Uncertainty Quantification of the time averaging of a Statistics Computed from Numerical Simulation of Turbulent Flow
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Rigorous assessment of the uncertainty is crucial to the utility of numerical simulation of Turbulent flow. The Turbulent flows are often stationary and ergodic, after some initial transient time. Therefore, the time averaged of a quantity (velocity, TKE (turbulence kinetic energy), total drag, etc) converges to a constant as the averaging interval increases. This infinite-time-average statistic is of particular interest in many problems, such as aerodynamic shape optimization. Since taking an average over the infinite time horizon is not possible, some finite-time approximation of the infinite-time-average statistic of interest is used in practice. However, because of the initial transient behavior of the turbulence simulations, this estimate is biased. This issue is solved by deleting the initial transient part of the simulation. The other important issue is the error of this approximation decreases slowly, like the reciprocal of the square roots of the averaging time. In this paper, we develop a framework to first automatically deleted the transient part of a turbulence simulation, then, quantify precisely the uncertainty of such a finite-time-average approximation of an infinite-time-average statistic of a stationary and ergodic process.
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