A method for constructing a model form for the Boltzmann equation

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Abstract
The model of the Boltzmann equation is a useful tool for researching the motion of rarefied gases. The Bhatnagar, Gross, and Krook (BGK) model has been widely used. Gross and Jackson suggested a hierarchy of models to improve the BGK model, thus introducing nonlinearities. In the present paper, a different method for constructing a model equation is suggested. The main point of this method is that in the two limiting cases, the viscous flow regime and the molecular flow regime, the solutions of the model equation must be the same as those of the Boltzmann equation. The model equation thus constructed is consistent with that obtained in the Gross and Jackson hierarchy with 13 moments. It satisfied the conservation laws and has an H theorem.