A Multiple-Relaxation-Time Lattice Boltzmann Model for General Nonlinear Anisotropic Convection–Diffusion Equations
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- 作者：Zhenhua Chai ; Baochang Shi ; Zhaoli Guo
- 关键词：Multiple ; relaxation ; time lattice Boltzmann model ; Nonlinear anisotropic convection–diffusion equations ; Chapman–Enskog analysis
- 刊名：Journal of Scientific Computing
- 出版年：2016
- 出版时间：October 2016
- 年：2016
- 卷：69
- 期：1
- 页码：355-390
- 全文大小：5,309 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Algorithms
Computational Mathematics and Numerical Analysis
Applied Mathematics and Computational Methods of Engineering
Mathematical and Computational Physics - 出版者：Springer Netherlands
- ISSN：1573-7691
- 卷排序：69
文摘
In this paper, based on the previous work (Shi and Guo in Phys Rev E 79:016701, 2009), we develop a multiple-relaxation-time (MRT) lattice Boltzmann model for general nonlinear anisotropic convection–diffusion equation (NACDE), and show that the NACDE can be recovered correctly from the present model through the Chapman–Enskog analysis. We then test the MRT model through some classic CDEs, and find that the numerical results are in good agreement with analytical solutions or some available results. Besides, the numerical results also show that similar to the single-relaxation-time lattice Boltzmann model or so-called BGK model, the present MRT model also has a second-order convergence rate in space. Finally, we also perform a comparative study on the accuracy and stability of the MRT model and BGK model by using two examples. In terms of the accuracy, both the analysis and numerical results show that a numerical slip on the boundary would be caused in the BGK model, and cannot be eliminated unless the relaxation parameter is fixed to be a special value, while the numerical slip in the MRT model can be overcome once the relaxation parameters satisfy some constrains. The results in terms of stability also demonstrate that the MRT model could be more stable than the BGK model through tuning the free relaxation parameters.