Effect of viscosity on stability and accuracy of the two-component lattice Boltzmann method with a multiple-relaxation-time collision operator investigated by the acoustic attenuation model
Le Bai(柏乐)1,2, Ming-Lei Shan(单鸣雷)1,2, Yu Yang(杨雨)1, Na-Na Su(苏娜娜)2, Jia-Wen Qian(钱佳文)2, and Qing-Bang Han(韩庆邦)1,2,†
1 Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, Hohai University, Changzhou 213022, China; 2 College of Internet of Things Engineering, Hohai University, Changzhou 213022, China
Abstract A two-component lattice Boltzmann method (LBM) with a multiple-relaxation-time (MRT) collision operator is presented to improve the numerical stability of the single relaxation time (SRT) model. The macroscopic and the momentum conservation equations can be retrieved through the Chapman—Enskog (C-E) expansion analysis. The equilibrium moment with the diffusion term is calculated, a diffusion phenomenon is simulated by utilizing the developed model, and the numerical stability is verified. Furthermore, the binary mixture channel model is designed to simulate the sound attenuation phenomenon, and the obtained simulation results are found to be consistent with the analytical solutions. The sound attenuation model is used to study the numerical stability and calculation accuracy of the LBM model. The simulation results show the stability and accuracy of the MRT model and the SRT model under different viscosity conditions. Finally, we study the influence of the error between the macroscopic equation of the MRT model and the standard incompressible Navier—Stokes equation on the calculation accuracy of the model to demonstrate the general applicability of the conclusions drawn by the sound attenuation model in the present study.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12174085, 11874140, and 11574072), the State Key Laboratory of Acoustics, Chinese Academy of Sciences (Grant No. SKLA201913), and the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX21_0478).
Corresponding Authors:
Qing-Bang Han
E-mail: 20111841@hhu.edu.cn
Cite this article:
Le Bai(柏乐), Ming-Lei Shan(单鸣雷), Yu Yang(杨雨), Na-Na Su(苏娜娜), Jia-Wen Qian(钱佳文), and Qing-Bang Han(韩庆邦) Effect of viscosity on stability and accuracy of the two-component lattice Boltzmann method with a multiple-relaxation-time collision operator investigated by the acoustic attenuation model 2022 Chin. Phys. B 31 034701
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