Multi-relaxation-time lattice Boltzmann method for anisotropic convection-diffusion equation with divergence-free velocity field

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.