# American Institute of Mathematical Sciences

March  2010, 3(1): 35-58. doi: 10.3934/krm.2010.3.35

## Discrete velocity models of the Boltzmann equation and conservation laws

 1 Department of Mathematics, Karlstad University, SE-651 88 Karlstad, Sweden, Sweden, Sweden

Received  October 2009 Revised  November 2009 Published  January 2010

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 DVMs with relatively small number $n$ of velocities ($n\leq 10$). Some results for models with larger number of velocities are also presented.
Citation: Alexander Bobylev, Mirela Vinerean, Åsa Windfäll. Discrete velocity models of the Boltzmann equation and conservation laws. Kinetic & Related Models, 2010, 3 (1) : 35-58. doi: 10.3934/krm.2010.3.35
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