Implicit LES Approaches via Discontinuous Galerkin Methods at Very Large Reynolds

  • R. C. MouraEmail author
  • J. Peiró
  • S. J. Sherwin
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 25)


We consider the suitability of implicit large-eddy simulation (iLES) approaches via discontinuous Galerkin (DG) schemes. These are model-free eddy-resolving approaches which solve the governing equations in unfiltered form and rely on numerical stabilization techniques to account for the missing scales. In DG, upwind dissipation from the Riemann solver provides the baseline mechanism for regularization. DG-based iLES approaches are currently under rapid dissemination due to their success in predicting complex transitional and turbulent flows at moderate Reynolds numbers (Uranga et al, Int J Numer Meth Eng 87(1–5):232–261, 2011, [1], Gassner and Beck, Theor Comput Fluid Dyn 27(3–4):221–237, 2013, [2], Beck et al, Int J Numer Methods Fluids 76(8):522–548, 2014, [3], Wiart et al Int J Numer Methods Fluids 78:335–354, 2015, [4]). However, at higher Reynolds number, accuracy and stability issues can arise due the highly under-resolved character of the computations and the suppression of stabilizing viscous effects.



RCM would like to acknowledge funding under the Brazilian Science without Borders scheme. JP and SJS acknowledge support from the Engineering and Physical Sciences Research Council (EPSRC) under grant EP/L000407/1. SJS additionally acknowledges support as Royal Academy of Engineering Research Chair under grant 10145/86.


  1. 1.
    Uranga, A., Persson, P.O., Drela, M., Peraire, J.: Implicit large eddy simulation of transition to turbulence at low Reynolds numbers using a Discontinuous Galerkin method. Int. J. Numer. Meth. Eng. 87(1–5), 232–261 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Gassner, G.J., Beck, A.D.: On the accuracy of high-order discretizations for underresolved turbulence simulations. Theor. Comp. Fluid Dyn. 27(3–4), 221–237 (2013)CrossRefGoogle Scholar
  3. 3.
    Beck, A.D., Bolemann, T, Flad, D., Frank, H., Gassner, G.J., Hindenlang, F., Munz, C.D.: High-order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations. Int. J. Numer. Methods Fluids 76(8), 522–548 (2014)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Wiart, C.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. Int. J. Numer. Methods. Fluids 78, 335–354 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Moura, R.C., Sherwin, S.J., Peiró, J.: Modified equation analysis for the discontinuous Galerkin formulation. Spectral and High Order Methods for PDEs – ICOSAHOM 2014. Springer, Cham (2015)Google Scholar
  6. 6.
    Moura, R.C., Sherwin, S.J., Peiró, J.: Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/\(hp\) methods. J. Comput. Phys. 298, 695–710 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Moura, R.C., Mengaldo, G., Peiró, J., Sherwin, S.J.: On the eddy-resolving capability of high-order discontinuous Galerkin approaches to implicit LES/under-resolved DNS of Euler turbulence. J. Comput, Phys (2016)Google Scholar
  8. 8.
    Moura, R.C., Mengaldo, G., Peiró, J., Sherwin, S.J.: An LES setting for DG-based implicit LES with insights on dissipation and robustness. Spectral and High Order Methods for PDEs – ICOSAHOM 2016. Springer, Cham (2017)zbMATHGoogle Scholar
  9. 9.
    Falkovich, G.: Bottleneck phenomenon in developed turbulence. Phys. Fluids 6(4), 1411 (1994)CrossRefGoogle Scholar
  10. 10.
    Coantic, M., Lasserre, J.: On pre-dissipative ‘bumps’ and a Reynolds-number-dependent spectral parameterization of turbulence. Eur. J. Mech. B 18(6), 1027–1047 (1999)CrossRefGoogle Scholar
  11. 11.
    Lamorgese, A.G., Caughey, D.A., Pope, S.B.: Direct numerical simulation of homogeneous turbulence with hyperviscosity. Phys. Fluids 17(1), 015106 (2005)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Frisch, U., Kurien, S., Pandit, R., Pauls, W., Ray, S.S., Wirth, A., Zhu, J.Z.: Hyperviscosity, Galerkin truncation, and bottlenecks in turbulence. Phys. Rev. Lett. 101(14), 144501 (2008)CrossRefGoogle Scholar
  13. 13.
    Gassner, G.J., Winters, A.R., Kopriva, D.A.: Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations. J. Comput. Phys. 327, 39–66 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Chong, M.S., Perry, A.E., Cantwell, B.J.: A general classification of three-dimensional flow fields. Phys. Fluids A 2(5), 765–777 (1990)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Laizet, S., Nedić, J., Vassilicos, C.: Influence of the spatial resolution on fine-scale features in DNS of turbulence generated by a single square grid. Int. J. Comput. Fluid D. 29(3–5), 286–302 (2015)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Imperial CollegeLondonUK

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