Optimal large-eddy simulation results for isotropic turbulence

A new class of large-eddy simulation (LES) models (optimal LES) was previously introduced by the authors. These models are based on multi-point statistical information, which here is provided by direct numerical simulation (DNS). In this paper, the performance of these models in LES of forced isotropic turbulence is investigated. It is found that both linear and quadratic optimal models yield good simulation results, with an excellent match between the LES and filtered DNS for spectra, and low-order structure functions. Optimal models were then used as a vehicle to investigate the effects of filter shape and the locality of model dependence on LES performance. Results indicate that a Fourier cutoff filter yields more accurate simulations than graded cutoff filters, leaving no motivation to use graded filters in spectral simulations. It was also found that optimal models formulated to depend on local information performed nearly as well as global models. This is important because in practical LES simulations in which spectral methods are not applicable, global model dependence would be prohibitively expensive.