On derivation and verification of a kinetic model for quantum vibrational energy of polyatomic gases in the gas-kinetic unified algorithm

In this paper, a kinetic Boltzmann model equation involving internal degrees of freedom is constructed for thermodynamic non-equilibrium polyatomic gases, in which the continuous distribution mode rotational energy and discrete quantum effect vibrational are both considered, respectively. By theoretically analyzing “recurrence feature” model, it found that root comes from translational-rotational-vibrational relaxation term (G3t,r,v), because additional relative to energy. Besides, some important properties also analyzed proved, including conservative property entropy inequality. Then, balance equations on each level about macroscopic variables derived by moment method. The corresponding relationship hydrodynamic limit simplified version Chapman-Enskog method, correct Prandtl number obtained. Numerical methods wall surface boundary condition solve presented here. Finally, planar flows past cylinder with different Mach numbers numerically simulated test verify reliability analyze influence rules excited gas flows.