In this paper, a new two-relaxation-time regularized (TRT-R) lattice Boltzmann (LB) model for convection-diffusion equation (CDE) with variable coefficients is proposed. Within this framework, we first derive a TRT-R collision operator by constructing a new regularized procedure through the high-order Hermite expansion of non-equilibrium. Then a first-order discrete-velocity form of discrete source term is introduced to improve the accuracy of the source term. Finally and most importantly, a new first-order space-derivative auxiliary term is proposed to recover the correct CDE with variable coefficients. To evaluate this model, we simulate a classic benchmark problem of the rotating Gaussian pulse. The results show that our model has better accuracy, stability and convergence than other popular LB models, especially in the case of a large time step.

翻译：本文提出了一种新的双松弛时间正则化（TRT-R）格子玻尔兹曼（LB）模型，用于求解变系数的对流扩散方程（CDE）。在该框架下，我们首先通过非平衡态的高阶Hermite展开构建新的正则化过程，推导出TRT-R碰撞算子；随后引入一阶离散速度形式的离散源项以提高源项精度；最后，也是最重要的，提出一种新的一阶空间导数辅助项，以恢复正确的变系数CDE。为评估该模型，我们模拟了旋转高斯脉冲经典基准问题。结果表明，我们的模型在准确性、稳定性和收敛性方面均优于其他流行的LB模型，尤其在采用大步长时间步长的情况下更为显著。