Estimating Uncertainties in Statistics Computed from DNS

ORAL

Abstract

Rigorous assessment of uncertainty is crucial to the utility of DNS results. Uncertainties in the computed statistics arise from two sources: finite sampling and the discretization of the Navier-Stokes equations. Due to the presence of non-trivial sampling error, standard techniques for estimating discretization error (such as Richardson Extrapolation) fail or are unreliable. This talk provides a systematic and unified approach for estimating these errors. First, a sampling error estimator that accounts for correlation in the input data is developed. Then, this sampling error estimate is used as an input to a probabilistic extension of Richardson extrapolation in order to characterize the discretization error. These techniques are used to investigate the sampling and discretization errors in the DNS of a wall-bounded turbulent flow at $Re_{\tau}$ = 180. We will show a well-resolved DNS simulation which, for the centerline velocity, possesses 0.02\% sampling error and discretization errors of 0.003\%. These results imply that standard resolution heuristics for DNS accurately predict required grid sizes.

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Authors

  • Nicholas Malaya

    The University of Texas at Austin, University of Texas at Austin, University of Texas Austin

  • Todd Oliver

    The University of Texas at Austin, University of Texas at Austin, Institute for Computational Engineering and Sciences, The University of Texas at Austin

  • Rhys Ulerich

    The University of Texas at Austin, University of Texas at Austin

  • Robert Moser

    The University of Texas at Austin, University of Texas at Austin, University of Texas, University of Texas Austin