  The Quasi-Spectral Viscosity (QSV) method is a novel closure for a high-order
finite-difference discretization of the filtered compressible Navier-Stokes
equations capable of unifying dynamic sub-filter scale (SFS) modeling and shock
capturing under a single mathematical framework. Its innovation lies in the
introduction of a physical-space implementation of a spectral-like SFS
dissipation term by leveraging residuals of filter operations, achieving two
goals: (1) estimating the energy of the resolved solution near the grid cutoff;
(2) imposing a plateau-cusp shape to the spectral distribution of the added
dissipation. The QSV approach has been tested in a variety of flows to showcase
its capability to act interchangeably as: a shock capturing method, in the
Shu-Osher, shock/vortex or shock/wall interactions problems; or as a SFS
closure, in subsonic Taylor Green Vortex (TGV), and supersonic/hypersonic
turbulent channel flows. QSV performs well compared to previous eddy-viscosity
closures and shock capturing methods in such test cases. In a supersonic TGV
flow, a case which exhibits shock/turbulence interactions, QSV alone
outperforms the simple superposition of separate numerical treatments for SFS
turbulence and shocks. QSV's combined capability of simulating shocks and
turbulence independently, as well as simultaneously, effectively achieves the
unification of shock capturing and Large-Eddy Simulation.
