We present a comprehensive analysis of the cumulant lattice Boltzmann model with the three-dimensional Taylor–Green vortex benchmark at Reynolds number 1600. The cumulant model is investigated in several different variants, using regularization, fourth-order convergent diffusion and fourth-order convergent advection with and without limiters. In addition, a cumulant model combined with a WALE sub-grid scale model is being evaluated. The turbulence model is found to filter out the high wave number contributions from the energy spectrum and the enstrophy, while the non-filtered cumulant methods show good correspondence to spectral simulations even for the high wave numbers. The application of the WALE turbulence model appears to be counter productive for the Taylor–Green vortex at a Reynolds number of 1600. At much higher Reynolds numbers ( $${\hbox {Re}}=160{,}000$$ ) a deviation from the ideal Kolmogorov theory can be observed in the absence of an explicit turbulence model. Cumulant models with fourth-order convergent diffusion show much better results than single relaxation time methods.

中文翻译：

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使用累积格子 Boltzmann 方法对衰减的泰勒-格林涡旋进行低分辨率和大涡模拟

我们使用雷诺数为 1600 的三维泰勒-格林涡旋基准对累积点阵玻尔兹曼模型进行了综合分析。 累积量模型在几种不同的变体中进行了研究，使用正则化、四阶收敛扩散和四阶收敛平流有和没有限制器。此外，正在评估与 WALE 子网格比例模型相结合的累积模型。发现湍流模型过滤掉了能量谱和熵中的高波数贡献，而未过滤的累积量方法即使对于高波数也显示出与光谱模拟的良好对应。WALE 湍流模型的应用似乎对雷诺数为 1600 的泰勒-格林涡旋产生反作用。在更高的雷诺数 ( $${\hbox {Re}}=160{,}000$$ ) 下，可以在没有明确湍流模型的情况下观察到与理想 Kolmogorov 理论的偏差。具有四阶收敛扩散的累积模型显示出比单一弛豫时间方法好得多的结果。