We consider an uncoupled, modular regularization algorithm for approximation of theNavier-Stokes equations. The method is: Step 1.1: Advance the NSEone time step, Step 1.1: Regularize to obtain the approximation atthe new time level. Previous analysis of this approach has been for specific time steppingmethods 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 timediscretization in Step 1.1, and (ii) more general (linear ornonlinear) regularization operators in Step 1.1. We give a completestability analysis, derive conditions on the Step 1.1regularization operator for which the combination has good stabilization effects,characterize the numerical dissipation induced by Step 1.1, provean asymptotic error estimate incorporating the numerical error of the method used in Step1.1 and the regularizations consistency error in Step 1.1 and provide numerical tests.
