On the Stability and Accuracy of the BGK, MRT and RLB Boltzmann Schemes for the Simulation of Turbulent Flows
On the Stability and Accuracy of the BGK, MRT and RLB Boltzmann Schemes for the Simulation of Turbulent Flows
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湍流模拟中BGK、MRT和RLB玻尔兹曼格式的稳定性和准确性
DOI：
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发表时间：
2018
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影响因子：
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通讯作者：
N. Adams
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文献类型：
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作者：
P. Nathen;D. Gaudlitz;M. Krause;N. Adams
本文分析了用于湍流直接数值模拟的不同格子Boltzmann格式的稳定性和精度。考虑了Bhatnagar，Gross和Krook的单弛豫时间格式（BGK），多弛豫时间格式（MRT）和正则格子Boltzmann格式（RLB）。通过计算代表均匀各向同性湍流的三维Taylor-Green涡，研究了这些格式的稳定性和精度。考虑了不同的雷诺数和网格分辨率。正如预期的那样，BGK方案需要足够高的网格分辨率来进行稳定和准确的模拟。令人惊讶的是，MRT方案在没有任何湍流模型的情况下使用时，无法获得这里考虑的流动类型的网格收敛。RLB计划允许稳定的模拟，但表现出很强的耗散行为。当采用上述LBM方案数值模拟不同雷诺数和分辨率的湍流槽道流动时，发现了类似的行为。所考虑的格子玻尔兹曼方法的精度和稳定性所获得的见解可以成为有用的，特别是用于高雷诺数流动的有效湍流模型的设计。AMS科目分类：35 Q20
This paper presents an analysis of the stability and accuracy of different Lattice Boltzmann schemes when employed for direct numerical simulations of turbulent flows. The Single-Relaxation-Time scheme of Bhatnagar, Gross and Krook (BGK), the Multi-Relaxation-Time scheme (MRT) and the Regularized Lattice Boltzmann scheme (RLB) are considered. The stability and accuracy properties of these schemes are investigated by computing three-dimensional Taylor-Green vortices representing homogeneous isotropic turbulent flows. Varying Reynolds numbers and grid resolutions were considered. As expected, the BGK scheme requires sufficiently high grid resolutions for stable and accurate simulations. Surprisingly, the MRT scheme when used without any turbulence model fails to obtain mesh convergence for the type of flow considered here. The RLB scheme allows for stable simulations but exhibits a strong dissipative behavior. A similar behavior was found when employing the mentioned LBM schemes for numerical simulations of turbulent channel flows at varying Reynolds numbers and resolutions. The obtained insights on accuracy and stability of the considered Lattice Boltzmann methods can become useful especially for the design of effective turbulence models to be used for high Reynolds number flows. AMS subject classifications: 35Q20