Numerical analysis of a bdf2 modular grad-div Stabilization method for the Navier-Stokes equations

Abstract

A second-order accurate modular algorithm is presented for a standard BDF2 code for the Navier-Stokes equations (NSE). The algorithm exhibits resistance to solver breakdown and increased computational efficiency for increasing values of grad-div parameters. We provide a complete theoretical analysis of the algorithms stability and convergency. Computational tests are performed and illustrate the theory and advantages over monolithic grad-div stabilizations.