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A block triple-relaxation-time lattice Boltzmann model for nonlinear anisotropic convection–diffusion equations
Computers & Mathematics with Applications ( IF 2.811 ) Pub Date : 2019-12-09 , DOI: 10.1016/j.camwa.2019.11.018
Yong Zhao; Yao Wu; Zhenhua Chai; Baochang Shi

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.
更新日期:2020-03-24

 

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