  The statistics obtained from turbulent flow simulations are generally
uncertain due to finite time averaging. The 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. The framework is completely
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.

Fluid Dynamics;Computational Physics;Data Analysis, Statistics and Probability