Chapter

Performance Improvements for Large-Scale Simulations using the Discontinuous Galerkin Framework FLEXI

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Abstract

Large-scale simulations pose significant challenges not only to the solver itself but also to the pre- and postprocessing framework. Hence, we present generally applicable improvements to enhance the performance of those tools and thus increase the feasibility of large-scale jobs and convergence studies. To accomplish this, we use a shared memory approach implemented in the Message Passing Interface (MPI) libraries. Additionally, we improve the read and write performance of the flow solver during runtime to minimize the load imposed on the file system. A detailed discussion of the current performance and scaling behavior is given for up to 262144 processes. FLEXI shows excellent scalability for all tested features. We conclude by showing selected applications, where we use the introduced improvements to maximize performance.

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... 3.4) restricts the presented multiphase framework to Cartesian grids, it internally still operates on an unstructured grid representation. The grid representation and the associated parallelization concept inherit from the work by [30] and are optimized towards massively parallelized computations, as shown in [4,39]. ...
... Computations with the previous code framework, published by Jöns et al. [35], applied a constant number of DOFs per element. To demonstrate the efficiency of the novel adaptive scheme, we compare the adaptive computation with N ∈ [2,4] and N FV = 9 against non-adaptive computations with N = 4 and N FV = 5. Table 5 lists the average number of DOFs and the computation time for all setups. ...
... Pressure distribution along the symmetry line x 2 = 0 of the shock-droplet interaction without cavity and We = 1000 at t * = 0.8. The results are compared against the data from Xiang and Wang[24] Table 5 Efficiency comparison of the non-adaptive discretization (setups 1 and 2) with the proposed adaptive scheme (Temperature field (top) and bulk discretization (bottom) of the 2D shock-droplet interaction with We = 1000 at t * = 11.8, comparing a static scheme with N = 4 and N FV = 5 (left, middle) to the proposed adaptive scheme with N ∈[2,4] and N FV = 9 (right). The element-local degree N is indicated by color, whereas FV sub-cell elements are marked in gray (Color figure online)Fig. ...
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... While the WENO scheme discretizing the Hamilton-Jacobi equations (section 3.4) restricts the presented multiphase framework to Cartesian grids, it internally still operates on an unstructured grid representation. The grid representation and the associated parallelization concept inherit from the work by [29] and are optimized towards massively parallelized computations, as shown in [37,4]. The parallelization concept exploits that the DG operator can be split into two building blocks, cf. ...
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... Temperature field (top) and bulk discretization (bottom) of the 2D shockdroplet interaction with We = 1000 at t * = 11.8, comparing a static scheme with N = 4 and N FV = 5 (left, middle) to the proposed adaptive scheme with N ∈[2,4] and N FV = 9 (right). The element-local degree N is indicated by color, whereas FV sub-cell elements are marked in gray. ...
... To do so, we conduct experiments in the trisonic wind tunnel at the RWTH Aachen University and use these results to validate wall-resolved large eddy simulation (WLRES) ran with the high-order accurate discontinuous Galerkin spectral element method (DGSEM) framework FLEXI, developed at the University of Stuttgart. The framework FLEXI has been applied to many LES applications in recent years including aero-acoustic simulations and has recently been further developed to account for efficient large eddy simulation [1,2]. ...
... This specific polynomial degree was chosen in order to utilize the strengths of a high order scheme, while still providing good domain decomposition capabilities by only having 512 DOFs per element. FLEXI has shown to work most efficient by using 3600 DOF per process and thus approximately 7 elements are contained in one decomposed domain [1]. We evaluate the polynomials at the Legendre-Gauss-Lobatto pointset in order to use kinetic energy preserving split form fluxes according to Pirozzoli [4]. ...
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Conference Paper
Shock wave/turbulent boundary-layer interaction and flow separation may induce self-sustained large-scale oscillations on a profile at transonic Mach number. This phenomenon, known as transonic buffet, is at the origin of intense pressure fluctuations which can have detrimental effects, both in external and internal aerodynamics. The present paper describes a new experiment executed in the ONERA S3Ch transonic wind tunnel on shock oscillations over the OAT15A supercritical profile. These experiments have allowed the precise definition of the conditions for buffet onset and the characterization of the properties of the periodic motion from unsteady surface pressure measurements. The flowfield behavior has been described in great detail thanks to high-speed schlieren cinematography and surveys with a two-component laser Doppler velocimetry along with a conditional sampling technique. The first aim of this study was to provide the computational fluid dynamics community with well-documented test cases to validate advanced computing methods. Concerning the physics of the phenomenon, it is suggested that it is mediated by acoustic waves which are produced at the trailing edge and which travel on the two sides of the airfoil. Also, the experimental results strongly suggest that the phenomenon is essentially two-dimensional, even if three-dimensional effects are also detected.
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A zonal detached eddy simulation (DES) method is presented that predicts the buffet phenomenon on a supercritical airfoil at conditions very near shock buffet onset. Some issues concerning grid generation, as well as the use of DES for thin-layer separation, are discussed. The periodic motion of the shock is well reproduced by averaged Navier-Stokes equations (URANS) and zonal DES, but the URANS calculation has needed to increase the angle of attack compared to the experimental value and the standard DES failed to reproduce the self-sustained motion in the present calculation. The main features, including spectral analysis, compare favorably with experimental measurements (Jacquin, L., Molton, P., Deck, S., Maury, B., and Soulevant, D., "An Experimental Study of Shock Oscillation over a Transonic Supercritical Profile," AIAA Paper 2005-4902, June 2005). A very simple model based on propagation velocities yields the main frequency of the motion. As suggested by Lee (Lee, B. H. K., "Transonic Buffet on a Supercritical Airfoil," Aeronautical Journal, May 1990, pp. 143-152), this calculation highlights that upstream propagating waves are generated by the impingment of large-scale structures on the upper surface of the airfoil in the vicinity of the trailing edge. These upstream propagating waves can regenerate an instability leading to a feedback mechanism.
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This paper deals with a high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier–Stokes equations. We extend a discontinuous finite element discretization originally considered for hyperbolic systems such as the Euler equations to the case of the Navier–Stokes equations by treating the viscous terms with a mixed formulation. The method combines two key ideas which are at the basis of the finite volume and of the finite element method, the physics of wave propagation being accounted for by means of Riemann problems and accuracy being obtained by means of high-order polynomial approximations within elements. As a consequence the method is ideally suited to compute high-order accurate solution of the Navier–Stokes equations on unstructured grids. The performance of the proposed method is illustrated by computing the compressible viscous flow on a flat plate and around a NACA0012 airfoil for several flow regimes using constant, linear, quadratic, and cubic elements.
A novel turbulent inflow method for zonal large eddy simulations with a discontinuous Galerkin solver
  • T Kuhn
  • D Kempf
  • A Beck
  • C.-D Munz