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This report extends the mathematical support of a subgrid artificialviscosity (SAV) method to simulate the incompressible Navier-Stokes equationsto better performing a linearly extrapolated BDF2 (BDF2LE) time discretization.The method considers the viscous term as a combination of the vorticity and thegrad-div stabilization term. SAV method introduces global stabilization byadding a term, then antidiffuses through the extra mixed variables. We presenta detailed analysis of conservation laws, including both energy and helicitybalance of the method. We also show that the approximate solutions of themethod are unconditionally stable and optimally convergent. Several numericaltests are presented for validating the support of the derived theoreticalresults.

An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows