论文标题
数值噪声的大规模影响是人造随机干扰对持续湍流的影响
Large-scale influence of numerical noises as artificial stochastic disturbances on a sustained turbulence
论文作者
论文摘要
我们研究了数值噪声的大规模影响，因为微小的人造随机干扰对持续的湍流。以二维（2D）湍流雷利 - 纳德（RB）对流为例，我们通过传统的算法（由RKWD标记）和所谓的清洁数值模拟（CNS）分别求解NS方程。 RKWD给出的数值模拟是“真”物理解决方案的混合物和随机的“ false”数值噪声的混合物，可以被视为一种人工随机干扰：不幸的是，“真”物理解决方案主要与“ false”数值noses相同。相比之下，中枢神经系统可以将背景数值噪声大大降低到任何所需的水平，以便与“ True”物理解决方案相比，“ false”数值噪声可以忽略不计，因此可以将CNS解决方案用作“干净”基准解决方案进行比较。发现作为微小的人造随机干扰的数值噪声确实可能导致大规模的模拟偏差，不仅在时空轨迹中，甚至在统计范围内。尤其是，这些数值噪声（作为人造随机干扰）甚至导致不同类型的流量：剪切对流发生在RKWD模拟中，其相应的流场变成了一种层次流动，但是CNS基准解决方案始终可以维持整个模拟过程中非剪切的涡流/滚动式的旋转旋转液体。因此，我们提供了一个严格的证据，表明数值噪声是一种小规模的人造随机干扰，对持续的湍流产生了数量和质量上的大规模影响，即本文考虑的2D湍流RB对流。
We investigate the large-scale influence of numerical noises as tiny artificial stochastic disturbances on a sustained turbulence. Using the two-dimensional (2D) turbulent Rayleigh-Bénard (RB) convection as an example, we numerically solve the NS equations, separately, by means of a traditional algorithm with double precision (marked by RKwD) and the so-called clean numerical simulation (CNS). The numerical simulation given by the RKwD is a mixture of the "true" physical solution and the "false" numerical noises that is random and can be regarded as a kind of artificial stochastic disturbances: unfortunately, the "true" physical solution is mostly at the same level as the "false" numerical noises. By contrast, the CNS can greatly reduce the background numerical noise to any a required level so that the "false" numerical noises are negligible compared with the "true" physical solution and thus the CNS solution can be used as a "clean" benchmark solution for comparison. It is found that the numerical noises as tiny artificial stochastic disturbances could indeed lead to large-scale deviations of simulations not only in spatio-temporal trajectories but also even in statistics. Especially, these numerical noises (as artificial stochastic disturbances) even lead to different types of flows: the shearing convection occurs for the RKwD simulations, and its corresponding flow field turns to a kind of zonal flow thereafter, however the CNS benchmark solution always sustains the non-shearing vortical/roll-like convection during the whole process of simulation. Thus, we provide a rigorous evidence that numerical noises as a kind of small-scale artificial stochastic disturbances have quantitatively and qualitatively large-scale influences on a sustained turbulence, i.e. the 2D turbulent RB convection considered in this paper.
