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Improving the Stability of the Multiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach

Published online by Cambridge University Press:  21 December 2015

Chunze Zhang ,
Yongguang Cheng ,
Shan Huang  and
Jiayang Wu
Chunze Zhang
Affiliation:
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
Yongguang Cheng*
Affiliation:
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
Shan Huang
Affiliation:
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
Jiayang Wu
Affiliation:
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
*
*Corresponding author. Email:ygcheng@whu.edu.cn (Y. G. Cheng)
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Abstract

Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method (LBM). The multiple-relaxation-time (MRT) model of the LBM can improve the accuracy and stability, but is still subject to numerical instability when simulating flows with large single-grid Reynolds number (Reynolds number/grid number). The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM. However, its effectiveness was only verified in the single-relaxation-time model of the LBM (SRT-LBM). This paper aims to propose the viscosity counteracting approach for the multiple-relaxation-time model (MRT-LBM) and analyze its numerical characteristics. The verification is conducted by simulating some benchmark cases: the two-dimensional (2D) lid-driven cavity flow, Poiseuille flow, Taylor-Green vortex flow and Couette flow, and three-dimensional (3D) rectangular jet. Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBM has better accuracy and stability than that for the SRT-LBM.

Keywords

65M1078A48Multiple-relaxation-time lattice Boltzmann methodviscosity counteractinghigh Reynolds number flowPoiseuille flowCouette flowTaylor-Green vortex flowlid-driven cavity flow
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 1 , February 2016 , pp. 37 - 51
Copyright
Copyright © Global-Science Press 2016 

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