Causal dissipation in the relativistic dynamics of barotropic fluids
Causal dissipation in the relativistic dynamics of barotropic fluids
复制标题
正压流体相对论动力学中的因果耗散
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
B. Temple
中科院分区：
文献类型：
--
作者：
H. Freistühler;B. Temple
本文发展了两个因果四场理论的相对论流体动力学，一个是正压粘性流体和其他粘性导热流体是“热正压”，一个属性，这是新定义的。虽然类似于作者的文章《理想气体相对论动力学的因果耗散》中的五场理论的推导[Freistuhler，H。坦普尔，B，程序R Soc. A 473，20160729（2017）]，论证始终以更接近Eckart的流动框架（而不是朗道的）的方式进行，并且结果直接与Eckart，Lichnerowicz和Choquet-Bruhat提出的早期建议产生的四场理论进行比较。关键的想法是强加二阶对称双曲的意义上的休斯，加藤，和马斯登[拱。理性Mech. Anal。63，273-294（1976）]，在自然Godunov变量中，使相应的完美流体守恒律系统在一阶意义上对称双曲。粘性导热热正压流体的新理论属于Hughes-Kato-Marsden类;粘性一般正压流体的新理论位于该类的边界。与五场理论一样，体粘滞系数η、剪切粘滞系数η以及热正压流体的导热系数χ都是自由参数，根据这些参数，相对论耗散张量在作者提出的三个条件下是唯一确定的：对称双曲性，尖锐的因果关系，以及与Eckart的一阶等价性--要求所得方程等价于Eckart方程的首阶，η和χ。一般粘性正压流体的新理论补充了上述关于大量理想气体的论文中给出的理论。粘性导热热正压流体的新理论特别包括纯辐射的情况，作为一个应用，对作者先前在纯辐射的相对论流体动力学中的因果耗散和激波剖面中的提议提供了定量校正[Freistuhler，H.坦普尔，B，程序R。本文发展了相对论流体动力学的两个因果四场理论，一个用于正压的粘性流体，另一个用于“热正压”的粘性导热流体，这是本文新定义的性质。虽然类似于作者的文章《理想气体相对论动力学的因果耗散》中的五场理论的推导[Freistuhler，H。坦普尔，B，程序R。Soc. A 473，20160729（2017）]，论证始终以更接近Eckart的流动框架（而不是朗道的）的方式进行，并且结果直接与Eckart，Lichnerowicz和Choquet-Bruhat提出的早期建议产生的四场理论进行比较。关键的想法是强加二阶对称双曲的意义上的休斯，加藤，和马斯登[拱。理性Mech. Anal。63，273-294（1976）]，在自然Goddom变量，使相应的系统的完美流体守恒律对称双曲的一阶意义下，...
This paper develops two causal four-field theories of relativistic fluid dynamics, one for viscous fluids that are barotropic and the other for viscous heat-conductive fluids that are “thermo-barotropic,” a property that is newly defined here. While similar to the deduction of a five-field theory in the authors’ article Causal dissipation for the relativistic dynamics of ideal gases [Freistuhler, H. and Temple, B., Proc. R. Soc. A 473, 20160729 (2017)], the argumentation is consistently carried out in a way that stays closer to Eckart’s flow frame (than to Landau’s), and the result is directly compared with the four-field theories resulting from early proposals made by Eckart, Lichnerowicz, and Choquet-Bruhat. The key idea is to impose second-order symmetric hyperbolicity in the sense of Hughes, Kato, and Marsden [Arch. Rational Mech. Anal. 63, 273–294 (1976)], in the natural Godunov variables that make the corresponding system of perfect-fluid conservation laws symmetric hyperbolic in the first order sense. The new theory for viscous heat-conductive thermo-barotropic fluids belongs to the Hughes-Kato-Marsden class; the new theory for viscous general barotropic fluids lies on the boundary of that class. As in the five-field theory, the coefficients of bulk viscosity ζ, shear viscosity η, and, in the case of thermo-barotropic fluids, that of heat conductivity χ are free parameters, and in terms of these, the relativistic dissipation tensor is uniquely determined under three conditions which the authors propose as definitive: symmetric hyperbolicity, sharp causality, and first-order equivalence with Eckart—the requirement that the resulting equations be equivalent to the Eckart equations to leading order in ζ, η, and χ. The new theory for general viscous barotropic fluids complements the one given in the abovementioned paper for massive ideal gases. The new theory for viscous heat-conductive thermo-barotropic fluids notably includes the case of pure radiation, providing as one application a quantitative correction to the authors’ previous proposal in Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation [Freistuhler, H. and Temple, B., Proc. R. Soc. A 470, 20140055 (2014)].This paper develops two causal four-field theories of relativistic fluid dynamics, one for viscous fluids that are barotropic and the other for viscous heat-conductive fluids that are “thermo-barotropic,” a property that is newly defined here. While similar to the deduction of a five-field theory in the authors’ article Causal dissipation for the relativistic dynamics of ideal gases [Freistuhler, H. and Temple, B., Proc. R. Soc. A 473, 20160729 (2017)], the argumentation is consistently carried out in a way that stays closer to Eckart’s flow frame (than to Landau’s), and the result is directly compared with the four-field theories resulting from early proposals made by Eckart, Lichnerowicz, and Choquet-Bruhat. The key idea is to impose second-order symmetric hyperbolicity in the sense of Hughes, Kato, and Marsden [Arch. Rational Mech. Anal. 63, 273–294 (1976)], in the natural Godunov variables that make the corresponding system of perfect-fluid conservation laws symmetric hyperbolic in the first order sen...