  This report extends the mathematical support of a subgrid artificial
viscosity (SAV) method to simulate the incompressible Navier-Stokes equations
to better performing a linearly extrapolated BDF2 (BDF2LE) time discretization.
The method considers the viscous term as a combination of the vorticity and the
grad-div stabilization term. SAV method introduces global stabilization by
adding a term, then antidiffuses through the extra mixed variables. We present
a detailed analysis of conservation laws, including both energy and helicity
balance of the method. We also show that the approximate solutions of the
method are unconditionally stable and optimally convergent. Several numerical
tests are presented for validating the support of the derived theoretical
results.
