Explicit filtering and subgrid-scale models in turbulent channel flow

In large eddy simulation (LES), the large energy carrying length scales of turbulence are resolved and the small structures are modeled. The separation of large and small scales is done by applying a low-pass filter to the Navier-Stokes equations. The effect of the small-scale turbulence on the resolved scales is modeled using a subgrid-scale (SGS) model. It is of great importance that the resolved length scales are captured accurately by the numerical scheme. Information from the smallest resolved length scales are commonly used to model the stresses of the unresolved scales in the SGS model. This requires that the numerical error of the scheme is sufficiently small. Therefore, high order numerical schemes are necessary in LES. One approach is to use high-order finite-difference schemes. However, all finite-difference schemes have a truncation error that increases with the wavenumber (Lund & Kaltenbach 1995). To reduce the influence of this error, an explicit filtering can be applied that re-duces or removes the small scales that otherwise would be largely affected by this error. In using explicit filtering, it is a requirement that the filtering operation and the dif