In large-eddy simulations (LES) a computational-domain translation velocity can be used to improve performance by allowing longer time-step intervals. The continuous equations are Galilean invariant, however, standard finite-difference-based discretizations are not discretely invariant with the error being proportional to the product of the local translation velocity and the truncation error. Even though such numerical errors are expected to be small, it is shown that in LES of buoyant convection the turbulent large-scale flow organization can modulate and amplify the error. Galilean invariance of global flow statistics is observed in well-resolved direct numerical simulations (DNS). In LES of single-phase convection under an inversion, flow statistics are nearly Galilean invariant and do not depend on the order of accuracy of the finite difference approximation. In contrast, in LES of cloudy convection, flow statistics show strong dependence on the frame of reference and the order of approximation. The error with respect to the frame of reference becomes negligible as the order of accuracy is increased from second to sixth in the present LES. Schemes with low resolving power can produce large dispersion errors in the surface-fixed frame that can be amplified by large-scale flow anisotropies, such as strong updrafts rising in a non-turbulent free troposphere in cumulus-cloud layers. Interestingly, in the present large-eddy simulations, a second-order discretization in the proper Galilean frame can yeild comparable accuracy as a high-order scheme in the surface-fixed frame.

在大涡流仿真（LES）中，可以通过允许更长的时间步长间隔来使用计算域转换速度来提高性能。连续方程是伽利略不变的，但是，基于标准差分的离散化并不是离散不变的，其误差与局部平移速度和截断误差的乘积成正比。即使预计这样的数值误差很小，也表明在浮力对流LES中，湍流的大规模流动组织可以调节和放大误差。在很好解析的直接数值模拟（DNS）中观察到全局流量统计信息的伽利略不变性。在反演下的单相对流LES中，流量统计几乎是Galilean不变的，并且不依赖于有限差分近似的精度顺序。相反，在多云对流的LES中，流量统计数据显示出强烈依赖于参考系和近似阶数。在当前LES中，随着精度等级从第二增加到第六，相对于参考系的误差可以忽略不计。具有低解析度的方案可能会在表面固定的框架中产生较大的色散误差，而该误差会被大规模的流动各向异性所放大，例如在积云层的非湍流自由对流层中上升的强烈上升气流。有趣的是，在当前的大涡模拟中，适当的伽利略框架中的二阶离散化可以产生与表面固定框架中的高阶方案相当的精度。