Multigrid acceleration of a block structured compressible flow solver

Abstract

We study a multiblock method for compressible turbulent flow simulations and present results obtained from calculations on a two-element airfoil. A cell-vertex or vertex-based spatial discretization method and explicit multistage Runge-Kutta time stepping are used. The vertex-based method is found to give better results than the cell-vertex method. In the latter method a larger amount of artificial dissipation is required since different control volumes are used for the discretization of the viscous and convective fluxes. The slow convergence of the time stepping method makes a multigrid acceleration technique indispensable. This technique leads to an acceleration by about a factor of 10. The numerical predictions are in good agreement with experimental results. It is shown that the convergence of the multigrid process depends considerably on the ordering of the various loops. If the block loop is put inside the stage loop the process converges more rapidly than if the block loop is situated outside the stage loop in case a three-stage Runge-Kutta method is used. If a five-stage scheme is adopted the process does not converge in the latter block ordering. Finally, the process based on the five-stage scheme is about 60% more efficient than with the three-stage scheme, if the block loop is inside the stage loop.