  We consider multigrid methods for finite volume discretizations of the
Reynolds Averaged Navier-Stokes (RANS) equations for both steady and unsteady
flows. We analyze the effect of different smoothers based on pseudo time
iterations, such as explicit and additive Runge-Kutta (ARK) methods.
Furthermore, we derive the new class of additive W (AW) methods from Rosenbrock
smoothers. This gives rise to two classes of preconditioned smoothers,
preconditioned ARK and additive W (AW), which are implemented the exact same
way, but have different parameters and properties. The new derivation allows to
choose some of these based on results for time integration methods. As
preconditioners, we consider SGS preconditioners based on flux vector splitting
discretizations with a cutoff function for small eigenvalues. We compare these
methods based on a discrete Fourier analysis. Numerical results on pitching and
plunging airfoils identify AW3 as the best smoother regarding overall
efficiency. Specifically, for the NACA 64A010 airfoil steady-state convergence
rates of as low as 0.85 were achieved, or a reduction of 6 orders of magnitude
in approximately 25 pseudo-time iterations. Unsteady convergence rates of as
low as 0.77 were achieved, or a reduction of 11 orders of magnitude in
approximately 70 pseudo-time iterations.
