A Posteriori Analysis of Numerical Errors in Computing Scalar Variance

Abstract

The results of a novel procedure for a posteriori testing show that the predictions of a dynamic model for the subfilter variance are sensitive to accumulated errors in the evolution of the filtered scalar field as well as to numerical errors incurred in evaluating the variance model at a single time step. Tests were performed on homogeneous, isotropic filtered scalar fields simulated using exact and modified wavenumbers corresponding to second, fourth, and sixth order accurate finite difference schemes. The sixth order scheme showed close agreement with the spectral method in terms of the distribution of predicted subfilter variance values, which were assessed using nonparametric techniques. The second order scheme produced, on average, substantially higher values of subfilter variance. Valid methods for comparing models were sought that account for the variability of statistical estimates made from a spatially correlated sample, and some preliminary approaches were presented.