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

TL;DR

This paper discusses an explicit filtering approach for large eddy simulation (LES) that uses spectral buffers to improve accuracy, demonstrating convergence to direct numerical simulation and relating it to other LES methods.

Contribution

It introduces a spectral buffer concept in explicit filtering LES, showing how it enhances convergence and relates to existing sub-grid-scale modeling techniques.

Findings

Spectral buffer acts as a high-wavenumber sponge zone.

Approach converges monotonically to DNS results.

Method adapts with increased spectral resolution.

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. The monotonic convergence of this approach to a direct numerical simulation, and the shifting of the spectral buffer to larger wavenumbers as the represented spectral range is increased, without altering the low wavenumber part of solutions, is demonstrated with LES of two sample flows. Connections to other widely used methods---the Smagorinsky model, MILES and another ILES---are also explained.