A block triple-relaxation-time lattice Boltzmann model for nonlinear anisotropic convection–diffusion equations. (1st May 2020)

• Record Type: Journal Article
• Authors: Zhao, Yong; Wu, Yao; Chai, Zhenhua; Shi, Baochang
• Is Part Of: Computers & mathematics with applications. Volume 79:issue 9(2020)
• Page Start: 2550
• Page End: 2573
• Publication Date: 2020-05-01
• Subjects: Lattice Boltzmann method -- Block triple-relaxation-time -- Nonlinear anisotropic convection–diffusion equations; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.11.018
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: A block triple-relaxation-time (B-TriRT) lattice Boltzmann model for general nonlinear anisotropic convection–diffusion equations (NACDEs) is proposed, and the Chapman–Enskog analysis shows that the present B-TriRT model can recover the NACDEs correctly. There are some striking features of the present B-TriRT model: firstly, the relaxation matrix of B-TriRT model is partitioned into three relaxation parameter blocks, rather than a diagonal matrix in general multiple-relaxation-time (MRT) model; secondly, based on the analysis of half-way bounce-back (HBB) scheme for Dirichlet boundary conditions, we obtain an expression to determine the relaxation parameters; thirdly, the anisotropic diffusion tensor can be recovered by the relaxation parameter block that corresponds to the first-order moment of non-equilibrium distribution function. A number of simulations of isotropic and anisotropic convection–diffusion equations are conducted to validate the present B-TriRT model. The results indicate that the present model has a second-order accuracy in space, and is also more accurate and more stable than some available lattice Boltzmann models.