다중격자 Navier-Stokes 해석을 위한 내재적 예조건화 기법의 수렴특성 해석

Abstract

In this paper, characteristics of the preconditioned multistage time stepping methods which are the well known multigrid smoothers are investigated and Fourier analysis of the preconditioned residual operators is performed for popular implicit preconditioners and upwind-biased residual operators. The damping characteristics of implicit preconditioners such as the point-Jacobi, line-Jacobi, DDADI, AF-ADI preconditioners and three upwind-biased residual operators are compared using the Fourier footprints and the convex hulls. The implicit preconditioners and residual operators which have good damping characteristic are suggested for the preconditioned multistage time stepping in the Navier-Stokes calculations with multigrid methods.