Assessment of LES Quality Measures Using the Error Landscape Approach

Abstract

A large-eddy simulation database of homogeneous isotropic decaying turbulence is used to assess four different LES quality measures that have been proposed in the literature. The Smagorinsky subgrid model was adopted and the eddy-viscosity ‘parameter’ $C_S$ and the grid spacing $h$ were varied systematically. It is shown that two methods qualitatively predict the basic features of an error landscape including an optimal refinement trajectory. These methods are based on variants of Richardson extrapolation and assume that the numerical error and the modelling error scale with a power of the mesh size. Hence they require the combination of simulations on several grids. The results illustrate that an approximate optimal refinement strategy can be constructed based on LES output only, without the need for DNS data. Comparison with the full error landscape shows the suitability of the different methods in the error assessment for homogeneous turbulence. The ratio of the estimated turbulent kinetic energy error and the ‘true’ turbulent kinetic energy error calculated from DNS is studied for different Smagorinsky parameters and different grid sizes. The behaviour of this quantity for decreasing mesh size gives further insight into the reliability of these methods.