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Linear and brute force stability of orthogonal moment multiple-relaxation-time lattice Boltzmann methods applied to homogeneous isotropic turbulence
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences ( IF 5 ) Pub Date : 2021-08-30 , DOI: 10.1098/rsta.2020.0405
Stephan Simonis 1, 2 , Marc Haussmann 1, 3 , Louis Kronberg 1, 2 , Willy Dörfler 2 , Mathias J Krause 1, 2, 3
Affiliation  

Multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) based on orthogonal moments exhibit lattice Mach number dependent instabilities in diffusive scaling. The present work renders an explicit formulation of stability sets for orthogonal moment MRT LBM. The stability sets are defined via the spectral radius of linearized amplification matrices of the MRT collision operator with variable relaxation frequencies. Numerical investigations are carried out for the three-dimensional Taylor–Green vortex benchmark at Reynolds number 1600. Extensive brute force computations of specific relaxation frequency ranges for the full test case are opposed to the von Neumann stability set prediction. Based on that, we prove numerically that a scan over the full wave space, including scaled mean flow variations, is required to draw conclusions on the overall stability of LBM in turbulent flow simulations. Furthermore, the von Neumann results show that a grid dependence is hardly possible to include in the notion of linear stability for LBM. Lastly, via brute force stability investigations based on empirical data from a total number of 22 696 simulations, the existence of a deterministic influence of the grid resolution is deduced.

This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.



中文翻译:

应用于均匀各向同性湍流的正交矩多重松弛时间格子 Boltzmann 方法的线性和蛮力稳定性

基于正交矩的多重松弛时间 (MRT) 晶格玻尔兹曼方法 (LBM) 在扩散缩放中表现出晶格马赫数依赖的不稳定性。目前的工作为正交矩 MRT LBM 提供了稳定集的明确公式。稳定性集是通过具有可变松弛频率的 MRT 碰撞算子的线性化放大矩阵的谱半径来定义的。对雷诺数为 1600 的三维泰勒-格林涡旋基准进行了数值研究。完整测试案例的特定松弛频率范围的广泛蛮力计算与冯诺依曼稳定性集预测相反。在此基础上,我们从数值上证明了对全波空间的扫描,包括按比例缩放的平均流量变化,需要在湍流模拟中得出 LBM 整体稳定性的结论。此外,冯诺依曼的结果表明,网格相关性几乎不可能包含在 LBM 的线性稳定性概念中。最后,通过基于来自总共 22 696 次模拟的经验数据的蛮力稳定性调查,推断出网格分辨率的确定性影响的存在。

本文是主题问题“流体动力学模拟中尺度方法的进展”的一部分。

更新日期:2021-08-30
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