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An Alternative Lattice Boltzmann Model for Incompressible Flows and its Stabilization

Published online by Cambridge University Press:  07 February 2017

Liangqi Zhang ,
Zhong Zeng ,
Haiqiong Xie ,
Zhouhua Qiu ,
Liping Yao ,
Yongxiang Zhang  and
Yiyu Lu
Liangqi Zhang*
Affiliation:
Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing 400044, P.R. China State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, P.R. China
Zhong Zeng*
Affiliation:
Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing 400044, P.R. China State Key laboratory of Crystal Material, Shandong University, Jinan 250100, P.R. China
Haiqiong Xie*
Affiliation:
Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing 400044, P.R. China
Zhouhua Qiu*
Affiliation:
Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing 400044, P.R. China
Liping Yao*
Affiliation:
College of Engineering and Technology, Southwest University, Chongqing 400716, P.R. China
Yongxiang Zhang*
Affiliation:
Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing 400044, P.R. China
Yiyu Lu*
Affiliation:
State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, P.R. China
*
*Corresponding author.Email addresses:liangqizhang@cqu.edu.cn, liangqizhang@ntu.edu.sg (L. Zhang), zzeng@cqu.edu.cn (Z. Zeng), xiehaiqiong@cqu.edu.cn (H. Xie), qiuzhouhua@cqu.edu.cn (Z. Qiu), lpyao@swu.edu.cn (L. Yao), zhangyx@cqu.edu.cn (Y. Zhang), luyiyu@cqu.edu.cn (Y. Lu)
*Corresponding author.Email addresses:liangqizhang@cqu.edu.cn, liangqizhang@ntu.edu.sg (L. Zhang), zzeng@cqu.edu.cn (Z. Zeng), xiehaiqiong@cqu.edu.cn (H. Xie), qiuzhouhua@cqu.edu.cn (Z. Qiu), lpyao@swu.edu.cn (L. Yao), zhangyx@cqu.edu.cn (Y. Zhang), luyiyu@cqu.edu.cn (Y. Lu)
*Corresponding author.Email addresses:liangqizhang@cqu.edu.cn, liangqizhang@ntu.edu.sg (L. Zhang), zzeng@cqu.edu.cn (Z. Zeng), xiehaiqiong@cqu.edu.cn (H. Xie), qiuzhouhua@cqu.edu.cn (Z. Qiu), lpyao@swu.edu.cn (L. Yao), zhangyx@cqu.edu.cn (Y. Zhang), luyiyu@cqu.edu.cn (Y. Lu)
*Corresponding author.Email addresses:liangqizhang@cqu.edu.cn, liangqizhang@ntu.edu.sg (L. Zhang), zzeng@cqu.edu.cn (Z. Zeng), xiehaiqiong@cqu.edu.cn (H. Xie), qiuzhouhua@cqu.edu.cn (Z. Qiu), lpyao@swu.edu.cn (L. Yao), zhangyx@cqu.edu.cn (Y. Zhang), luyiyu@cqu.edu.cn (Y. Lu)
*Corresponding author.Email addresses:liangqizhang@cqu.edu.cn, liangqizhang@ntu.edu.sg (L. Zhang), zzeng@cqu.edu.cn (Z. Zeng), xiehaiqiong@cqu.edu.cn (H. Xie), qiuzhouhua@cqu.edu.cn (Z. Qiu), lpyao@swu.edu.cn (L. Yao), zhangyx@cqu.edu.cn (Y. Zhang), luyiyu@cqu.edu.cn (Y. Lu)
*Corresponding author.Email addresses:liangqizhang@cqu.edu.cn, liangqizhang@ntu.edu.sg (L. Zhang), zzeng@cqu.edu.cn (Z. Zeng), xiehaiqiong@cqu.edu.cn (H. Xie), qiuzhouhua@cqu.edu.cn (Z. Qiu), lpyao@swu.edu.cn (L. Yao), zhangyx@cqu.edu.cn (Y. Zhang), luyiyu@cqu.edu.cn (Y. Lu)
*Corresponding author.Email addresses:liangqizhang@cqu.edu.cn, liangqizhang@ntu.edu.sg (L. Zhang), zzeng@cqu.edu.cn (Z. Zeng), xiehaiqiong@cqu.edu.cn (H. Xie), qiuzhouhua@cqu.edu.cn (Z. Qiu), lpyao@swu.edu.cn (L. Yao), zhangyx@cqu.edu.cn (Y. Zhang), luyiyu@cqu.edu.cn (Y. Lu)
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Abstract

In this paper, an alternative lattice Boltzmann (LB)model for incompressible flows is proposed. By modifying directly the moments of the equilibrium distribution function (EDF), the continuous expression of the EDF in tensor Hermite polynomials is derived using the moment expansion and then discretizedwith the discrete velocity vectors of the D2Q9 lattice. The present model as well as its counterpart, the incompressible LB model proposed by Guo, reproduces the incompressible Navier-Stokes (N-S) equations for both steady and unsteady flows. Besides, an alternative pressure formula, which represents the pressure as the diagonal part of the stress tensor, is adopted in the present model. Furthermore, in order to enhance the stability of the present LB model, an additional relaxation time pertaining to the non-hydrodynamic mode is added to the BGK collision operator. The present LB model is validated by two benchmark tests: the cavity flow with different Reynolds number (Re) and the flow past an impulsively started cylinder at Re=40 and 550.

Keywords

Lattice Boltzmann methodincompressible flowscavity flowdeviatoric stresscompressibility effect

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Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 2 , February 2017 , pp. 443 - 465
Copyright
Copyright © Global-Science Press 2017 

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