Application of single-level, pointwise algebraic, and smoothed aggregation multigrid methods to direct numerical simulations of incompressible turbulent flows

摘要

Single- and multi-level iterative methods for sparse linear systems are applied to unsteady flow simulations via implementation into a direct numerical simulation solver for incompressible turbulent flows on unstructured meshes. The performance of these solution methods, implemented in the well-established SAMG and ML packages, are quantified in terms of computational speed and memory consumption, with a direct sparse LU solver (SuperLU) used as a reference. The classical test case of unsteady flow over a circular cylinder at low Reynolds numbers is considered, employing a series of increasingly fine anisotropic meshes. As expected, the memory consumption increases dramatically with the considered problem size for the direct solver. Surprisingly, however, the computation times remain reasonable. The speed and memory usage of pointwise algebraic and smoothed aggregation multi-grid solvers are found to exhibit near-linear scaling. As an alternative to multi-level solvers, a single-level ILUT-preconditioned GMRES solver with low drop tolerance is also considered. This solver is found to perform sufficiently well only on small meshes. Even then, it is outperformed by pointwise algebraic multigrid on all counts. Finally, the effectiveness of pointwise algebraic multigrid is illustrated by considering a large three-dimensional direct numerical simulation case using a novel parallelization approach on a large distributed memory computing cluster.