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Application and Development of the High Order Discontinuous Galerkin Spectral Element Method for Compressible Multiscale Flows

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High Performance Computing in Science and Engineering ' 18

Abstract

This paper summarizes our progress in the application and feature development of a high-order discontinuous Galerkin (DG) method for scale resolving fluid dynamics simulations on the Cray XC40 Hazel Hen cluster at HLRS. We present the extension to Chimera grid techniques which allow efficient computations on flexible meshes, and discuss data-based development of subgrid closure terms through machine learning algorithms. We also show the first results of the simulation of a challenging, high Reynolds number supersonic dual nozzle flow.

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  1. 1.

    www.flexi-project.org.

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 ’14. (Springer International Publishing, 2015), pp. 499–518

    Google Scholar 

  2. J. Bardina, J. Ferziger, W. Reynolds, Improved subgrid-scale models for large-eddy simulation. In 13th Fluid and Plasma Dynamics Conference (1980), p. 1357

    Google Scholar 

  3. A.R. Barron, Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inf. Theory 39(3), 930–945 (1993)

    Article  MathSciNet  Google Scholar 

  4. G. Batchelor, A. Townsend, Decay of isotropic turbulence in the initial period. Proc. R. Soc. Lond. Math. Phys. Eng. Sci. 193(1035), 539–558 (1948)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  6. 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 

  7. A. Beck, D. Flad, C. Tonhäuser, G. Gassner, C.-D. Munz, On the influence of polynomial de-aliasing on subgrid scale models. Flow Turbul. Combust. 1–37 (2016)

    Google Scholar 

  8. G. Cybenko, Approximation by superpositions of a sigmoidal function. Math. Control Signals Syst. 2(4), 303–314 (1989)

    Article  MathSciNet  Google Scholar 

  9. D. Flad, A. Beck, C.-D. Munz, Simulation of underresolved turbulent flows by adaptive filtering using the high order discontinuous Galerkin spectral element method. J. Comput. Phys. 313, 1–12 (2016)

    Article  MathSciNet  Google Scholar 

  10. D. Flad, G. Gassner, On the use of kinetic energy preserving DG-schemes for large eddy simulation. J. Comput. Phys. 350, 782–795 (2017)

    Article  MathSciNet  Google Scholar 

  11. M. Galbraith, J. Benek, P. Orkwis, M. Turner, A discontinuous Galerkin chimera scheme. Comput. Fluids 98, 27–53 (2014)

    Article  MathSciNet  Google Scholar 

  12. M. Gamahara, Y. Hattori, Searching for turbulence models by artificial neural network. Phys. Rev. Fluids 2(5), 054604 (2017)

    Article  Google Scholar 

  13. G. Gassner, A. Beck, On the accuracy of high-order discretizations for underresolved turbulence simulations. Theor. Comput. Fluid Dyn. 27(3–4), 221–237 (2013)

    Article  Google Scholar 

  14. K. He, X. Zhang, S. Ren, J. Sun, Deep residual learning for image recognition. in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2016), pp. 770–778

    Google Scholar 

  15. S. Hickel, N. Adams, A. Domaradzki, An adaptive local deconvolution method for implicit LES. J. Comput. Phys. 213(1), 413–436 (2006)

    Article  MathSciNet  Google Scholar 

  16. D. Kim, H. Choi, Laminar flow past a sphere rotating in the streamwise direction. J. Fluid Mech. 461, 365–386 (2002)

    Article  MathSciNet  Google Scholar 

  17. A. Krizhevsky, I. Sutskever, and G. Hinton, ImageNet classification with deep convolutional neural networks. in F. Pereira, C. Burges, L. Bottou, and K. Weinberger, (Eds.), Advances in Neural Information Processing Systems 25, (Curran Associates, Inc., 2012), pp. 1097–1105

    Google Scholar 

  18. Y. LeCun, B. Boser, J. Denker, D. Henderson, R. Howard, W. Hubbard, L. Jackel, Handwritten digit recognition with a back-propagation network. In Advances in Neural Information Processing Systems (1990), pp. 396–404

    Google Scholar 

  19. W. McCulloch, W. Pitts, A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5(4), 115–133 (1943)

    Article  MathSciNet  Google Scholar 

  20. M. Minsky, S. Papert, Perceptron (expanded edition) (1969)

    Google Scholar 

  21. S. Reuschen, Development of artificial neural networks to determine the closure terms in large eddy simulations (University of Stuttgart, Thesis, 2018)

    Google Scholar 

  22. R. Rogallo, Numerical Experiments in Homogeneous Turbulence, vol. 81315. (National Aeronautics and Space Administration) (1981)

    Google Scholar 

  23. J. Slotnick, A. Khodadoust, J. Alonso, D. Darmofal, W. Gropp, E. Lurie, D. Mavriplis, CFD vision 2030 study: a path to revolutionary computational aerosciences. Technical Report (NASA Langley Research Center; Hampton, VA, United States, 2014)

    Google Scholar 

  24. J. Smagorinsky, General circulation experiments with the primitive equations: I. the basic experiment. Month. Weather Rev. 91(3), 99–164 (1963)

    Article  Google Scholar 

  25. M. Sonntag, C.-D. Munz, Efficient parallelization of a shock capturing for discontinuous Galerkin methods using finite volume sub-cells. J. Sci. Comput. 70(3), 1262–1289 (2017)

    Article  MathSciNet  Google Scholar 

  26. M. Spraul, Numerical simulation of a dual nozzle with the discontinuous Galerkin spectral element method. Thesis, University of Stuttgart, 2018

    Google Scholar 

  27. V. Zapryagaev, Test case p4. bypass noise-suppressing nozzle test case. Test case description, ITAM, Novosibirsk

    Google Scholar 

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Acknowledgements

The research presented in this paper was supported in parts by the Deutsche Forschungsgemeinschaft (DFG), the Boysen Stiftung and the Simtech Cluster of Excellence PN5-21. We truly appreciate the ongoing kind support by HLRS and Cray in Stuttgart.

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Correspondence to Nico Krais .

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Beck, A., Bolemann, T., Flad, D., Krais, N., Zeifang, J., Munz, CD. (2019). Application and Development of the High Order Discontinuous Galerkin Spectral Element Method for Compressible Multiscale Flows. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering ' 18. Springer, Cham. https://doi.org/10.1007/978-3-030-13325-2_18

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