Normal, high order discrete velocity models of the Boltzmann equation

Abstract

This paper aims at approximations of the collision operator in the Boltzmann equation. The developed framework guarantees the “normality” of the approximation, which means correct collision invariants, H-Theorem, and equilibrium solutions. It fits into the discrete velocity model framework, is given in such a way that it is understandable with undergraduate level mathematics and can be used to construct approximations with arbitrary high convergence orders. At last we give an example alongside a numerical verification. Here the convergence orders range up to 3 (2) and the time complexity is given by 3+12 (4+23) in 2 (3) dimensions.