Monatomic gas as a singular limit of polyatomic gas in molecular extended thermodynamics with many moments
Monatomic gas as a singular limit of polyatomic gas in molecular extended thermodynamics with many moments
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DOI：
10.1016/j.aop.2016.04.015
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发表时间：
2016-09-01
影响因子：
3
通讯作者：
Taniguchi, Shigeru
中科院分区：
文献类型：
--
作者：
Arima, Takashi;Ruggeri, Tommaso;Taniguchi, Shigeru
从脱离局域平衡假设的稀薄气体分子扩展热力学(MET)的观点出发，讨论了处于高度非平衡态的单原子气体和多原子气体的理论结构差异。这两种气体的MET理论都是基于具有不同层次结构的力矩平衡方程，这是因为分子的内部自由度是否包含在其分布函数中。特别是多原子气体的MET理论中的平衡方程个数大于相应的单原子气体理论中的平衡方程个数。采用了最近一篇论文(Arima等人，2014)中获得的多原子气体平衡方程组的闭合程序。我们证明了，只要施加与单原子气体相容的适当初始条件，多原子气体的解在分子D的自由度趋于3的极限内收敛到单原子气体的解。因此，稀薄单原子气体的MET理论可以被认为是相应的稀薄多原子气体MET理论的奇异极限。作为例证，给出了D>；3在超声波频散关系和冲击波结构中的渐近行为。(C)2016 Elsevier Inc.保留所有权利。
The difference in the theoretical structure between monatomic and polyatomic gases in highly nonequilibrium states is discussed from the viewpoint of molecular extended thermodynamics (MET) of rarefied gases, which is free from the local equilibrium assumption. The MET theories of these two types of gases are based on the moment balance equations with different hierarchy structures due to whether the internal degrees of freedom of a molecule are incorporated in their distribution functions or not. In particular, the number of balance equations in the MET theory of polyatomic gases is greater than the number in the corresponding theory of monatomic gases. The closure procedure for the system of balance equations of polyatomic gases obtained in a recent paper (Arima et al., 2014) is adopted. We prove that the solutions for polyatomic gases converge, in the limit where the degrees of freedom of a molecule D tend to 3, to the ones for monatomic gases provided that we impose appropriate initial conditions compatible with monatomic gases. Thus a MET theory of rarefied monatomic gases can be identified as a singular limit of the corresponding MET theory of rarefied polyatomic gases. As illustrative examples, the asymptotic behaviors when D -> 3 in the dispersion relation of ultrasonic waves and in the shock wave structure are shown. (C) 2016 Elsevier Inc. All rights reserved.