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.

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。