Agglomeration Multigrid and Parallel Processing for the Numerical Solution of the Euler Equations on 2d and 3d Unstructured Grids

Abstract. This paper aims at coupling two known CFD techniques, namely multigrid and parallelization, in an existing Euler equations solver for 2D and 3D unstructured grids. The solver is based on a time-marching formulation for the high-subsonic/transonic flow equations and a pointwise implicit solution algorithm. The gain from the combined use of multigrid and parallelization is the reduction of both CPU cost and elapsed computational time associated with the use of the aforementioned software. Multigrid is employed using a finitevolume agglomeration algorithm without explicitly defining coarser grids, the latter being a common practice in structured grids’ multigrid. Parallelization relies on the concurrent processing of grid subsets on a cluster of networked processors. The unstructured grid is partitioned through a genetic algorithm based tool which yields equal load per processor and minimal inter-processor communication of data during the iterative scheme. The computational gain is demonstrated in two problems, for which the quality of the numerical solutions has been assessed in previous publications. These problems are: the study of the quasi-3D flow in a controlled diffusion compressor cascade, meshed using triangular elements, and that of the 3D flow around an aircraft wing, meshed using tetrahedral elements.