Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation
Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation
复制标题
纯辐射相对论流体动力学中的因果耗散和冲击剖面
DOI：
10.1098/rspa.2014.0055
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
B. Temple
中科院分区：
文献类型：
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作者：
H. Freistühler;B. Temple
目前的理论在相对论制度的耗散遭受两个赤字之一：要么他们的耗散不是因果关系或没有配置文件的强冲击波存在。本文提出了一个相对论性的Navier-Stokes-Fourier型粘性和热传导张量，从而产生的二阶系统的偏微分方程的纯辐射的流体动力学是对称双曲型。该系统具有因果耗散以及任意强度的所有冲击波具有光滑剖面的性质。熵产生是积极的梯度附近的无耗散方程的解决方案和梯度的冲击剖面。这表明新的耗散应力张量符合热力学原理的主导阶。是否需要高阶修正的Ancestor，以获得充分的兼容性与第二定律远离零耗散平衡留给进一步的调查。该系统具有三个先验自由参数χ、η、τ，物理上对应于热导率、剪切粘度和体积粘度。如果体积粘度为零（如文献中所述），并且总应力-能量张量是无迹的，则整个粘度和热传导张量被确定为在常数因子内。
Current theories of dissipation in the relativistic regime suffer from one of two deficits: either their dissipation is not causal or no profiles for strong shock waves exist. This paper proposes a relativistic Navier–Stokes–Fourier-type viscosity and heat conduction tensor such that the resulting second-order system of partial differential equations for the fluid dynamics of pure radiation is symmetric hyperbolic. This system has causal dissipation as well as the property that all shock waves of arbitrary strength have smooth profiles. Entropy production is positive both on gradients near those of solutions to the dissipation-free equations and on gradients of shock profiles. This shows that the new dissipation stress tensor complies to leading order with the principles of thermodynamics. Whether higher order modifications of the ansatz are required to obtain full compatibility with the second law far from the zero-dissipation equilibrium is left to further investigations. The system has exactly three a priori free parameters χ,η,ζ, corresponding physically to heat conductivity, shear viscosity and bulk viscosity. If the bulk viscosity is zero (as is stated in the literature) and the total stress–energy tensor is trace free, the entire viscosity and heat conduction tensor is determined to within a constant factor.