A fast algorithm for the estimation of statistical error in DNS (or experimental) time averages

Russo, Serena; Luchini, Paolo

doi:10.1016/j.jcp.2017.07.005

Cited by 33 publications

(19 citation statements)

References 13 publications

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“…The sampling errors for some key properties discussed in this paper have been estimated using the method of Russo & Luchini (2017), based on an extension of the classical batch means approach. The results of the uncertainty estimation analysis are listed in table 2, where we provide expected values and associated standard deviation for the friction factor (), mean centreline velocity (), peak axial velocity variance and its position ( and , respectively), and the dissipation rate of axial velocity variance ().…”

Section: The Numerical Datasetmentioning

confidence: 99%

One-point statistics for turbulent pipe flow up to

et al. 2021

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We study turbulent flows in a smooth straight pipe of circular cross-section up to friction Reynolds number $({\textit {Re}}_{\tau }) \approx 6000$ using direct numerical simulation (DNS) of the Navier–Stokes equations. The DNS results highlight systematic deviations from Prandtl friction law, amounting to approximately $2\,\%$ , which would extrapolate to approximately $4\,\%$ at extreme Reynolds numbers. Data fitting of the DNS friction coefficient yields an estimated von Kármán constant $k \approx 0.387$ , which nicely fits the mean velocity profile, and which supports universality of canonical wall-bounded flows. The same constant also applies to the pipe centreline velocity, thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at ${\textit {Re}}_{\tau } \gtrsim 10^4$ , as a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.

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Section: The Numerical Datasetmentioning

confidence: 99%

One-point statistics for turbulent pipe flow up to

et al. 2021

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“…Upper 95% CI Lower 95% CI [ u ] Accurate quantification of the uncertainties due to finite time-averaging using methods similar to those investigated in [57,44,71] will be considered in the feature.…”

Section: Mean Observationmentioning

confidence: 99%

An Uncertainty-Quantification Framework for Assessing Accuracy, Sensitivity, and Robustness in Computational Fluid Dynamics

Rezaeiravesh¹,

Vinuesa²,

Schlatter³

2020

Preprint

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A framework is developed based on different uncertainty quantification (UQ) techniques in order to assess validation and verification (V&V) metrics in computational physics problems, in general, and computational fluid dynamics (CFD), in particular. The metrics include accuracy, sensitivity and robustness of the simulator's outputs with respect to uncertain inputs and computational parameters. These parameters are divided into two groups: based on the variation of the first group, a computer experiment is designed, the data of which may become uncertain due to the parameters of the second group. To construct a surrogate model based on uncertain data, Gaussian process regression (GPR) with observation-dependent (heteroscedastic) noise structure is used. To estimate the propagated uncertainties in the simulator's outputs from first and also the combination of first and second groups of parameters, standard and probabilistic polynomial chaos expansions (PCE) are employed, respectively. Global sensitivity analysis based on Sobol decomposition is performed in connection with the computer experiment to rank the parameters based on their influence on the simulator's output. To illustrate its capabilities, the framework is applied to the scale-resolving simulations of turbulent channel flow using the open-source CFD solver Nek5000. Due to the high-order nature of Nek5000 a thorough assessment of the results' accuracy and reliability is crucial, as the code is aimed at high-fidelity simulations. The detailed analyses and the resulting conclusions can enhance our insight into the influence of different factors on physics simulations, in particular the simulations of wall-bounded turbulence.

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“…Just as in the previous work of [28], the amplitude ε of the wall oscillation has to strike a compromise between linearity and statistical fluctuation error of time averaging, which had to be found by trial and error. For this purpose a new algorithm was developed [36] in order to estimate the expected error of the time average. Re = 1450 (Re = 100); computational box up to 8π.…”

Section: Immersed-boundary Direct Numerical Simulation Of Turbulent Flow Past a Wavy Bottommentioning

confidence: 99%

Surprising Behaviour and Singularity in the Saint Venant Approximation for a Fluid

Luchini¹

2018

INCONTRI

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A research line is reviewed which, over a few years, led to a substantial change of perspective about the simplified models that underlie the description of quasi-onedimensional streams, their instabilities, and their effects upon sandy beds. Even when the flow is assumed to be laminar, the Saint-Venant equation of quasi-onedimensional fluid flow can be formulated in more than one manner; it will be shown that only one of these choices is consistent with the complete three-dimensional Navier- Stokes equations. When the flow is turbulent, an added complication is the presence of a turbulence model, most often of the eddy-viscosity type; it will be shown that such a model can be in strong contrast with a direct numerical simulation of the same phenomenon, even to the point of producing results of opposite sign. In addition, the complete numerical simulation of flow past an undulated bottom exhibits a non-monotonic approach to its long-wave, quasi-onedimensional limit, with a surprising resonance that has no laminar counterpart and must become the subject of future investigations.

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A fast algorithm for the estimation of statistical error in DNS (or experimental) time averages

Cited by 33 publications

References 13 publications

One-point statistics for turbulent pipe flow up to

One-point statistics for turbulent pipe flow up to

An Uncertainty-Quantification Framework for Assessing Accuracy, Sensitivity, and Robustness in Computational Fluid Dynamics

Surprising Behaviour and Singularity in the Saint Venant Approximation for a Fluid

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