Acceleration of a Navier-Stokes equation solver for unstructured grids using agglomeration multigrid and parallel processing

Abstract This paper focuses on the parallelization of the agglomeration multigrid technique for the numerical solution of the 2D and 3D Favre-averaged Navier–Stokes equations on unstructured grids. The agglomeration algorithm conforms with the finite-volume discretization scheme and operates independently of the algorithm used to define the concurrently treated subdomains. The computational platform is a cluster of interconnected processors, each of which is associated with one subdomain and requires repetitive communication with the other processors, carried out through the PVM library. Emphasis is laid on (a) the agglomeration strategy, by comparing isotropic and directional agglomeration techniques depending on grid stretching, (b) the discretization schemes for the inviscid fluxes, based on identical edge-wise computations at any multigrid level along with flux limiting techniques, (c) the discretization schemes for the viscous fluxes, for which the triangle- or tetrahedron-based scheme on the fine mesh switches to a computationally less demanding edge-wise scheme on the coarser grids and (d) the modification to the multigrid operators for the one- and two-equation turbulence models. Isolated airfoil, wing and turbomachinery cascade flow problems are used to demonstrate the efficiency of multigrid.

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