We propose a multiple-relaxation-time lattice Boltzmann method for anisotropic convection-diffusion equation with a divergence-free velocity field. In this approach, the convection term is handled as a source term in the lattice Boltzmann evolution equation; thus, the derivation term that may be induced by the convection term disappears. By using the Chapman-Enskog analysis, the anisotropic convection-diffusion equation is recovered up to second-order accurate in space. In particular, we also present a local scheme for computing the convection term, indicating that the present method retains the main advantages of the lattice Boltzmann method. We then test the proposed model by considering the Gaussian hill problem and an anisotropic convection diffusion equation with constant velocity and diffusion tensor. The results illustrate that our model has acceptable numerical accuracy and can be a good candidate for simulating anisotropic convection-diffusion equation.

中文翻译：

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无散度速度场各向异性对流扩散方程的多弛豫时间格子玻尔兹曼法


我们提出了一种用于具有无散度速度场的各向异性对流扩散方程的多重弛豫时间格子玻尔兹曼方法。在这种方法中，对流项被处理为格子玻尔兹曼演化方程中的源项；因此，对流项可能引起的导数项消失了。通过使用 Chapman-Enskog 分析，各向异性对流扩散方程在空间中恢复到二阶精度。特别是，我们还提出了计算对流项的局部方案，表明本方法保留了格子玻尔兹曼方法的主要优点。然后，我们通过考虑高斯山问题和具有恒定速度和扩散张量的各向异性对流扩散方程来测试所提出的模型。结果表明，我们的模型具有可接受的数值精度，可以成为模拟各向异性对流扩散方程的良好候选者。