An improved method to assess the quality of large eddy simulations in the context of implicit filtering

Large eddy simulation (LES) quality assessment is very important in view of predictive LES applications, but it is more complex than the verification of solutions from the Reynolds averaged Navier–Stokes equations. One reason is that the numerical discretization error and the subgrid scale model contribution depend on the grid resolution and that both terms interact. Recently, a method has been proposed to evaluate these error contributions by a systematic grid and model variation, assuming that the numerical error and the modeling error scale like a power of the grid spacing resp. filter width. A second-order dissipation error has been assumed in that work. However, theoretical arguments suggest that the true subgrid stresses scale like Δ^2/3. The determination of the suitability and generality of this assumption is part of the present work. It will be shown that smaller values of the scaling exponent for the modeling error, i.e. m≈ 2/3, seem to be more appropriate. Furthermore, a more conservative measure for estimating the uncertainty is proposed. Besides a wall bounded flow (channel flow) and a shear flow (plane jet) the new procedure will be applied to a third important flow category, swirling flows.

Acknowledgements

The authors gratefully acknowledge the financial support by the DFG (German Research Council) Sonderforschungsbereich 568 ‘Flow and Combustion in Future Gas Turbine Combustion Chambers’. Furthermore, the authors would like to thank Professor I. Celik for fruitful discussions.