用于求解 Poisson 方程的格子 Boltzmann 模型

摘要

A lattice Boltzmann model for the Poisson equation was proposed.By means of the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales was obtained.Moreover,the equilibrium distribution functions and the modified partial differential equation of the Poisson equation with the third-order truncation error were obtained.In numerical examples,the Kolmogorov flow and Green-Taylor vortex flow were simulated,and the comparison between numerical results of the lattice Boltzmann models and exact solutions were given.The numerical results are acceptable.%提出一个求解 Poisson 方程的格子 Boltzmann 模型。通过使用 Chapman-Enskog 展开和多尺度展开得到了在不同时间尺度下的系列偏微分方程及平衡态分布函数和具有三阶截断的误差修正 Poisson 方程。用该模型计算 Kolmogorov 流和 Green-Taylor 涡流，并与解析解进行比较，计算结果表明，数值结果与经典解析结果基本相符。