Stability analysis of pressure correction schemes for the Navier–Stokes equations with traction boundary conditions

Abstract

We present a stability analysis for two different rotational pressure correction schemes with open and traction boundary conditions. First, we provide a stability analysis for a rotational version of the grad–div stabilized scheme of Bonito et al. (2015). This scheme turns out to be unconditionally stable, provided the stabilization parameter is suitably chosen. We also establish a conditional stability result for the boundary correction scheme presented in Bänsch (2014). These results are shown by employing the equivalence between stabilized gauge Uzawa methods and rotational pressure correction schemes with traction boundary conditions.