The BGK-model with velocity-dependent collision frequency

Abstract

We consider the BGK-model with velocity dependent collision frequency. By use of the Chapman-Enskog method we calculate thermal conductivity and viscosity. We show that a simple power law for the collision frequency may lead to the proper Prandtl number. Moreover we use Grad’s moment method to calculate thermal conductivity and viscosity. We show that the results of both methods coincide if Grad’s method is based on a large number of moments.