Discrete velocity models of the Boltzmann equation and conservationlaws

Alexander Bobylev; Mirela Vinerean; Åsa Windfäll

doi:10.3934/krm.2010.3.35

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2010, Volume 3, Issue 1: 35-58. Doi: 10.3934/krm.2010.3.35

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Discrete velocity models of the Boltzmann equation and conservation laws

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

Received: October 2009

Revised: November 2009

Published: March 2010

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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 DVMs with relatively small number $n$ of velocities ($n\leq 10$). Some results for models with larger number of velocities are also presented.

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Mathematics Subject Classification: Primary: 82C40; Secondary: 76P05.

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