标题： 三维湍流科莫戈罗夫流的清洁数值模拟 显示英文标题

标题： Clean numerical simulation (CNS) of three-dimensional turbulent Kolmogorov flow

摘要： 湍流在各种科学和工程学科中具有重要意义。 Orszag于1970年提出的湍流直接数值模拟（DNS）是流体力学中的一个里程碑，开启了湍流的数值实验时代。 许多研究人员报告称，由于时空轨迹对小扰动非常敏感，湍流应该是混沌的。 2006年，E.D. Lorenz发现数值噪声可能对混沌系统的统计特性产生重大影响。 上述事实逻辑上导致了这样的结论：作为混沌系统的湍流的数值噪声可能对湍流场产生重大影响。 事实上，对于二维（2D）Kolmogorov湍流来说，这一点已被一种比DNS更精确的算法——“干净数值模拟”（CNS）所证实。 与DNS不同，CNS可以将截断误差和舍入误差降低到任何所需的小水平，从而使人工数值噪声在整个足够长的时间间隔内严格可忽略。 然而，在物理学中，3D湍流比2D湍流更重要，正如诺贝尔奖得主T.D. Lee所指出的。 因此，本文首次利用CNS求解三维（3D）Kolmogorov湍流，并详细比较了我们的CNS结果与DNS给出的结果。 发现由DNS给出的三维Kolmogorov湍流的时空轨迹很快就被人工数值噪声严重污染，DNS结果不仅在流场和能量级联方面，甚至在统计方面都与CNS基准解存在巨大偏差。 显示英文摘要

摘要： Turbulence holds immense importance across various scientific and engineering disciplines. The direct numerical simulation (DNS) of turbulence proposed by Orszag in 1970 is a milestone in fluid mechanics, which began an era of numerical experiment for turbulence. Many researchers have reported that turbulence should be chaotic, since spatiotemporal trajectories are very sensitive to small disturbance. In 2006 E.D. Lorenz discovered that numerical noise might have a great influence on statistic characteristics of chaotic systems. The above-mentioned facts logically lead to the conclusion that numerical noises of turbulence (as a chaotic system) might have great influence on turbulent flows. This is indeed true for a two-dimensional (2D) Kolmogorov turbulent flow, as currently revealed by a much more accurate algorithm than DNS, namely the ``clean numerical simulation'' (CNS). Different from DNS, CNS can greatly reduce both of truncation error and round-off error to any required small level so that artificial numerical noise can be rigorously negligible throughout a time interval long enough for calculating statistics. However, In physics, 3D turbulent flow is more important than 2D turbulence, as pointed out by Nobel Prize winner T.D. Lee. So, for the first time, we solve a 3D turbulent Kolmogorov flow by means of CNS in this paper, and compare our CNS result with that given by DNS in details. It is found that the spatial-temporal trajectories of the 3D Kolmogorov turbulent flow given by DNS are badly polluted by artificial numerical noise rather quickly, and the DNS result has huge deviations from the CNS benchmark solution not only in the flow field and the energy cascade but also even in statistics.