A multigrid scheme for the implicit solution of the compressible flow equations

Abstract

A multigrid scheme has been developed for the acceleration of the solution of compressible inviscid and viscous flow problems. A higher order accurate upwind conservative finite volume scheme has been used for the discretization of the Euler and the Reynolds-Averaged Navier-Stokes equations. For the multigrid implementation, the “alternative point of view” of the Full Approximation scheme has been employed together with a conservative restriction operator to maintain the fine grid accuracy. The present multigrid scheme has been designed to take full advantage of the implicit unfactored solution scheme of the single grid code by introducing an alternative multigrid V-cycle. The proposed method attains up to 25-fold acceleration with respect to the single grid solution for moderate size grids. Moreover, the results demonstrate that the computational time increases proportional to the number of volumes when global refinements are applied so, the present multigrid scheme is very favorable for large scale computations.