论文标题
Navier中的比例依赖性误差增长 - Stokes模拟
Scale-dependent Error Growth in Navier--Stokes Simulations
论文作者
论文摘要
我们估计在不同的分辨率和雷诺数中的最大lyapunov指数中的大量涡流（LES）和正弦驱动的Navier的直接数值模拟（DNS） - 在三个维度上Stokes方程。 Les Lyapunov指数与雷诺夫单元非二量化时，与雷诺数无关，而Les Lyapunov指数作为有效网格间距的逆功率分歧，表明细规结构的误差速率比较大的结构更快。即有效地，即忽略了这种现象在Kolmogorov量表上的截止，这种行为引入了预测范围的上限，可以通过提高测量网格来提高初始条件的精度来实现。
We estimate the maximal Lyapunov exponent at different resolutions and Reynolds numbers in large eddy (LES) and direct numerical simulations (DNS) of sinusoidally-driven Navier--Stokes equations in three dimensions. Independent of the Reynolds number when nondimensionalized by Kolmogorov units, the LES Lyapunov exponent diverges as an inverse power of the effective grid spacing showing that the fine scale structures exhibit much faster error growth rates than the larger ones. Effectively, i.e., ignoring the cut-off of this phenomenon at the Kolmogorov scale, this behavior introduces an upper bound to the prediction horizon that can be achieved by improving the precision of initial conditions through refining of the measurement grid.
