1,720,985 research outputs found
P-multigrid preconditioners applied to high-order DG and HDG discretizations
No full textIn this work the use of a p-multigrid preconditioned flexible GMRES solver to deal with the solution of stiff linear systems arising from high order time discretization is explored in the context of two high-order spatial discretizations. The first one is a standard modal discontinuous Galerkin method, while the second one is an hybridizable discontinuous Galerkin method, which for high order has fewer globally-coupled degrees of freedom compared to DG. The efficiency of the proposed solution strategy is assessed on low-Mach, two-dimensional, compressible flow problems. The numerical results highlight that a considerable reduction in the number of GMRES iterations can be achieved for both space discretizations, but that only with DG is this gain reflected in the CPU time. Moreover, a comparison of the performance shed light on the convenience of using the former or the latter space discretization
Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations
Full text linkThis work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of HDG, applied to the implicit solution of unsteady compressible flows. The matrix-free implementation allows for a reduction of the memory footprint of the solver when dealing with implicit time-accurate discretizations. HDG reduces the number of globally-coupled degrees of freedom relative to DG, at high order, by statically condensing element-interior degrees of freedom from the system in favor of face unknowns. The primal formulation further reduces the element-interior degrees of freedom by eliminating the gradient as a separate unknown. This paper introduces a p-multigrid preconditioner implementation for these discretizations and presents results for various flow problems. Benefits of the p-multigrid strategy relative to simpler, less expensive, preconditioners are observed for stiff systems, such as those arising from low-Mach number flows at high-order approximation. The p-multigrid preconditioner also shows excellent scalability for parallel computations. Additional savings in both speed and memory occur with a matrix-free/reduced version of the preconditioner
High-order DG solutions of separating and reattaching flows
No full textWe report high-order implicit Large Eddy Simulations of flows around elongated bluff bodies with massive flow separation and reattachment. The aim is to provide evidence of the influence of relevant flow parameters such as the geometry of the leading-edge corners and the presence or not of a trailing-edge flow separation, on the behaviour of the initially laminar recirculating flow. Attention will be devoted also on the possible repercussions of such a results on the understanding of the nature of the main unsteadinesses of separating and reattaching flows. We finally prove the computational efficiency and the reliability of the proposed solution strategy for the time implicit high-order Discontinuous Galerkin (DG) discretization of the three-dimensional incompressible Navier-Stokes equations. The algorithm uses a linearly implicit Runge-Kutta scheme of the Rosenbrock type, and a p-multigrid preconditioned matrix-free linear solver
An implicit discontinuous galerkin method with reduced memory footprint for the simulation of turbulent flows
No full textOn the kinematics and dynamics parameters governing the flow in oscillating foils
Full text linkBased on a high-order implicit discontinuous Galerkin method, numerical simulations of a two-dimensional oscillating foil are performed to explore the origin of basic aspects of the flow such as the generation of interesting flow structures in the wake and the associated aerodynamic forces. Dimensional arguments suggest that the flow is characterized by non dimensional aerodynamic coefficients depending on the kinematics of the oscillation, such its frequency and amplitude, and on the dynamics of the flow, such as the Reynolds number. Most of the studies have concentrated their attention on the role played by the kinematic of the oscillation with less or no attention to the effect of the Reynolds number. Here, we show that this effect cannot be neglected in the study of the phenomena at the basis of the generation of lift and thrust. We found that the Reynolds number plays a fundamental role for the development of thrust by defining critical values Rec for the switch from drag to thrust conditions. It is also shown that for Re>Rec, the Reynolds number defines additional subcritical values which are at the basis of flow instabilities leading to smooth and sharp transitions of the structure of the wake and of the related aerodynamic forces. For the analysis of the behaviour of the flow, the space of phases composed by the instantaneous lift and thrust (cL,cT) is introduced. It is shown how the orbits in the (cL,cT)-space allow us for a clear understanding of the physical evolution of the flow system and of the cyclical phenomena composing it
OpenMP Parallelization Strategies for a Discontinuous Galerkin Solver
