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

• Published in: Computing and visualization in science Vol. 11; no. 1; pp. 27 - 40
• Main Authors: Larson, Gregory, Snyder, Deryl, Abeele, David Vanden, Clees, Tanja
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 2008; Springer
• Subjects: Algorithms; Applied sciences; Calculus of Variations and Optimal Control; Optimization; Computational Mathematics and Numerical Analysis; Computational techniques; Computer Applications in Chemistry; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Mathematical methods in physics; Mathematics; Mathematics and Statistics; Memory and file management (including protection and security); Memory organisation. Data processing; Numerical Analysis; Physics; Regular Article; Software; Visualization; Memory Usage; Large Eddy Simulation; Multigrid Method; Circular Cylinder; Direct Numerical Simulation; Turbulent flow; Calculator cluster; Sparse matrices; Aggregation; Distributed memory; Direct method; Low Reynolds number; Flow simulation; Multigrid; Size effect; Modelling; Computer networks; Iterative methods; Mesh generation; Unstructured mesh; LU factorization; Unsteady flow; Distributed system; Incompressible flow; Anisotropy; Memory management; Circular cylinder; Incompressible fluid; Preconditioning; Parallelization
• ISSN: 1432-9360; 1433-0369
• DOI: 10.1007/s00791-006-0055-4

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 multigrid 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.