Kinetic model for uniform shear flow

V. Garzó

Physica A: Statistical Mechanics and its Applications, 1997, vol. 243, issue 1, 113-128

Abstract: The so-called ellipsoidal statistical (ES) kinetic model is used to study the uniform shear flow problem in a dilute gas. This model is an extension of the well-known BGK kinetic to account for the correct Prandtl number. The velocity moments and the velocity distribution function are obtained in terms of the shear rate and a parameter Pr which plays the role of the Prandtl number. It is shown that, independently of the numerical value of Pr, the expressions of the second-degree velocity moments (which are related to the pressure tensor) coincide with the ones derived from the Boltzmann equation for Maxwell molecules. A comparison with previous results obtained from the Boltzmann equation for the fourth-degree velocity moments and for the velocity distribution function is carried out. Surprisingly enough, the comparison shows a superiority of the BGK model (Pr = 1) over the ES model (Pr = 23) in this problem. If one chooses values of Pr larger than one, the ES predictions are improved significantly.

Keywords: Dilute gas; Kinetic model; Prandtl number; Uniform shear flow (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:243:y:1997:i:1:p:113-128

DOI: 10.1016/S0378-4371(97)00262-8

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