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.

提出了用于一般非线性各向异性对流扩散方程（NACDEs）的块三重松弛时间（B-TriRT）点阵玻尔兹曼模型，Chapman-Enskog分析表明，当前的B-TriRT模型可以正确地恢复NACDEs。目前的B-TriRT模型具有一些惊人的特征：首先，将B-TriRT模型的弛豫矩阵划分为三个弛豫参数块，而不是一般的多次弛豫时间（MRT）模型中的对角矩阵。其次，在分析狄利克雷边界条件的中途反弹（HBB）方案的基础上，得到了确定松弛参数的表达式。第三，可以通过与非平衡分布函数的一阶矩相对应的弛豫参数块来恢复各向异性扩散张量。进行了各向同性和各向异性对流扩散方程的模拟，以验证当前的B-TriRT模型。结果表明，该模型在空间上具有二阶精度，并且比某些可用的格子Boltzmann模型更准确，更稳定。