The paper is devoted to the analysis of characteristic-based (CB) schemes for the simulation of the convection–diffusion equation by the lattice Boltzmann method (LBM). Numerical schemes from the first order to fourth one are considered. The stability analysis is realized by the von Neumann method. The stability domains of the schemes are constructed. It is demonstrated that the areas of the stability domains for CB schemes are larger than the domains for the schemes, constructed by the traditional approach, based on the discretization at the Cartesian axes directions. By the solution of the numerical examples with the smooth initial conditions, it is demonstrated that the practical convergence rates of the schemes are consistent with the theoretical values. As it is shown, the proposed schemes can be used for the cases of the Peclet number values, when the classical LBM is unstable.

本文致力于分析基于特征 (CB) 的方案，用于通过格子玻尔兹曼方法 (LBM) 模拟对流-扩散方程。考虑了从一阶到四阶的数值方案。稳定性分析是通过冯诺依曼方法实现的。构建了方案的稳定性域。结果表明，CB 方案的稳定性域的面积大于基于笛卡尔轴方向离散化的传统方法构建的方案的域。通过初始条件光滑的数值算例的求解，证明了该方案的实际收敛速度与理论值一致。如图所示，所提出的方案可用于 Peclet 数值的情况，