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

作　　者：Chunze Zhang Yongguang Cheng Shan Huang Jiayang Wu 

机构地区：[1]State Key Laboratory of Water Resources and Hydropower Engineering Science,Wuhan University,Wuhan 430072,China

出　　处：《Advances in Applied Mathematics and Mechanics》2016年第1期37-51,共15页应用数学与力学进展（英文）

基　　金：supported by the National Natural Science Foundation of China(NSFC,Grant Numbers 10572106,10872153 and 11172219);the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130141110013).

摘　　要：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-relaxationtime 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 threedimensional(3D)rectangular jet.Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBMhas better accuracy and stability than that for the SRT-LBM.

关 键 词：Multiple-relaxation-time lattice Boltzmann method viscosity counteracting high Reynolds number flow Poiseuille flow Couette flow Taylor-Green vortex flow lid-driven cavity flow. 

分 类 号：O35[理学—流体力学]