A comparison of several implicit residual smoothing methods in combination with multigrid

Abstract

Today, it is a standard technique to accelerate the convergence of explicit multistage time-stepping schemes to steady state using implicit residual smoothing (IRS) together with multigrid. In the past, various IRS methods have been developed. They all artificially extend the stability region of the basic explicit time-stepping scheme and thus they permit higher CFL-numbers. Additionally, residual smoothing strongly effects the damping properties of a scheme which are essential for the robustness and fast convergence of multigrid. The different IRS methods can be divided mainly into two categories. The first one contains smoothers with a centrally weighted form of the implicit operator [1, 31. The second category includes smoothers with an upwind biased form of the operator as developed in [2, 3]. The objective of this paper is to explore the capabilities of different IRS methods in combination with both central [1] as well as upwind [4] spatial discretizations and to compare their efficiency for various 2-D inviscid and viscous flow problems.