Sharp Cut-oo vs. Smooth Filtering in Les Typeset Using Revt E X 2

The large eddy simulation (LES) equations of turbulent ows are formally derived by applying a low-pass lter to the Navier-Stokes equations. As a result the subgrid-scale (SGS) stress tensor strongly depends on the assumed lter shape, which causes an SGS model to be lter dependent. In particular, depending on the choice of the lter the corresponding SGS model should satisfy very diierent requirements in terms of large scale dynamics and kinetic energy budget. This paper is an attempt to systematically study the eeect of the lter shape on the subgrid scale model and its subsequent eeect on LES. For the sake of simplicity, we consider numerical simulation of a one-dimensional homogeneous ow, governed by the viscous Burgers equation. Large eddy simulations of the solution of the Burgers problem are performed using subgrid scale models obtained by ltering data from direct numerical simulations (DNS). Diagnostics include temporal evolution of energy and dis-sipation as well as energy spectra. It is demonstrated both theoretically and numerically that the assumed lter shape can have a signiicant eeect on LES 1 in terms of spectral content and physical interpretation of the solution. The results are generalized for LES of three-dimensional turbulent ows and spe-ciic recommendations for the use of lters and corresponding SGS models are made.