A Priori Assessments of Numerical Uncertainty in Large-Eddy Simulations

Abstract

Current suggestions for estimating the numerical uncertainty in solutions by the Large-Eddy Simulation (LES) methodology require either a posteriori input or reflect global assessments. In most practical applications, this approach is rather costly for the user and especially time consuming due to the CPU effort needed to reach the statistical steady state. Herein, we demonstrate two alternate a priori graphical exercises. An evaluation of the numerical uncertainty uses the turbulent quantities given by the area under the wave number spectra profiles. These profiles are easily constructed along any grid line in the flow domain prior to the collection of the turbulent statistics. One exercise involves a completion of the spectrum profile beyond the cutoff wave number to the inverse of Kolmorgorov’s length scale by a model of isotropic turbulence. The other extends Richardson Extrapolation acting on multiple solutions. Sample test cases of both LES solutions and direct numerical simulations as well as published experimental data show excellent agreement between the integrated matched spectra and the respective turbulent statistics. Thus, the resultant uncertainties themselves provide a useful measure of accumulated statistical error in the resolved turbulent properties.