Accuracy analysis of high-order lattice Boltzmann models for rarefied gas flows
Accuracy analysis of high-order lattice Boltzmann models for rarefied gas flows
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DOI：
10.1016/j.jcp.2010.10.023
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发表时间：
2009-08
期刊：
影响因子：
--
通讯作者：
J. Meng;Yonghao Zhang
中科院分区：
文献类型：
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作者：
J. Meng;Yonghao Zhang
在这项工作中，我们已经从理论上分析和数值评估的准确性，高阶格子玻尔兹曼（LB）模型捕捉稀薄气体流动中的非平衡效应。在不可压缩极限下，LB方程可以简化为线性化的Bhatnagar-Gross-Krook（BGK）方程。因此，当使用相同的Gauss-Hermite求积时，LB方法非常类似于离散速度方法（DVM）。此外，厄米展开的平衡分布函数的顺序被发现是不直接相关的近似阶的Knudsen数的BGK方程的不可压缩流。同时，我们数值评估了LB模型的驻波剪切波问题，这是专门设计用于评估模型的准确性，排除气体分子/表面相互作用的影响，在壁边界。数值模拟结果表明，对于低速流动，离散平衡分布函数中的高阶项对捕捉非平衡效应的作用可以忽略不计。相比之下，合适的高斯-厄米求积对LB模型是否能准确描述稀薄气体的基本流动物理性质影响最大。我们的模拟结果，其中壁/气体相互作用的影响被排除在外，可以导致LB建模能力的结论，具有高阶求积的模型提供更准确的结果。对于同阶Gauss-Hermite求积，精确横坐标也会适度影响数值精度。使用相同的Gauss-Hermite求积，LB和DVM方法的数值结果在很宽的Knudsen数范围内的流动是非常一致的，这证实了LB模拟是类似的DVM过程。因此，LB方法可以提供灵活的模型，适用于模拟连续流动的Navier-Stokes水平和稀薄气体流动的线性Boltzmann模型方程水平。
In this work, we have theoretically analyzed and numerically evaluated the accuracy of high-order lattice Boltzmann (LB) models for capturing non-equilibrium effects in rarefied gas flows. In the incompressible limit, the LB equation is shown to be able to reduce to the linearized Bhatnagar–Gross–Krook (BGK) equation. Therefore, when the same Gauss–Hermite quadrature is used, LB method closely resembles the discrete velocity method (DVM). In addition, the order of Hermite expansion for the equilibrium distribution function is found not to be directly correlated with the approximation order in terms of the Knudsen number to the BGK equation for incompressible flows. Meanwhile, we have numerically evaluated the LB models for a standing-shear-wave problem, which is designed specifically for assessing model accuracy by excluding the influence of gas molecule/surface interactions at wall boundaries. The numerical simulation results confirm that the high-order terms in the discrete equilibrium distribution function play a negligible role in capturing non-equilibrium effect for low-speed flows. By contrast, appropriate Gauss–Hermite quadrature has the most significant effect on whether LB models can describe the essential flow physics of rarefied gas accurately. Our simulation results, where the effect of wall/gas interactions is excluded, can lead to conclusion on the LB modeling capability that the models with higher-order quadratures provide more accurate results. For the same order Gauss–Hermite quadrature, the exact abscissae will also modestly influence numerical accuracy. Using the same Gauss–Hermite quadrature, the numerical results of both LB and DVM methods are in excellent agreement for flows across a broad range of the Knudsen numbers, which confirms that the LB simulation is similar to the DVM process. Therefore, LB method can offer flexible models suitable for simulating continuum flows at the Navier–Stokes level and rarefied gas flows at the linearized Boltzmann model equation level.