Non-Equilibrium Solutions of a Hierarchy of Discrete Velocity Models in the Transport Theory of Dilute Gases Including Internal Degrees of Freedom

Kinetic equations based on the microscopic collision behaviour of molecules, atoms and photons govern the physical behaviour of gases in highly non-equilibrium states. These kinetic equations as e.g. the Boltzmann equations can be solved generally only under very restrictive or ideal conditions. Our intention is to overcome this problem by means of so-called discrete velocity models. They only allow a finite number of particle velocities and therefore reduce the mathematical complexity of the kinetic equations considerably. Nevertheless they still keep many important properties of real gases. Thus solutions of these systems give insight into the principle mechanisms governing non-equilibrium states of gases like shock waves, strongly exothermic chemical reactions, laser irradiated atomic beams, etc.