Which moments are appropriate to describe gases with internal structure in Rational Extended Thermodynamics?
Which moments are appropriate to describe gases with internal structure in Rational Extended Thermodynamics?
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DOI：
10.1016/j.ijnonlinmec.2021.103820
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发表时间：
2021-10-06
影响因子：
3.2
通讯作者：
Ruggeri, Tommaso
中科院分区：
文献类型：
--
作者：
Arima, Takashi;Carrisi, Maria Cristina;Ruggeri, Tommaso
受 Pennisi 最近在相对论框架 Pennisi (2021) 中发表的论文的启发，我们批判性地重新审视了之前的两种矩层次方法，并提出了一种新的自然物理矩层次来描述分子有理扩展热力学框架中的经典稀薄非多变多原子气体。证明前一种方法的微分系统是本方法的主要系统。主要思想是，在分子水平上，总能量是动能加上由于旋转和振动而产生的内模态能量，并且增加力矩包含该总能量作为功率，其中功率指数随着张量指数的数量而增加。特别地，我们考虑15个矩的情况，并使用最大熵原理的变分法来封闭系统。我们证明了熵的凸性以及将系统置于对称形式的可能性。这种更丰富的动力学框架也可能很有趣，因为它可能应用于生物数学或最近成功应用动力学模型的其他领域。
Motivated by a recent paper of Pennisi in the relativistic framework Pennisi (2021), we revisit the previous approach of two hierarchies of moments critically and propose a new natural physical hierarchy of moments to describe classical rarefied non-polytropic polyatomic gas in the framework of Molecular Rational Extended Thermodynamics. The differential system of the previous approach is proved to be a principal sutsystem of the present one. The main idea is that at the molecular level, the total energy is the kinetic energy plus the energy of internal mode due to the rotation and vibration, and the increasing moments contain this total energy as power in which the power index increases with the number of tensorial indexes. In particular, we consider the case of 15 moments, and we close the system using the variational method of the Maximum Entropy Principle. We prove the convexity of entropy and the possibility to put the system in symmetric form. This more rich kinetic framework may be interesting also as possible applications to biomathematics or other fields in which kinetic models were applied recently with success.