The use of explicit filters in large eddy simulation

Explicit filtering is considered as a means of controlling the numerical errors that result when finite-difference methods are used in large eddy simulation (LES). The notion that the finite-difference expressions themselves act as an effective filter is shown to be false for three-dimensional simulations performed on nonuniform meshes. For consistency, the nonlinear terms in the Navier-Stokes equations should be filtered explicitly at each time step in order to insure that the spectral content of the solution remains fixed at the desired filter level. The explicit filtering operation allows a separation between the filter size and the mesh spacing and can be used to control the impact of the numerical errors. Numerical tests of the explicit filtering approach in turbulent channel flow are used to investigate the effectiveness of the explicit filtering approach and to assess its associated cost. Explicit filtering is shown to improve the computed results, but this improvement comes at a rather high computational cost. The explicitly-filtered approach is also compared with straightforward mesh refinement as an alternative means of improving the computed results. Mesh refinement is also seen to increase the accuracy of the simulation but some traces of numerical error appear to persist in the solution.