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A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models
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Year:    2015

Author:    Songze Chen, Kun Xu, Qingdong Cai

Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 2 : pp. 245–266

Abstract

The Ellipsoidal Statistical model (ES-model) and the Shakhov model (S-model) were constructed to correct the Prandtl number of the original BGK model through the modification of stress and heat flux. With the introduction of a new parameter to combine the ES-model and S-model, a generalized kinetic model can be developed. This new model can give the correct Navier-Stokes equations in the continuum flow regime. Through the adjustment of the new parameter, it provides abundant dynamic effect beyond the ES-model and S-model. Changing the free parameter, the physical performance of the new model has been tested numerically. The unified gas kinetic scheme (UGKS) is employed for the study of the new model. In transition flow regime, many physical problems, i.e., the shock structure and micro-flows, have been studied using the generalized model. With a careful choice of the free parameter, good results can be achieved for most test cases. Due to the property of the Boltzmann collision integral, the new parameter in the generalized kinetic model cannot be fully determined. It depends on the specific problem. Generally speaking, the S-model predicts more accurate numerical solutions in most test cases presented in this paper than the ES-model, while ES-model performs better in the cases where the flow is mostly driven by temperature gradient, such as a channel flow with large boundary temperature variation at high Knudsen number.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2014.m559

Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 2 : pp. 245–266

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:   

Author Details

Songze Chen

Kun Xu

Qingdong Cai

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