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Assessment of High-Order Discontinuous Galerkin Methods for LES of Transonic Flows

  • J. S. Cagnone
  • Z. ZerenEmail author
  • A. Châtel
  • M. Rasquin
  • K. Hillewaert
  • L. Bricteux
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 25)

Abstract

This paper concerns implicit large eddy simulation (ILES) of turbulent flows of industrial interest using high order discontinuous Galerkin method (DGM). DGM has a high potential for industrial applications using ILES. As dissipation is only active on very small scale features, the method mimics a subgrid scale model, while its high accuracy ensures that large scale dynamics are not contaminated by dispersive/dissipative errors. Previously DGM/ILES has been assessed on many low Mach number canonical test cases (e.g. Carton et al. Numer Methods Fluids, 78:335–354, (2015), [3]). This paper recapitulates recent validation on transonic benchmarks (Hillewaert et al. Proceedings of CTR summer program, pp. 363–372, Stanford University, (2016), [6]) and proceeds to the application on the LS89 cascade, a well-known turbomachinery benchmark.

Notes

Acknowledgements

The present research benefited from computational resources made available on the Tier-1 supercomputer of the Fédération Wallonie-Bruxelles, infrastructure funded by the Walloon Region under the grant agreement n\(^{\circ }\)1117545.

References

  1. 1.
    Arnold, D., Brezzi, F., Cockburn, B., Marini, L.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749–1779 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Arts, T., Lambert de Rouvroit, M.: Aero-thermal performance of a two-dimensional highly loaded transonic turbine nozzle guide vane : a test case for inviscid and viscous flow computations. J. Turbomach. 114, 147–154 (1992)CrossRefGoogle Scholar
  3. 3.
    Carton de Wiart, C., Hillewaert, K., Bricteux, L., Winckelmans, G.: Implicit LES of free and wall-bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method. Numer. Methods Fluids 78, 335–354 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Cockburn, B., Karniadakis, G.E., Shu, C.-W.: The development of discontinuous Galerkin methods. In: Cockburn, B., Karniadakis, G.E., Shu, C.-W. (eds.) Discontinuous Galerkin Methods: Theory, Computation and Applications. Volume 11 of Lecture Notes in Computer Science and Engineering, pp. 350. Springer, Berlin (2000)Google Scholar
  5. 5.
    Davidson, L.: Using isotropic synthetic fluctuations as inlet boundary conditions for unsteady simulations. Adv. Appl. Fluid Mech. 1(1), 2007, 1–35 (2006)Google Scholar
  6. 6.
    Hillewaert, K., Cagnone, J.S., Murman, S., Garai, A., Lv, Y., Ihme, M.: Assessment of high-order DG methods for LES of free-stream transonic turbulence. In: Proceedings of CTR Summer Program, pp. 363–372. Stanford University (2016)Google Scholar
  7. 7.
    Johnsen, E., Larsson, J., Bhagatwala, A.V., Cabot, W.H., Moin, P., Olson, B.J., Rawat, P.S., Shankar, S.K., Sjgreen, B., Yee, H., Zhong, X., Lele, S.K.: Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves. J. Comput. Phys. 229, 1213–1237 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Larsson, J., Lele, S.K.: Direct numerical simulation of canonical shock/turbulence interaction. Phys. Fluids 21, 126101 (2009)CrossRefGoogle Scholar
  9. 9.
    Persson, P., Peraire, J.: Sub-cell shock capturing for discontinuous Galerkin methods. In: 44th AIAA Aerospace Sciences Meeting and Exhibit, pp. 112. Reno, Nevada (2006)Google Scholar
  10. 10.
    Rogallo, R.: Numerical experiments in homogeneous turbulence. NASA TM-81315 (1981)Google Scholar
  11. 11.
    Segui, L., Gicquel, L., Duchaine, F., de Laborderie, J.: LES of the LS89 cascade: influence of inflow turbulence on the flow predictions. In: Proceedings of 12th European Conference on Turbomachinery Fluid dynamics and Thermodynamics ETC12. Stockholm, Sweden, 3–7 April (2017)Google Scholar
  12. 12.
    Xiong, Z., Nagarajan, S., Lele, S.K.: Simple method for generating inflow turbulence. AIAA J. 42, 2164–2166 (2004)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • J. S. Cagnone
    • 1
  • Z. Zeren
    • 1
    Email author
  • A. Châtel
    • 2
  • M. Rasquin
    • 1
  • K. Hillewaert
    • 1
  • L. Bricteux
    • 2
  1. 1.CenaeroGosseliesBelgium
  2. 2.Université de Mons (UMONS)MonsBelgium

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