Towards optimal Runge-Kutta smoothers for multigrid methods for unsteady flow problems

We consider Runge-Kutta smoothers in a dual time stepping multigrid method for unsteady flow problems. These smoothers are easily parallelizable and Jacobian-free, making them very attractive for 3D calculations. Existing methods have been designed for steady flows, leading to slow convergence for unsteady problems. Here we determine the free parameters of the smoother to provide optimal damping for high frequency components for the unsteady linear advection equation. This is compared with an RK smoother designed for steady state problems, as commonly used in CFD codes. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)