Sharp cutoff versus smooth filtering in large eddy simulation

Abstract

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