On numerical diffusion of simplified lattice Boltzmann method,International Journal for Numerical Methods in Fluids

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On numerical diffusion of simplified lattice Boltzmann method
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-02-27 , DOI: 10.1002/fld.4823
Zhen Chen ₁ , Chang Shu ₁

Affiliation

In this article, we analyze the numerical diffusion in the recently developed simplified lattice Boltzmann method (SLBM) and propose amending strategies towards lower numerical diffusion. It is noted that, in the original SLBM, the intermediate flow properties are utilized to evaluate the nonequilibrium distribution function, which may bring in excessive numerical diffusion. In the revised scheme, this evaluation strategy is nurtured by using the corrected flow properties to calculate the nonequilibrium distribution function. In the meantime, the numerically evaluated nonequilibrium distribution function only approximately fulfills the conservation relationship in the second order of accuracy. Although such approximation does not violate the global order of accuracy, offsetting the extra error would contribute to reducing the numerical diffusion. After implementing the proposed amending strategies, the revised SLBM (RSLBM) is validated through three numerical examples. The results indicate that RSLBM bears comparable order of accuracy as the original SLBM but shows lower numerical error on the same mesh size. And the reduced numerical error facilitates recovery of delicate flow structures. The proposed RSLBM can be flexibly implemented on nonuniform or body‐fitted meshes, and in three‐dimensional simulations.

中文翻译：

关于简化格子玻尔兹曼方法的数值扩散

在本文中，我们分析了最近开发的简化格子Boltzmann方法（SLBM）的数值扩散，并提出了降低数值扩散的修正策略。请注意，在原始SLBM中，利用中间流动特性来评估非平衡分布函数，这可能会导致过度的数值扩散。在修订方案中，通过使用校正后的流量特性来计算非平衡分布函数，从而确立了该评估策略。同时，数值评估的非平衡分布函数仅以二阶精度近似满足守恒关系。尽管这种近似并不违反全局精度顺序，但抵消额外的误差将有助于减少数值扩散。在实施建议的修订策略之后，通过三个数值示例对修订后的SLBM（RSLBM）进行了验证。结果表明，RSLBM具有与原始SLBM相当的精度等级，但在相同的网格尺寸下显示出较低的数值误差。减少的数值误差有助于恢复精细的流动结构。所提出的RSLBM可以在非均匀或适合人体的网格上以及在三维模拟中灵活地实现。

更新日期：2020-02-27

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