DNS-aided explicitly filtered LES of channel flow

The equations for large-eddy simulation (LES) are formally derived by applying a low-pass filter to the Navier–Stokes (NS) equations (Leonard 1975). However, in most numerical simulations, no explicit filter form is specified, and the computational grid and the low-pass characteristics of the discrete differentiation operators act as an effective implicit filter. The resulting velocity field is then assumed to be representative of the filtered velocity. Although the discrete operators have a low-pass filtering effect, the associated filter acts only in the single spatial direction in which the derivative is applied (Lund 2003); thus each term in the NS equations takes on a different filter form. In addition, numerical errors and the frequency content are uncontrolled for the implicit filter approach, and the solutions are grid dependent (Kravchenko & Moin 2000; Meyers & Sagaut 2007).