Symmetric-hyperbolic system of conservative equations for a viscous heat conducting fluid
Symmetric-hyperbolic system of conservative equations for a viscous heat conducting fluid
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粘性导热流体的对称双曲保守方程组
DOI：
10.1007/bf01189206
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
T. Ruggeri
中科院分区：
文献类型：
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作者：
T. Ruggeri
对“广义不可逆热力学”模型提出了一些重要的考虑。本文从广义不可逆热力学的基本思想出发，结合“理性热力学”中的“熵原理”，提出了一种新的方法（“生成元不变性”），并由此建立了牛顿热粘性流体的理论。与以前的理论相比，该理论具有以下新的性质：a）对于任何场变量值，只要通常的热力学稳定性条件满足，方程组都是双曲的。（平衡时的最大熵）成立;所有的波传播速度都是真实的和有限的; B）系统是保守的，并且有可能寻求弱解，特别是冲击波;此外，该系统是Friedrichs意义下的双曲系统，因此对于弱解和激波具有特殊性质; c）在非平衡态下，相对于平衡态下的相应热力学变量，唯一的热力学变量是熵密度和化学势;因此，只有一个绝对温度，在弛豫中起着重要作用;（4）熵原理自动满足。
Some critical considerations on the models of “extended irreversible thermodynamics” are given. By developing a methodology (“invariance of the generators”) based both on the ideas of the “extended irreversible thermodynamics” and the “entropy principle” in its general formulation of “rational thermodynamics”, a theory for a newtonian thermoviscous fluid is proposed. The theory has the following properties, new when compared with previous ones: a) the system of equations is hyperbolic for any value of the field variables, provided that the usual thermodynamic stability condition (maximum entropy at equilibrium) holds; all wave-propagation speeds are then real and finite; b) the system is conservative and it is possible to seek for weak solutions and, in particular, for shockwaves; moreover, the system is symmetric-hyperbolic in the sense of Friedrichs; special properties hold therefore for weak solutions and shocks; c) the only thermodynamic variables at non-equilibrium, modified with respect to the corresponding ones at equilibrium, are the entropy density and chemical potential; consequentely, there exists only a single absolute temperature, playing an important role in relaxations; d) the entropy principle is automatically satisfied.