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Leopoldo S. García-Colín, Rosa María Velasco, Francisco Javier Uribe

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

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.

Journal of Non-Equilibrium Thermodynamics, Walter de Gruyter

Print ISSN: 0340-0204
Volume: 29, 09/2004
Pages: 257 - 277

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