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Towards Efficient and Scalable Discontinuous Galerkin Methods for Unsteady Flows
Get PDFNegli ultimi anni, la crescente disponibilit`a di risorse computazionali ha contribuito alla diffusione della fluidodinamica computazionale per la ricerca e per la progettazione industriale. Uno degli approcci pi promettenti si basa sul metodo agli elementi finiti discontinui di Galerkin (dG).
Nell’ambito di queste metodologie, il contributo della tesi e' triplice. Innanzi- tutto, il lavoro introduce un algoritmo di parallelizzazione ibrida MPI/OpenMP per l’utilizzo efficiente di risorse di super calcolo. In secondo luogo, propone strategie di soluzione efficienti, scalabili e con limitata allocazione di memoria per la soluzione di problemi complessi. Infine, confronta le strategie di soluzione introdotte con nuove tecniche di discretizzazione dette “ibridizzabili”, su problemi riguardanti la soluzione delle equazioni di Navier–Stokes non stazionarie.
L’efficienza computazionale e' stata valutata su casi di crescente complessita' riguardanti la simulazione della turbolenza. In primo luogo, e' stata considerata la convezione naturale di Rayleigh-Benard e il flusso turbolento in un canale a numeri di Reynolds moderatamente alti. Le strategie di soluzione proposte sono risultate fino a cinque volte piu` veloci rispetto ai metodi standard allocando solamente il 7% della memoria. In secondo luogo, e' stato analizzato il flusso attorno ad una piastra piana con bordo arrotondato sottoposta a diversi livelli di turbolenza in ingresso. Nonostante la maggiore complessità' dovuta all’uso di elementi curvi ed anisotropi, l’algoritmo proposto e' risultato oltre tre volte piu` veloce allocando il 15% della memoria rispetto ad un metodo standard. Concludendo, viene riportata la simulazione del “Boeing Rudimentary Landing Gear” a Re = 10^6. In tutti i casi i risultati ottenuti sono in ottimo accordo con i dati sperimentali e con precedenti simulazioni numeriche pubblicate in letteratura.In recent years the increasing availability of High Performance Computing (HPC) resources strongly promoted the widespread of high fidelity simulations, such as the Large Eddy Simulation (LES), for industrial research and design. One of the most promising approaches to those kind of simulations is based on the discontinuous Galerkin (dG) discretization method.
The contribution of the thesis towards this research area is three-fold. First, the work introduces an efficient hybrid MPI/OpenMP parallelisation paradigm to fruitfully exploit large HPC facilities. Second, it reports efficient, scalable and memory saving solution strategies for stiff dG discretisations. Third, it compares those solution strategies, for the first time using the same numerical framework, to hybridizable discontinuous Galerkin (HDG) methods, including a novel implementation of a p-multigrid preconditioning approach, on unsteady flow problems involving the solution of the NavierStokes equations.
The improvements in computational efficiency have been evaluated on cases of growing complexity involving large eddy simulations of turbulent flows. First, the Rayleigh-Benard convection problem and the turbulent channel flow at moderately high Reynolds numbers is presented. The solution strategies proposed resulted up to five times faster than standard matrix-based methods while al- locating the 7% of the memory. A second family of test cases involve the LES simulation of a rounded leading edge flat plate under different levels of free-stream turbulence. Although the increased stiffness of the iteration matrix due to the use of curved and stretched elements, the solver resulted more than three times faster while allocating the 15% of the memory if compared to standard methods. Finally, the large eddy simulation of the Boeing Rudimentary Landing Gear at Re = 10^6 is reported. In all the cases, a remarkable agreement with experimental data as well as previous numerical simulations is documented
Parallel Computing is Everywhere
No full textThe paper deals with the OpenMP parallel implementation of a high-order Discontinuous Galerkin solver for computational fluid dynamics (CFD) and computational aeroacoustics (CAA) applications. The use of the shared memory view of the OpenMP paradigm is here explored through three different parallel implementation strategies. The numerical experiments on 2D and 3D test cases, which consider the effects of different platforms, compilers and space discretizations, indicate that all the code versions perform quite satisfactory. In particular, the OpenMP domain decomposition algorithm reaches the highest level of parallel efficiency at low computational loads, while a colouring approach excels for the largest simulations. The performance gain observed in using a hybrid MPI/OpenMP version of the DG code on large HPC facilities will be demonstrated
Dataset for Fast Identification of Transonic Buffet Envelope using Computational Fluid Dynamics
No full textSupplementary material for "Fast Identification of Transonic Buffet Envelope using Computational Fluid Dynamics" by Drofelnik et al. published in Aircraft Engineering and Aerospace Technology.</span
Fast identification of transonic buffet envelope using computational fluid dynamics
No full textPurpose – The paper presented a numerical method based on computational fluid dynamics that allows investigating the buffet envelope of reference equivalent wings at the equivalent cost of several two-dimensional, unsteady, turbulent flow analyses. The method bridges the gap between semi-empirical relations, generally dominant in the early phases of aircraft design, and three-dimensional turbulent flow analyses, characterised by high costs in analysis setups and prohibitive computing times.Design/methodology/approach – Accuracy in the predictions and efficiency in the solution are two key aspects. Accuracy is maintained by solving a specialised form of the Reynolds–averaged Navier–Stokes equations valid for infinite-swept wing flows. Efficiency of the solution is reached by a novel implementation of the flow solver, as well as by combining solutions of different fidelity spatially.Findings – Discovering the buffet envelope of a set of reference equivalent wings is accompanied with