Analysis of a RK/implicit smoother for multigrid

Abstract

The steady-state compressible Navier - Stokes equations are solved with a finite-volume, second-order accurate scheme. The equations are solved with a multigrid algorithm that uses a 3-stage Runge - Kutta scheme with an implicit preconditioner as a smoother. We analyze this smoother in which the implicit system is approximately inverted by a few symmetric Gauss - Seidel relaxation sweeps. The analysis for the linear system determines the Fourier spectrum of the multigrid smoother. Improved performance of the algorithm based on the analysis is demonstrated by computing laminar flow in a rocket motor and turbulent flow over a wing. © 2011 Springer-Verlag Berlin Heidelberg.