We study the Kolmogorov model of a shear flow by means of a newly developed Asymptotic-Preserving method for the numerical resolution of the two-dimensional vorticity-Poisson (Navier-Stokes) system. The scheme is validated by comparing the results with those obtained with an explicit spectral code and with an analytic result about the linear instability regime. We show that the AP-properties of the method allow one to deal efficiently with the multi-scale nature of the problem by tuning the time step to the physical one and not by stability constraints. As a result, we investigate the long time scale evolution of the Kolmogorov flow, observing that it evolves into a final stable stationary state characterised by a seemingly universal relation between stream-function and vorticity.

我们通过新开发的渐近保持方法研究了剪切流的 Kolmogorov 模型，该方法用于二维涡度-泊松 (Navier-Stokes) 系统的数值分辨率。该方案通过将结果与使用显式谱代码获得的结果和线性不稳定状态的分析结果进行比较来验证。我们表明，该方法的 AP 属性允许通过将时间步长调整为物理时间步长而不是稳定性约束来有效处理问题的多尺度性质。因此，我们研究了 Kolmogorov 流的长时间尺度演化，观察到它演化为最终稳定的静止状态，其特征是流函数和涡度之间看似普遍的关系。