A discrete Hermite moments based multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations

In this work, a multiple-relaxation-time lattice Boltzmann (MRT-LB) model based on discrete Hermite moments is proposed for nonlinear convection-diffusion equations (NCDEs). First, we use the block-weighted orthogonality of Hermite matrix to give a general expression of equilibrium distribution function (EDF) with adjustable parameter d0. This expression is suitable for NCDEs and Navier-Stokes equations and can be easily extended to higher order form. In this paper, we mainly construct the discrete Hermite moments based MRT-LB (HMRT-LB) model for NCDEs. Different from the previous Hermite moment LB model, the collision matrix of the present model consists of a block-weighted orthogonal Hermite matrix with d0. By the direct Taylor expansion, our model is recovered to NCDEs macroscopically. Then, we analyze the choice of order of EDF and the influence of d0 on the stability region of the model. At the same time, we also give the changes of the stable region of the model with different d0 when EDF is taken as a higher order form. Finally, the influence of different orders of EDF and d0 on stability is simulated by numerical experiments, and the numerical results are in agreement with the analytical results.