In this paper, we consider the kinetic model of continuous type describing a polyatomic gas in two different settings corresponding to a different choice of the functional space used to define macroscopic quantities. Such a model introduces a single continuous variable supposed to capture all the phenomena related to the more complex structure of a polyatomic molecule. In particular, we provide a direct comparison of these two settings, and show their equivalence after the distribution function is rescaled and the cross section is reformulated. We then focus on the kinetic model for which the rigorous existence and uniqueness result in the space homogeneous case is recently proven. Using the cross section proposed in that analysis together with the maximum entropy principle, we establish macroscopic models of six and fourteen fields. In the case of six moments, we calculate the exact, nonlinear, production term and prove its total agreement with extended thermodynamics. Moreover, for the fourteen moments model, we provide new expressions for relaxation times and transport coefficients in a linearized setting, that yield both matching with the experimental data for dependence of the shear viscosity upon temperature and a satisfactory agreement with the theoretical value of the Prandtl number.

中文翻译：

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动力学和宏观水平的多相气体模拟

在本文中，我们考虑了连续类型的动力学模型，该模型描述了两种不同设置下的多原子气体，对应于用于定义宏观量的功能空间的不同选择。这种模型引入了单个连续变量，该变量应该捕获与多原子分子更复杂结构有关的所有现象。特别是，我们提供了这两种设置的直接比较，并在重新分配分布函数并重新制定了横截面后显示了它们的等效性。然后，我们关注动力学模型，对于该模型，最近证明了其在空间齐次情况下的严格存在性和唯一性。利用分析中提出的横截面以及最大熵原理，我们建立了六到十四个场的宏观模型。在六个时刻的情况下，我们计算出精确的，非线性的生产项，并证明其与扩展的热力学完全吻合。此外，对于十四阶矩模型，我们提供了线性化条件下的弛豫时间和传输系数的新表达式，其与剪切粘度对温度的依赖性实验数据相匹配，并且与Prandtl的理论值令人满意。数字。