p-Multigrid matrix-free discontinuous Galerkin solution strategies for the under-resolved simulation of incompressible turbulent flows
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In recent years several research efforts focused on the development of high-order discontinuous Galerkin (dG) methods for scale resolving simulations of turbulent flows. Nevertheless, in the context of incompressible flow computations, the computational expense of solving large scale equation systems characterized by indefinite Jacobian matrices has often prevented from dealing with industrially-relevant computations. In this work we seek to improve the efficiency of Rosenbrock-type linearly-implicit Runge-Kutta methods by devising robust, scalable and memory-lean solution strategies. In particular, we combined p-multigrid preconditioners with matrix-free Krylov iterative solvers: the p-multigrid preconditioner relies on specifically crafted rescaled-inherited coarse operators and cheap block-diagonal smoother's preconditioners to obtain satisfactory convergence rates and a low memory occupation. Extensive numerical validation is performed. The rescaled-inherited p-multigrid algorithm for the BR2 dG discretization is firstly validated solving Poisson problems. The Rosenbrock formulation is then applied to test cases of growing complexity: the laminar unsteady flow around a two-dimensional cylinder at Re=200 and around a sphere at Re=300, and finally the transitional T3L1 flow problem of the ERCOFTAC test case suite with different levels of free-stream turbulence. For the latter good agreement with experimental data is documented, moreover, strong memory savings and execution time gains with respect to state-of-the art preconditioners are reported.
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