Efficiency of high accuracy DRP schemes in direct numerical simulations of incompressible turbulent flows

We investigate the ability of Dispersion Relation Preserving (DRP) schemes to provide accurate numerical solutions in incompressible turbulent flows. DRP and compact schemes have been implemented in a finite differences Direct Numerical Simulation (DNS) of a fully developed turbulent channel flow. The results are compared with standard second order difference schemes and pseudo-spectral strategies. Compact and DRP schemes both lead to satisfactory results even when the wall normal grid spacing exceeds the Kolmogorov scale in high buffer and logarithmic layers. This is explained by the appropriate spectral characteristics of these schemes that can subsequently be efficiently used in other non-homogeneous configurations.