2018/09/04 by Matteo Franciolini, Lorenzo Botti, Franciolini, Matteo +5
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Engineering #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Finance #Fluid Dynamics (physics.flu-dyn) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.1809.00866
openalex publication_date 2018/09/04 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
In recent years several research efforts focused on the development of\nhigh-order discontinuous Galerkin (dG) methods for scale resolving simulations\nof turbulent flows. Nevertheless, in the context of incompressible flow\ncomputations, the computational expense of solving large scale equation systems\ncharacterized by indefinite Jacobian matrices has often prevented from dealing\nwith industrially-relevant computations. In this work we seek to improve the\nefficiency of Rosenbrock-type linearly-implicit Runge-Kutta methods by devising\nrobust, scalable and memory-lean solution strategies. In particular, we\nintroduce memory saving p-multigrid preconditioners coupling matrix-free and\nmatrix-based Krylov iterative smoothers. The p-multigrid preconditioner relies\non cheap block-diagonal smoother's preconditioners on the fine space to reduce\nassembly costs and memory allocation, and ensures an adequate resolution of the\ncoarsest space of the multigrid iteration using Additive Schwarz precondioned\nsmoothers to obtain satisfactory convergence rates and optimal parallel\nefficiency of the method. Extensive numerical validation is performed. The\nRosenbrock formulation is applied to test cases of growing complexity: the\nlaminar unsteady flow around a two-dimensional cylinder at Re=200 and around a\nsphere at Re=300, the transitional flow problem of the ERCOFTAC T3L test case\nsuite with different levels of free-stream turbulence. As proof of concept, the\nnumerical solution of the Boeing Rudimentary Landing Gear test case at Re=106\nis reported. A good agreement of the solutions with experimental data is\ndocumented, as well as strong memory savings and execution time gains with\nrespect to state-of-the art solution strategies.\n