Kinetic Models on Orthogonal Groups and the Simulation of the Boltzmann Equation

The minimal requirement for a mathematical structure to be the basis of a kinetic model is a group. We show how this observation may be used to construct kinetic models on integer lattices via their automorphism groups. Using these models for numerical simulations we find that they are valuable tools for the understanding of a variety of phenomena of rarefied gas dynamics. In some detail we discuss thermal creep flow and an evaporation condensation problem for a binary gas mixture.