Increasing the Flexibility of the High Order Discontinuous Galerkin Framework FLEXI Towards Large Scale Industrial Applications

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High Performance Computing in Science and Engineering '20

Abstract

This paper summarizes our progress in the application and improvement of a high order discontinuous Galerkin (DG) method for scale resolving fluid dynamics simulations towards robust and flexible industrial applications. We report the results obtained on the Cray XC40 Hazel Hen cluster at HLRS and show code performance. We present three application cases and developments: An implicit time integration scheme for split-form DG schemes allows us to solve stiff problems with increased efficiency, which will open up new classes of problems for simulations with FLEXI. We follow this by discussing a Large Eddy Simulation (LES) of a compressible turbulent boundary layer and provide comparison to DNS data. Lastly, we demonstrate how to extend the high order scheme with a consistent and conservative sliding mesh interface, and present results of a 1.5 stage turbine simulation with wall-resolved LES.

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References

  1. M. Atak, A. Beck, T. Bolemann, D. Flad, H. Frank, F. Hindenlang, C.-D. Munz, Discontinuous Galerkin for high performance computational fluid dynamics, in High Performance Computing in Science and Engineering 2014 (Springer International Publishing, 2015), pp. 499–518

    Google Scholar 

  2. A. Beck, T. Bolemann, D. Flad, H. Frank, N. Krais, K. Kukuschkin, M. Sonntag, C.-D. Munz, Application and development of the high order discontinuous Galerkin spectral element method for compressible multiscale flows, in High Performance Computing in Science and Engineering’17 (Springer, 2018), pp. 387–407

    Google Scholar 

  3. A. Beck, P. Ortwein, P. Kopper, N. Krais, D. Kempf, C. Koch, Towards high-fidelity erosion prediction: on time-accurate particle tracking in turbomachinery. Int. J. Heat Fluid Flow 79, 108457 (2019)

    Article  Google Scholar 

  4. A.D. Beck, T. Bolemann, D. Flad, H. Frank, G.J. Gassner, F. Hindenlang, C.-D. Munz, High-order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations. Int. J. Numer. Meth. Fluids 76(8), 522–548 (2014)

    Article  MathSciNet  Google Scholar 

  5. A.D. Beck, T. Bolemann, D. Flad, N. Krais, J. Zeifang, C.-D. Munz, Application and development of the high order discontinuous Galerkin spectral element method for compressible multiscale flows, in High Performance Computing in Science and Engineering’18 (Springer, 2019), pp. 291–307

    Google Scholar 

  6. A.D. Beck, G.J. Gassner, T. Bolemann, H. Frank, F. Hindenlang, C.-D. Munz, Underresolved turbulence simulations with stabilized high order discontinuous Galerkin methods, in Direct and Large-Eddy Simulation IX (Springer, 2015), pp. 103–108

    Google Scholar 

  7. S. Bocquet, P. Sagaut, J. Jouhaud, A compressible wall model for large-eddy simulation with application to prediction of aerothermal quantities. Phys. Fluids 24(6), 065103 (2012)

    Article  Google Scholar 

  8. M.H. Carpenter, C.A. Kennedy, Fourth-order 2N-storage Runge-Kutta schemes, NASA TM-109112 (National Aeronautics and Space Administration, Langley Research Center, Hampton, VA, 1994)

    Google Scholar 

  9. H.M. Frank, C.-D. Munz, Large eddy simulation of tonal noise at a side-view mirror using a high order discontinuous Galerkin method, in 22nd AIAA/CEAS Aeroacoustics Conference, pp. 2847 (2016)

    Google Scholar 

  10. H. Gallus, Ercoftac test case 6: axial flow turbine stage, in Seminar and Workshop on 3D Turbomachinery Flow Prediction III, Les Arcs, France (1995)

    Google Scholar 

  11. G.J. Gassner, A.R. Winters, D.A. Kopriva, Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations. J. Comput. Phys. 327, 39–66 (2016)

    Article  MathSciNet  Google Scholar 

  12. F. Haselbach, H.-P. Schiffer, M. Horsman, S. Dressen, N. Harvey, S. Read, The application of ultra high lift blading in the BR715 LP turbine. J. Turbomach. 124(1), 45–51 (2001)

