vector, the mechanical force variable to a four-by-four tensor, and by representing the Hamiltonian of the system with the time component of the energy-momentum tensor. For the Poisson and dissipation brackets we assume the same general structure as in the nonrelativistic case, but with the phenomenological coefficients in the dissipation bracket describing friction to heat and viscous effects being properly constrained for the resulting dynamic equations to be manifest Lorentz-covariant. The final relativistic equations are identical to those derived by Öttinger but the present approach seems to be more general in the sense that one could think of alternative forms of the phenomenological coefficients describing friction that could ensure Lorentz-covariance.
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来源期刊
CiteScore
9.10
自引率
18.20%
发文量
31
审稿时长
1 months
期刊介绍: The Journal of Non-Equilibrium Thermodynamics serves as an international publication organ for new ideas, insights and results on non-equilibrium phenomena in science, engineering and related natural systems. The central aim of the journal is to provide a bridge between science and engineering and to promote scientific exchange on a) newly observed non-equilibrium phenomena, b) analytic or numeric modeling for their interpretation, c) vanguard methods to describe non-equilibrium phenomena. Contributions should – among others – present novel approaches to analyzing, modeling and optimizing processes of engineering relevance such as transport processes of mass, momentum and energy, separation of fluid phases, reproduction of living cells, or energy conversion. The journal is particularly interested in contributions which add to the basic understanding of non-equilibrium phenomena in science and engineering, with systems of interest ranging from the macro- to the nano-level. The Journal of Non-Equilibrium Thermodynamics has recently expanded its scope to place new emphasis on theoretical and experimental investigations of non-equilibrium phenomena in thermophysical, chemical, biochemical and abstract model systems of engineering relevance. We are therefore pleased to invite submissions which present newly observed non-equilibrium phenomena, analytic or fuzzy models for their interpretation, or new methods for their description.
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