一种用于Poisson方程的四阶差分型格子Boltzmann模型 A Four-Order Difference Type Lattice Boltzmann Model for the Poisson Equation

本文给出了用于求解Poisson方程的四阶差分型格子Boltzmann模型，应用定常的格子Boltzmann方程和空间多尺度展开，得到了截断误差是四阶精度的Poisson方程。数值例子表明，该模型在精度上较相应的二阶模型有所提高。 A four-order difference type lattice Boltzmann model is employed to investigate the Poisson equation in this paper. By using the steady lattice Boltzmann equation and the multi-spatial scale expansion, the Poisson equation with four-order accuracy is obtained. Examples show that the numerical results agree well with exact solutions.