We consider an uncoupled, modular regularization algorithm for approximation of the
Navier-Stokes equations. The method is: Step 1.1: Advance the NSE
one time step, Step 1.1: Regularize to obtain the approximation at
the new time level. Previous analysis of this approach has been for specific time stepping
methods in Step 1.1 and simple stabilizations in Step 1.1. In this report we extend the mathematical support for uncoupled,
modular stabilization to (i) the more complex and better performing BDF2 time
discretization in Step 1.1, and (ii) more general (linear or
nonlinear) regularization operators in Step 1.1. We give a complete
stability analysis, derive conditions on the Step 1.1
regularization operator for which the combination has good stabilization effects,
characterize the numerical dissipation induced by Step 1.1, prove
an asymptotic error estimate incorporating the numerical error of the method used in Step
1.1 and the regularizations consistency error in Step 1.1 and provide numerical tests.