an estimate of the uncertainties in the numerical predictions. Just over 2,000 CPU hours are needed if it is admissible to deal with an uncertainty of ±1.0 deg in the angle of attack at which buffet onset/offset occurs. Halving the uncertainty requires significantly more computing resources, close to a factor 200 compared with the larger uncertainty case.Practical implications – To permit the use of the proposed method as a practical design tool in the conceptual/preliminary aircraft design phases, the method offers the designer with the ability to gauge the sensitivity of buffet on primary design variables, such as wing sweep angle and chord to thickness ratio.Originality/value – The infinite-swept wing, unsteady Reynolds–averaged Navier–Stokes equations have been successfully applied, for the first time, to identify buffeting conditions. This demonstrates the adequateness of the proposed method in the conceptual/preliminary aircraft design phases
On the efficiency of a matrix-free linearly implicit time integration strategy for high-order Discontinuous Galerkin solutions of incompressible turbulent flows
No full textExtension of analytical indicial aerodynamics to generic trapezoidal wings in subsonic flow
No full textAnalytical indicial aerodynamic functions are calculated for a number of trapezoidal wings in subsonic flow, with Mach number 0.3 ≤ Ma ≤ 0.7. The formulation herein proposed extends well-known aerodynamic theories, which are limited to thin aerofoils in incompressible flow, to generic trapezoidal wing planforms. First, a thorough study is executed to assess the accuracy and limitation of analytical predictions, using unsteady results from two state of the art computational fluid dynamics solvers as cross validated benchmark. Indicial functions are calculated for a step change in angle of attack and for a sharp edge gust, each for four wing configurations and three Mach numbers. Then, analytical and computational indicial responses are used to predict dynamic derivatives and the maximum lift coefficient following the encounter with a one-minus-cosine gust. It is found that the analytical results are in excellent agreement with the computational results for all test cases. In particular, the deviation of the analytical results from the computational results is within the scatter or uncertainty in the data arising from using two computational fluid dynamics solvers. This indicates the usefulness of the developed analytical theories
Adaptive design of experiments for efficient and accurate estimation of aerodynamic loads
No full textAerodynamic design, which aims at developing the outer shape of the aircraft while meeting several contrasting requirements, demands an accurate and reliable aerodynamic database. Computing forces and moments with the highest level of ?fidelity is a prerequisite, but practically limited by wall clock time and available computing resources. An e?fficient and robust approach is therefore sought after. This study investigates two design of experiments algorithms in combination with surrogate modelling. In traditional design of experiments, the samples are selected a priori before running the numerical explorative campaign. It is well-?known that this may result in either poor prediction capabilities or high computational costs. The second strategy employs an adaptive design of experiments algorithm. As opposed to the former, this is a self?-learning technique that iteratively: i) identi?fies the regions of the design space that are characterised by stronger non?linearities; and ii) select the new samples in order to maximise the information contentassociated with the simulations to be performed during the next iteration. In this work, the Reynolds?-averaged Navier-?Stokes equations are solved around a complete aircraft confi?guration. A representative ?flight envelope is created taking the angle of attack and Mach number as design parameters. The adaptive strategy is found to perform better than the traditional counterpart. This is quantifi?ed in terms of the sum of the squared error between the surrogate model predictions and CFD results. For the pitch moment coe?fficient, which shows strong non?linearities, the error metric using the adaptive strategy is reduced by about one order of magnitude compared to the traditional approach. Furthermore, the proposed adaptive methodology, which is employed on a high performance computing facility, requires no extra costs or complications than a traditional methodolog
HYBRID OPENMP/MPI PARALLELIZATION OF A HIGH–ORDER DISCONTINUOUS GALERKIN CFD/CAA SOLVER
No full textThis paper describes the implementation of an hybrid OpenMP/MPI parallelization
strategy in a Discontinuous Galerkin solver used for DNS and LES or CAA computations, to
fruitfully exploit the modern massively parallel HPC facilities. It is usually believed that the
sheared memory view of OpenMP can easily increase the parallel efficiency of codes dealing
with multi–core clusters. The idea consists of running calculations on those machines restricting
as much as possible the use of the MPI library to the communications between nodes and
exploiting the shared memory paradigm within a node. However, in practice, the achievement
of a real parallel performance gain is not straightforward. Moreover, as far as DG solvers are
concerned, almost nothing is reported in the current literature about the hybrid MPI/OpenMP
implementation. In this work a colouring algorithm has been employed for OpenMP. The resulting
hybrid strategy performs quite satisfactory, since generally it is more efficient of the pure
MPI implementation. However, the performances are heavily dependent on hardware platforms,
as well as on computational details such as the polynomial order of space discretization or the
number of computational elements. Several scalability tests have been performed, resulting in
the conclusion that the best performance can be achieved only with a proper choice of the number
of MPI partition and OpenMP threads to be used within a single node. The reliability of
the method was here assessed by solving the Taylor Green vortex problem at Reynolds numbers
equal to 800 and 1600 and the Linear Euler acustic scattering from a rigid sphere
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