The statistics obtained from turbulent flow simulations are generally uncertain due to finite time averaging. Most techniques available in the literature to accurately estimate these uncertainties typically only work in an offline mode, that is, they require access to all available samples of a time series at once. In addition to the impossibility of online monitoring of uncertainties during the course of simulations, such an offline approach can lead to input/output (I/O) deficiencies and large storage/memory requirements, which can be problematic for large-scale simulations of turbulent flows. Here, we designed, implemented and tested a framework for estimating time-averaging uncertainties in turbulence statistics in an in-situ (online/streaming/updating) manner. The proposed algorithm relies on a novel low-memory update formula for computing the sample-estimated autocorrelation functions (ACFs). Based on this, smooth modeled ACFs of turbulence quantities can be generated to accurately estimate the time-averaging uncertainties in the corresponding sample mean estimators. The resulting uncertainty estimates are highly robust, accurate, and quantitatively the same as those obtained by standard offline estimators. Moreover, the computational overhead added by the in-situ algorithm is found to be negligible allowing for online estimation of uncertainties for multiple points and quantities. The framework is general and can be used with any flow solver and also integrated into the simulations over conformal and complex meshes created by adopting adaptive mesh refinement techniques. The results of the study are encouraging for the further development of the in-situ framework for other uncertainty quantification and data-driven analyses relevant not only to large-scale turbulent flow simulations, but also to the simulation of other dynamical systems leading to time-varying quantities with autocorrelated samples.

中文翻译：

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湍流模拟中时间平均不确定性的原位估计


由于时间有限，从湍流模拟中获得的统计数据通常是不确定的。文献中可用于准确估计这些不确定性的大多数技术通常仅在离线模式下有效，也就是说，它们需要一次访问时间序列的所有可用样本。除了在仿真过程中无法在线监控不确定性外，这种离线方法还会导致输入/输出 （I/O） 缺陷和大量存储/内存要求，这对于湍流的大规模仿真可能是个问题。在这里，我们设计、实施和测试了一个框架，用于以原位（在线/流媒体/更新）方式估计湍流统计中的时间平均不确定性。所提出的算法依赖于一种新的低内存更新公式来计算样本估计的自相关函数 （ACF）。基于此，可以生成湍流量的平滑建模 ACF，以准确估计相应样本均值估计器中的时间平均不确定性。由此产生的不确定性估计值非常稳健、准确，并且在数量上与标准离线估计器获得的估计相同。此外，发现原位算法增加的计算开销可以忽略不计，允许在线估计多个点和数量的不确定性。该框架是通用的，可以与任何流动求解器一起使用，也可以集成到通过采用自适应网格细化技术创建的共形网格和复杂网格的仿真中。 该研究的结果令人鼓舞，有助于进一步开发用于其他不确定性量化和数据驱动分析的原位框架，这些框架不仅与大规模湍流模拟有关，还与导致自相关样本的时变量的动力学系统模拟有关。