Development and Application of Parallel Agglomerated Multigrid Methods for Complex Geometries

We report further progress in the development of agglomerated multigrid techniques for fully unstructured grids in three dimensions. Following the previous studies that identified key elements to grid-independent multigrid convergence for a model equation, and that demonstrated impressive speed-up in single-processor computations for a model diffusion equation, inviscid flows, and Reynolds-averaged Navier-Stokes (RANS) simulations for realistic geometries, we now present a parallelized agglomerated multigrid technique for 3D complex geometries. We demonstrate a robust parallel fully-coarsened agglomerated multigrid technique for the Euler, the Navier-Stokes, and the RANS equations for 3D complex geometries, incorporating the following key developments: consistent and stable coarse-grid discretizations, a hierarchical agglomeration scheme, and line-agglomeration/relaxation using prismatic-cell discretizations in the highly-stretched grid regions. A significant speed-up in computer time over state-of-art large-scale computations is demonstrated for RANS simulations over 3D realistic geometries.