Consistency and accuracy of LES by explicit filtering

An explicit filtering method was proposed as an equivalent implementation of the approximate deconvolution method for large eddy simulation (LES).  The essential requirement of this method was that all spatial numerical operations (finding derivatives, interpolations) be of high resolution---be spectrally accurate over a large part of the computed, low-wavenumber range.  A natural expectation is that the range of scales over which the dynamics are more accurately represented increases with grid-refinement. Second, beyond some level of refinement, large scale dynamics do not change significantly because the energy in small scale content is orders of magnitude smaller.  Third, as Reynolds number is increased, in many flows where the spectral range of the active scales increases at the small scale end only, an LES should return the same large scale dynamics.  Systematic studies at different resolutions and Reynolds numbers in forced, homogeneous isotropic turbulence and round jets (low-speed and high-speed ones with multiple shock cells, at Reynolds numbers of the order of a million), will be presented that show these expectations to be met in LES by explicit filtering.  Such a posteriori consistency and accuracy make this a reliable method for LES.