  In this note, the importance of spectral properties of viscous flux
discretization in solving compressible Navier-Stokes equations for turbulent
flow simulations is discussed. We studied six different methods, divided into
two different classes, with poor and better representation of spectral
properties at high wavenumbers. Both theoretical and numerical results have
revealed that the method with better properties at high wavenumbers, denoted as
$\alpha$-damping type discretization, produced superior solutions compared to
the other class of methods. The proposed compact $\alpha$-damping method
converged towards the direct numerical simulation (DNS) solution at lower grid
resolution compared with the other class of methods and is, therefore, a better
candidate for high fidelity large-eddy simulations (LES) and DNS studies.
