On Multigrid Methods for the Compressible Navier-Stokes Equations

Abstract

An investigation of the efficiency of multigrid algorithms for the compressible Navier-Stokes equations is presented. The computational code that forms the basis for this investigation utilises a hybrid Godunov-type method and central differences for discretising the inviscid and viscous fluxes, respectively, as well as implicit-unfactored and explicit solvers. To accelerate the numerical convergence towards a steady state solution we have employed a non-linear multigrid method. Further, we have also implemented a dynamically adaptive multigrid algorithm in conjunction with the explicit solver. Computations have been conducted for low Reynolds number compressible flows around an aerofoil bothat subsonic and supersonic flow conditions. Results from several numerical experiments are presented in order to examine the performance of the multigrid algorithms in conjunction with the explicit and implicit solvers.