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Inconsistency in the Moment’s method for solving the Boltzmann equation

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Published/Copyright: June 1, 2005
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Journal of Non-Equilibrium Thermodynamics
From the journal Volume 29 Issue 3

Abstract

Moment’s methods devised to solve the Boltzmann kinetic equation for a simple, inert, dilute gas exhibit inconsistencies. These are brought up in a general way for the ordinary Boltzmann equation (BE), the Bhatnagar-Gross-Krook (BGK) model, and the Mott-Smith ansatz. Although also present in the Chapman-Enskog method the nature of its perturbation expansion in terms of Knudsen’s number takes care of the problem in a natural way. We show that indeed another step based on this idea is required to arrive at a closure condition in the moment’s solution. Also, a general proof is offered showing why these inconsistencies appear when appealing to moment expansions.

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Published Online: 2005-06-01
Published in Print: 2004-09-01

© Walter de Gruyter

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