Kinetic Models and the Linearized Boltzmann Equation

Abstract

Attention is directed to some unsatisfactory features of kinetic theory treatments of problems for which the linearized Boltzmann equation is applicable. The main defects are in the region where nearly free molecular flow conditions prevail. They can be overcome when the problems are treated by simplified kinetic models. In this paper relations between the linearized Boltzmann equation and some models are established. The method is based on a comparison of the eigenvalue spectra of the respective collision operators. Particular attention is paid to inverse fifth molecules. This allows evaluation of the limitations of a given model and shows how more accurate models can be constructed. It is shown how one may overcome the chief shortcomings of approximate solutions of the linearized Boltzmann equation.