Second order time relaxation model for accelerating convergence to steady-state equilibrium for Navier-Stokes equations

This paper deals with the problem of accelerating convergence to equilibrium for the Navier-Stokes equation using time relaxation models. We show that the BDF2 based semidiscrete solution of the regularized scheme converges to the steady-state solution of the continuous Navier-Stokes equations, under appropriate conditions. The proof also shows that time relaxation model can be used to accelerate the convergence with the appropriate choice of the parameters. Numerical experiment is presented to illustrate the theory.