• Corpus ID: 216553172

Kinetic and macroscopic modelling of a rarefied polyatomic gas.

@article{DJordjic2020KineticAM,
  title={Kinetic and macroscopic modelling of a rarefied polyatomic gas.},
  author={Vladimir DJordji'c and Milana Pavi'c-vColi'c and Nikola Spasojevi{\'c}},
  journal={arXiv: Mathematical Physics},
  year={2020}
}

• Vladimir DJordji'c, Milana Pavi'c-vColi'c, N. Spasojević
• Published 25 April 2020
• Mathematics
• arXiv: Mathematical Physics

In this paper, we consider the two kinetic models of continuous type for a polyatomic gas [12, 8], that introduce a single continuous variable supposed to capture all the phenomena related to the more complex structure of a molecule having more than one atom, such as internal degrees of freedom in a collision. In particular, we provide a direct comparison of these two models, and show their equivalence after the distribution function is rescaled and the cross section is reformulated, by elaborating the argument of [4]. We then focus on the kinetic model [8] for which the rigorous existence and uniqueness result in a space homogeneous setting is recently proven in [13]. Using the cross section proposed in this model 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 [1], as it satisfies the entropy residual inequality on the whole range of model validity. 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, on the room temperature range when only translational and rotational modes of molecules are taken into account, as much as on higher temperatures when vibrational modes appear as well.