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Volume 8, Issue 1
Improving the Stability of the Multiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach

Chunze Zhang, Yongguang Cheng, Shan Huang & Jiayang Wu

DOI: 10.4208/aamm.2014.m512

Adv. Appl. Math. Mech., 8 (2016), pp. 37-51.

Published online: 2018-05

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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.

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@Article{AAMM-8-37, author = {Zhang , ChunzeCheng , YongguangHuang , Shan and Wu , Jiayang}, title = {Improving the Stability of the Multiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {1}, pages = {37--51}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m512}, url = {http://global-sci.org/intro/article_detail/aamm/12075.html} }
TY - JOUR T1 - Improving the Stability of the Multiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach AU - Zhang , Chunze AU - Cheng , Yongguang AU - Huang , Shan AU - Wu , Jiayang JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 37 EP - 51 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m512 UR - https://global-sci.org/intro/article_detail/aamm/12075.html KW - AB -

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.

Zhang , ChunzeCheng , YongguangHuang , Shan and Wu , Jiayang. (2018). Improving the Stability of the Multiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach. Advances in Applied Mathematics and Mechanics. 8 (1). 37-51. doi:10.4208/aamm.2014.m512
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