How to estimate the resolution of an LES of recirculating flow

Paper in proceeding, 2010

How should the resolution of an LES be estimated? There exist guidelines for boundary layers for how to create a grid in terms of the grid size expressed in viscous units. However, in other flow regions there are few if any guidelines for how to generate a grid that ensures accurate results. Worse, it is not even clear how to estimate the resolution after having carried out an LES. The present study evaluates the following quantities: energy spectra, dissipation energy spectra, two-point correlations, the ratio of SOS shear stress to resolved shear stress, the ratio of the SOS viscosity to the molecular and the ratio of the SOS dissipation due to the resolved fluctuating velocity gradients to that due to the mean velocity gradients. Two flows are analyzed, namely the flow in a plane asymmetric diffuser and decaying grid turbulence. The main conclusions are that two-point correlations are the best way to estimate the resolution and that energy spectra are not suitable. It is usually assumed that the SOS dissipation takes place at wavenumbers close to cut-off. The present work shows that this idealized picture is not true, but that the SOS dissipation takes place at rather low wavenumbers.