Discrete velocity models of the Boltzmann equation and conservation laws

Abstract

We consider in this paper the general problem of construction and classification of normal, i.e. without spurious invariants, discrete velocity models (DVMs)of the classical (elastic) Boltzmann equation. We explain in detail how this problem can be solved and present a complete classification of (i.e. we present all distinct) normal plane DVMswith relatively small number $n$ of velocities ($n\leq 10$). Some results for models with larger number of velocities are also presented.