Kinetic Models and the Linearized Boltzmann Equation

TLDR

Kinetic theory treatments of the linearized Boltzmann equation exhibit unsatisfactory features, especially in nearly free molecular flow regimes, which simplified kinetic models can address. The paper aims to establish relationships between the linearized Boltzmann equation and selected simplified kinetic models. This is achieved by comparing the eigenvalue spectra of the collision operators, with particular focus on inverse fifth‑molecule interactions. The analysis reveals the limitations of existing models and demonstrates how to construct more accurate models that overcome the main shortcomings of approximate solutions to 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.