Inconsistency in the Moment’s method for solving the Boltzmann equation
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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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© Walter de Gruyter
Articles in the same Issue
- Gerard A. Maugin, 60 years young
- Non-linear phenomena in thermoacoustic engines
- Entropy production in polarizable bodies with internal variables
- Thermodynamic interaction between two discrete systems in non-equilibrium
- Inconsistency in the Moment’s method for solving the Boltzmann equation
- Modelling mass transport through a porous partition: Effect of pore size distribution
- Time scales for energy transfer
Articles in the same Issue
- Gerard A. Maugin, 60 years young
- Non-linear phenomena in thermoacoustic engines
- Entropy production in polarizable bodies with internal variables
- Thermodynamic interaction between two discrete systems in non-equilibrium
- Inconsistency in the Moment’s method for solving the Boltzmann equation
- Modelling mass transport through a porous partition: Effect of pore size distribution
- Time scales for energy transfer