    Article  Google Scholar 

  13. F. Hindenlang, G. Gassner, C. Altmann, A. Beck, M. Staudenmaier, C.-D. Munz, Explicit discontinuous Galerkin methods for unsteady problems. Comput. Fluids 61, 86–93 (2012)

    Article  MathSciNet  Google Scholar 

  14. C.W. Hirt, A.A. Amsden, J. Cook, An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14(3), 227–253 (1974)

    Article  Google Scholar 

  15. C.A. Kennedy, M.H. Carpenter, Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Appl. Numer. Math. 44, 139–181 (2003)

    Article  MathSciNet  Google Scholar 

  16. D.A. Knoll, D.E. Keyes, Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193, 357–397 (2004)

    Article  MathSciNet  Google Scholar 

  17. N. Krais, A. Beck, T. Bolemann, H. Frank, D. Flad, G. Gassner, F. Hindenlang, M. Hoffmann, T. Kuhn, M. Sonntag et al., Flexi: a high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws. Comput. Math. Appl. 81, 186–219 (2020)

    Article  MathSciNet  Google Scholar 

  18. T. Kuhn, J. Dürrwächter, F. Meyer, A. Beck, C. Rohde, C.-D. Munz, Uncertainty quantification for direct aeroacoustic simulations of cavity flows. J. Theoret. Comput. Acoust. 27(01), 1850044 (2019)

    Article  MathSciNet  Google Scholar 

  19. T. Kuhn, D. Kempf, A. Beck, C.-D. Munz, A novel turbulent inflow method for zonal large eddy simulations with a discontinuous Galerkin solver

    Google Scholar 

  20. S. Pirozzoli, Numerical methods for high-speed flows. Annu. Rev. Fluid Mech. 43, 163–194 (2011)

    Article  MathSciNet  Google Scholar 

  21. S. Pirozzoli, M. Bernardini, Turbulence in supersonic boundary layers at moderate Reynolds number. J. Fluid Mech. 688, 120–168 (2011)

    Article  MathSciNet  Google Scholar 

  22. J. Rossiter, Wind tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds, Technical report, Ministry of Aviation; Royal Aircraft Establishment; RAE Farnborough, 1964

    Google Scholar 

  23. Y. Saad, M.H. Schultz, GMRES: a generalized minimal residual algorithm for solving non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856–869 (1986)

    Article  Google Scholar 

  24. J.C. Tyacke, P.G. Tucker, Future use of large eddy simulation in aero-engines. J. Turbomach. 137(8), 081005 (2015)

    Article  Google Scholar 

  25. S. Vangelatos, On the efficiency of implicit discontinuous Galerkin spectral element methods for the unsteady compressible Navier-Stokes equations, Ph.D. thesis, University of Stuttgart, 2019

    Google Scholar 

  26. T. Volmar, B. Brouillet, H. Benetschik, H. Gallus, Test case 6: 1-1/2 stage axial flow turbine-unsteady computation, in ERCOFTAC Turbomachinery Seminar and Workshop (1998)

    Google Scholar 

  27. R. Walraevens, H. Gallus, Testcase 6-1-1/2 stage axial flow turbine. Ercoftac Testcase 6, 201–212 (1997)

    Google Scholar 

  28. C. Wenzel, B. Selent, M. Kloker, U. Rist, DNS of compressible turbulent boundary layers and assessment of data/scaling-law quality. J. Fluid Mech. 842, 428–468 (2018)

    Article  MathSciNet  Google Scholar 

  29. B. Zhang, C. Liang, A simple, efficient, and high-order accurate curved sliding-mesh interface approach to spectral difference method on coupled rotating and stationary domains. J. Comput. Phys. 295, 147–160 (2015)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

We thank the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) for supporting this work by funding - EXC2075 – 390740016 under Germany’s Excellence Strategy. We acknowledge the support by the Stuttgart Center for Simulation Science (SimTech) and the DFG International Research Training Group GRK 2160. Min Gao recognizes the support of the China Scholarship Council (CSC). We all truly appreciate the ongoing kind support by HLRS in Stuttgart.

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Correspondence to Andrea Beck .

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Beck, A. et al. (2021). Increasing the Flexibility of the High Order Discontinuous Galerkin Framework FLEXI Towards Large Scale Industrial Applications. In: Nagel, W.E., Kröner, D.H., Resch, M.M. (eds) High Performance Computing in Science and Engineering '20. Springer, Cham. https://doi.org/10.1007/978-3-030-80602-6_22

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