  We present a stable spectral vanishing viscosity for discontinuous Galerkin
schemes, with applications to turbulent and supersonic flows. The idea behind
the SVV is to spatially filter the dissipative fluxes, such that it
concentrates in higher wavenumbers, where the flow is typically under-resolved,
leaving low wavenumbers dissipation-free. Moreover, we derive a stable
approximation of the Guermond-Popov fluxes with the Bassi-Rebay 1 scheme, used
to introduce density regularization in shock capturing simulations. This
filtering uses a Cholesky decomposition of the fluxes that ensures the entropy
stability of the scheme, which also includes a stable approximation of boundary
conditions for adiabatic walls. For turbulent flows, we test the method with
the three-dimensional Taylor-Green vortex and show that energy is correctly
dissipated, and the scheme is stable when a kinetic energy preserving
split-form is used in combination with a low dissipation Riemann solver.
Finally, we test the shock capturing capabilities of our method with the
Shu-Osher and the supersonic forward facing step cases, obtaining good results
without spurious oscillations even with coarse meshes.
