A numerical model for the Boltzmann equation with applications to micro flows

Given an integer lattice L Rd, we define G as the orthogonal group leaving L invariant. Starting from a basic kinetic model on G we construct a collision operator onLwhich keeps all the essential features of the classical Boltzmann collision operator. For a particular 3D lattice we demonstrate the suitability of this discrete model for the numerical simulation of rarefied flows. For several examples, e.g. in the context of micro flows, we find a good qualitative and quantitative agreement of our simulation results with test data.