Explicit filtering for large eddy simulation as use of a spectral buffer

Abstract

The explicit filtering method for large eddy simulation (LES), which comprises integration of the governing equations without any added terms for sub-grid-scale modeling, and the application of a low-pass filter to transported fields, is discussed. The shapes of filter response functions of numerical schemes for spatial derivatives and the explicit filter that have been used for several LES are examined. Generally, these are flat (no filtering) over a range of low wavenumbers and then fall off over a small range of the highest represented wavenumbers. It is argued that this high wavenumber part can be viewed as a spectral buffer analogous to physical buffer (or sponge) zones used near outflow boundaries. With grid refinement, this buffer moves to higher wavenumbers and solutions are obtained with little change over a range of low wavenumbers but with added, correct, high wavenumber content. Examples show LES solutions to converge toward direct numerical simulations monotonically. Connections to other widely used methods are also explained.