Boltzmann Equation and Discrete Velocity Models : A discrete velocity model for polyatomic molecules

Sammanfattning: In the study of kinetic theory and especially in the study of rarefied gas dynamics one often turns to the Boltzmann equation. The mathematical theory developed by Ludwig Boltzmann was at first sight applicable in aerospace engineering and fluid mechanics. As of today, the methods in kinetic theory are extended to other fields, for instance, molecular biology and socioeconomics, which makes the need of finding efficient solution methods still important. In this thesis, we study the underlying theory of the continuous and discrete Boltzmann equation for monatomic gases. We extend the theory where needed, such that, we cover the case of colliding molecules that possess different levels of internal energy. Mainly, we discuss discrete velocity models and present explicit calculations for a model of a gas consisting of polyatomic molecules modelled with two levels of internal energy.