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A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

Published online by Cambridge University Press:  10 March 2015

Songze Chen ,
Kun Xu  and
Qingdong Cai
Songze Chen
Affiliation:
Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Kun Xu*
Affiliation:
Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong LTCS and CAPT, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
Qingdong Cai*
Affiliation:
LTCS and CAPT, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
*
*Corresponding author. Email: jacksongze@pku.edu.cn (S. Z. Chen), makxu@ust.hk (K. Xu), caiqd@pku.edu.cn (Q. D. Cai)
*Corresponding author. Email: jacksongze@pku.edu.cn (S. Z. Chen), makxu@ust.hk (K. Xu), caiqd@pku.edu.cn (Q. D. Cai)
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Abstract

The Ellipsoidal Statistical model (ES-model) and the Shakhov model (Smodel) 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 Smodel 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.

Keywords

65M1078A48Kinetic modelsunified gas kinetic schemerarefied flow
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 2 , April 2015 , pp. 245 - 266
Copyright
Copyright © Global-Science Press 2015 

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