Spectro-consistent discretization of Navier-Stokes:a challenge to RANS and LES

In this paper, we discuss the results of a fourth-order, spectre-consistent discretization of the in compressible Navier-Stokes equations. In such an approach the discretization of a (skew-)symmetric operator is given by a (skew-)symmetric matrix. Numerical experiments with spectro-consistent discretizations and traditional methods are presented for a one-dimensional convection-diffusion equation. LES and RANS are challenged by giving a number of tramples for which a fourth-order, spectre-consistent discretization of the Navier-Stokes equations without any turbulence model yields better (or at least equally good) results as large-eddy simulations or RANS computations, whereas the grids are comparable. The examples are taken from a number of recent workshops on complex turbulent flows.