Moment equations for a polytropic gas reproducing adjustable transport coeffcients
Kdy: 02/03/2022 17:00 - 02/03/2022 18:30
Kde: Online via Zoom
In this talk we will consider the kinetic model of continuous type describing a polyatomic gas in the non-weighted
setting. Such a model introduces a single continuous variable supposed to capture all the phenomena related to the
more complex structure of a polyatomic molecule. For the complete polyatomic collision operator we propose a
convex combination of purely polyatomic (nonfrozen) and frozen collisions. Motivated by recently proven rigorous
existence and uniqueness result in the space homogeneous case, we use the cross section proposed in that analysis and
establish macroscopic models. In order to see contribution of frozen collisions and moment hierarchy, we compute
relaxation times and transport coecients in a linearized setting for fourteen and seventeen moments system. Then,
in the case of seventeen moments with included frozen collision show both matching with the experimental data for
dependence of the shear viscosity upon temperature and agreement with the theoretical value of Prandtl number given
by the Eucken formula. Finally, we conclude that higher order system together with frozen collisions gives more
adjustable transport coecients.
In addition, the consistency with the monatomic case is achieved by properly rescaling the collision frequency.