A model for rotational energy exchange in polyatomic gases

Abstract

Numerical methods for solving the Boltzmann equation must rely upon simplified models of the differential scattering cross-section. Whereas a variety of useful models are known for monatomic gases, little else is available for polyatomic gases than the traditional rough spheres and various smooth exisymmetric bodies. Kinematic models with only one new variable - the rotational energy - seem preferable. However, blind mathematical construction runs the risk of violating the detailed-balance symmetry. The Borgnakke-Larsen model avoids this trouble, as does a new model where the redistribution of rotational energy is pictured as resulting from a continous Markov process. Both models are easily adjusted so as to reproduce the known values of viscosity, volume viscosity and thermal conductivity. With some modification the temperature dependence of viscosity can also be incorporated.