  We analyse numerical errors (dissipation and dispersion) introduced by the
discretisation of inviscid and viscous terms in energy stable discontinuous
Galerkin methods. First, we analyse these methods using a linear von Neumann
analysis (for a linear advection-diffusion equation) to characterise their
properties in wave-number space. Second, we validate these observations using
the 3D Taylor-Green Vortex Navier-Stokes problem to assess
transitional/turbulent flows. We show that the dissipation introduced by upwind
Riemann solvers affects primarily high wave-numbers. This dissipation may be
increased, through a penalty parameter, until a critical value. However,
further augmentation of this parameter leads to a decrease of dissipation,
reaching zero for very large values. Regarding the dissipation introduced by
second order derivatives, we show that this dissipa- tion acts at low and
medium wave-numbers (lower wave-numbers compared to upwind Riemann solvers). In
addition, we analyse the Spectral Vanishing Viscosity (SVV) technique,
previously used in continuous discretisations (e.g. Fourier), to find that with
an appropriate kernel (which damps selected modes) it is possible to control
the amount of dissipation introduced in the low and medium wave-number range.
Combining these ideas, we finally propose a DG-SVV approach that uses a
Smagorinsky model to compute the numerical viscosity. This DG-SVV approach is
tested in an isotropic laminar/turbulent under-resolved scenario. Combining the
SVV technique with a low dissipation Riemann solver, we obtain a scheme capable
of maintaining low dissipation levels for laminar flows, whilst providing the
correct dissipation for all wave-number ranges in turbulent regimes.
