Abstract
While the standard Bhatnagar–Gross–Krook (BGK) model leads to the wrong Prandtl number, the BGK model with velocity dependent collision frequency as well as the ellipsoidal statistical BGK (ES-BGK) model can be adjusted to give its proper value of 2/3. In this paper, the BGK model with velocity dependent collision frequency is considered in some detail. The corresponding thermal conductivity and viscosity are computed from the Chapman–Enskog method, and several velocity-dependent collision frequencies are introduced which all give the proper Prandtl number. The models are tested for Couette flow, and the results are compared to solutions obtained with the ES-BGK model, and the direct simulation Monte Carlo method. The simulations rely on a numerical scheme that ensures positivity of solutions, conservation of moments, and dissipation of entropy. The advantages and disadvantages of the various BGK models are discussed.
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