A finite element formulation for transient incompressible viscous flows stabilized by local time-steps

Stabilized finite element formulations are well suited for convection dominated flows and for the solution of the incompressible Navier-Stokes equations in primitive variables. In this paper, we present a method where the structure of stabilization terms appear naturally from a least-squares minimization of the time-discretized momentum balance. Local time-steps, chosen according to the time-scales of convection-diffusion of momentum, play the role of stabilization parameters. Numerical solutions of incompressible viscous flows demonstrate the usefulness of the proposed stabilized formulation.