No full textThis paper aims to report on the open multi-processing (OpenMP) parallel implementation of a fully unstructured high-order discontinuous Galerkin (DG) solver for computational fluid dynamics and computational aeroacoustics applications. Even if the use of OpenMP paradigm is confined to shared memory systems, it has some advantages over the use of the message passing interface (MPI) library, and getting the best of this approach potentially improves the parallel efficiency of codes running on clusters of multi-core nodes. While with MPI the use of a domain decomposition algorithm is almost unavoidable, the OpenMP shared memory context offers several opportunities. Three strategies, here optimised for a DG solver, are presented and compared: the first refers to a customization of a colouring approach, the second mimics an MPI implementation in the OpenMP context, while the third method is somehow half way between the previous two. The numerical tests performed on both inviscid and viscous test cases indicate that, thanks to the compactness of the DG discretization, all the code versions perform quite satisfactory. In particular, the domain decomposition algorithm reaches the highest level of parallel efficiency at low computational loads while the colouring approach excels at larger computational loads and it can be easily implemented within an existing MPI code. Moreover, colouring is very well suited to deal with hardware accelerators, an opportunity given by the OpenMP 4.0 standard. Finally, the performance gain observed in using a hybrid MPI/OpenMP version of the DG code on high performance computing facilities is demonstrated
p-Multigrid matrix-free discontinuous Galerkin solution strategies for the under-resolved simulation of incompressible turbulent flows
Full text linkIn 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 the simulation of 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 introduce memory saving p-multigrid preconditioners coupling matrix-free and matrix-based Krylov iterative smoothers. The p-multigrid preconditioner relies on cheap element-wise block-diagonal smoothers on the fine space to reduce assembly costs and memory allocation, and ensures an adequate resolution of the coarsest space of the multigrid iteration using Additive Schwarz smoothers to obtain satisfactory convergence rates and optimal parallel efficiency of the method. In addition, the use of specifically crafted rescaled-inherited coarse operators to overcome the excess of stabilization provided by the standard inheritance of the fine space operators is explored. Extensive numerical validation is performed. The Rosenbrock formulation is 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, the transitional flow problem of the ERCOFTAC T3L test case suite with different levels of free-stream turbulence. As proof of concept, the numerical solution of the Boeing rudimentary landing gear test case at Re=106 is reported. A good agreement of the solutions with experimental data is documented, whereas a reduction in memory footprint of about 92% and an execution time gain of up to 3.5 is reported with respect to state-of-the-art solution strategies
h-p-hp-Multilevel discontinuous Galerkin solution strategies for elliptic operators
No full textIn this work, we investigate the performance of {h−p−hp}-multilevel preconditioners for discontinuous Galerkin (dG) discretisations of elliptic operators with constant coefficients. Recent publications targeting multilevel solution strategies for incompressible fluid flow computations demonstrated that dG discretisation of viscous terms require ad hoc inherited multilevel preconditioners. Accordingly, we consider elliptic operators discretised by means of the BR2 dG method introduced by Bassi and Rebay and we compare agglomeration-based hp-coarsening with previously introduced {h−p}
-multilevel strategies. The numerical results show that, when the polynomial degree is sufficiently high and the mesh is sufficiently dense, the hp-multilevel preconditioner can be fruitfully exploited
Numerical experiments in separating and reattaching flows
Full text linkWe report high-order implicit large Eddy simulations of flows around flat plates with massive flow separation and reattachment. The aim is to provide evidence of the influence of relevant flow parameters such as the geometry of the leading-edge corner, the presence of a trailing-edge flow separation, and of a flow coupling between the two sides of the plate. The results reveal that flows with right-angled corners develop taller flow recirculations, which promote very-slow instability of the bubble itself. This large-scale unsteadiness is then found to be the basis of negative turbulence production mechanisms that in turn enhance the height of the bubble itself, thus closing a self-sustained cycle. The absence of these phenomena in flows with smooth leading-edge corners is also found to explain their high sensitivity to free-stream turbulence. The observed behaviors may have strong repercussions for theories and closures of separating and reattaching flows and should be carefully taken into account in control strategies used in the applications
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