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

Given an integer lattice L⊂RdL⊂Rd, we define GG as the orthogonal group leaving LL invariant. Starting from a basic kinetic model on GG we construct a collision operator on LL which 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.