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首页> 外文期刊>Journal of Scientific Computing >Lattice Boltzmann Model Based on the Rebuilding-Divergency Method for the Laplace Equation and the Poisson Equation
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Lattice Boltzmann Model Based on the Rebuilding-Divergency Method for the Laplace Equation and the Poisson Equation

机译：基于重建分歧方法的Laplace方程和Poisson方程的格子Boltzmann模型

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摘要

In this paper, a new lattice Boltzmann model based on the rebuilding-divergency method for the Poisson equation is proposed. In order to translate the Poisson equation into a conservation law equation, the source term and diffusion term are changed into divergence forms. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales and several higher-order moments of equilibrium distribution functions are obtained. Thus, by rebuilding the divergence of the source and diffusion terms, the Laplace equation and the Poisson equation with the second accuracy of the truncation errors are recovered. In the numerical examples, we compare the numerical results of this scheme with those obtained by other classical method for the Green-Taylor vortex flow, numerical results agree well with the classical ones.
机译：提出了一种基于重建散度法的泊松方程格子Boltzmann模型。为了将泊松方程转换为守恒律方程，将源项和扩散项更改为发散形式。通过使用Chapman-Enskog展开和多尺度时间展开，获得了一系列在不同时间尺度上的偏微分方程和一些平衡分布函数的高阶矩。因此，通过重建源项和扩散项的散度，具有截断误差的第二精度的拉普拉斯方程和泊松方程得以恢复。在数值例子中，我们将该方案的数值结果与通过Green-Taylor涡流的其他经典方法获得的数值结果进行了比较，数值结果与经典结果非常吻合。

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