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Optimizing free parameters in the D3Q19 Multiple-Relaxation lattice Boltzmann methods to simulate under-resolved turbulent flows
Journal of Computational Science ( IF 3.1 ) Pub Date : 2020-06-22 , DOI: 10.1016/j.jocs.2020.101170
M. Chávez-Modena , A. Martínez-Cava , G. Rubio , E. Ferrer

We present a D3Q19 lattice scheme based in MRT with central moments (MRT-CM), where the free parameters of the model are optimized to dissipate under-resolved flow structures with high wavenumbers. In Chávez-Modena et al. in Computers & Fluids 172:397-409, 2018 [1], we compared the BGK, MRT-RM and MRT-CM for the D2Q9 lattice scheme using von Neumann analyses and quantified their numerical properties. Based on this study, we proposed an optimized 2D MRT-CM scheme with enhanced stability for under-resolved flows. Here, we extend this idea to the D3Q19 MRT-CM scheme.

As before, we base our optimization for the free parameters, on the k-1% dispersion-error rule, that states that waves with dispersive errors above 1% should be dissipated since they pollute the solution and may cause instabilities. To this aim we increase dissipation in the scheme for waves with dispersive errors above 1%.

The resulting optimized scheme is verified through a von Newmann analysis and validated for the three-dimensional Taylor-Green isotropic turbulent flow. We show how the original D3Q19 MRT-CM (d’Humières version) leads to unrealistic kinetic energy accumulation at high wave numbers, whilst our optimized MRT-CM provides the correct energy dissipated rate, avoiding energy build up at high wavenumbers. These results suggest that our optimization strategy enhances stability and allows for accurate energy spectra in under-resolved flow simulations such as typically found in Large Eddy Simulations.



中文翻译:

在D3Q19多重松弛晶格Boltzmann方法中优化自由参数以模拟欠解析的湍流

我们提出了一种基于MRT且具有中心矩(MRT-CM)的D3Q19晶格方案,其中优化了模型的自由参数,以消除高波数下欠解析的流动结构。在查韦斯·摩德纳(Chávez-Modena)等人中。在计算机与流体172:397-409,2018 [1]中,我们使用冯·诺依曼分析比较了BGK,MRT-RM和MRT-CM用于D2Q9晶格方案,并量化了它们的数值特性。在此研究的基础上,我们提出了一种优化的二维MRT-CM方案,该方案对于欠解析的流具有增强的稳定性。在这里,我们将此想法扩展到D3Q19 MRT-CM方案。

如前所述,我们基于k-1%的色散误差规则对自由参数进行了优化,该规则指出色散误差大于1%的波应被消散,因为它们会污染溶液并可能导致不稳定性。为此,我们在色散误差大于1%的波中增加了方案的耗散。

通过von Newmann分析验证了所得的优化方案,并针对三维泰勒-格林各向同性湍流进行了验证。我们展示了原始的D3Q19 MRT-CM(d'Humières版本)如何导致高波数下不切实际的动能积聚,而我们经过优化的MRT-CM提供了正确的能量耗散率,避免了高波数下的能量积聚。这些结果表明,我们的优化策略可增强稳定性,并在欠解析的流动模拟(例如大型涡流模拟中常见的模拟)中获得准确的能谱。

更新日期:2020-06-22
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