Parallel Multigrid Reesults for Euler Equations and Grid Partitioning into a Large Number of Blocks

The convergence behaviour of multigrid is investigated for compressible Euler equations discretized on a block-structured grid, partitioned into many blocks. It is found that with one additional boundary relaxation and an extra update of the overlap region multigrid convergence is not much affected by grid partitioning for many splittings investigated. For a splitting into very many blocks (256) with little points per block on the finest level satisfactory convergence can still be obtained with a smaller underrelaxation, but level-independency is impaired without an agglomeration strategy. For defect correction with the second order accurate κ-scheme an overlap of two cells is needed in order to reach the required accuracy. The lift coefficient, the criterium for defect correction convergence, converges almost independent of the number of blocks, with again both additions. Solution times obtained on different parallel computers show a promising performance on IBM SP1.