The Dynamic Smagorinsky Model in \(512^{3}\) Pseudo-Spectral LES of Decaying Homogeneous Isotropic Turbulence at Very High \(Re_\lambda \)

  • O. Thiry
  • G. WinckelmansEmail author
  • M. Duponcheel
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 25)


We consider the large-eddy simulation (LES) of turbulent flows, in the classical view where no regular explicit filtering is added to the truncation/projection due to the LES grid. The truncation of the complete field \(u_i\) (experimental or from direct numerical simulation, DNS) to the much coarser LES grid corresponds to the incomplete LES field and is noted \(\overline{u}_i\). Assuming perfect numerics, the “effective subgrid-scales (SGS) stress” is then obtained as Open image in new window : i.e., the product of LES quantities minus the product of complete quantities, and further truncated to the LES grid. The divergence of that stress (i.e., the “effective SGS force”) represents the effect of the removed scales on the LES scales. As there is no information beyond the LES grid cutoff, the SGS stress (or the SGS force) can only be modeled.


  1. 1.
    Cholet, J.-P., Lesieur, M.: Parameterization of small scales of three-dimensional isotropic turbulence utilizing spectral closures. J. Atmos. Sci. 38, 2747 (1981)CrossRefGoogle Scholar
  2. 2.
    Cocle, R., Bricteux, L., Winckelmans, G.: Scale dependence and asymptotic very high Reynolds number spectral behavior of multiscale models. Phys. Fluids 21, 085101 (2009)CrossRefGoogle Scholar
  3. 3.
    Duponcheel, M., Orlandi, P., Winckelmans, G.: Time-reversibility of the Euler equations as a benchmark for energy conserving schemes. J. Comput. Phys. 227(19), 8736–8752 (2008)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgrid-scale eddy-viscosity model. Phys. Fluids A 3(7), 1760–1765 (1991)CrossRefGoogle Scholar
  5. 5.
    Lilly, D.K.: On the application of the eddy viscosity concept in the inertial sub-range of turbulence. NACAR Manuscript 123, Boulder, CO (1966)Google Scholar
  6. 6.
    Meneveau, C., Lund, T.S.: The dynamic Smagorinsky model and scale-dependent coefficients in the viscous range of turbulence. Phys. Fluids 9(12), 3932–3934 (1997)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Mohamed, M.S., LaRue, J.C.: The decay power law in grid-generated turbulence. J. Fluid Mech. 219, 195 (1990)CrossRefGoogle Scholar
  8. 8.
    Smagorinsky, J.: General circulation experiments with the primitive equations. Mon. Weather. Rev. 93, 99–165 (1963)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mechanics, Material and Civil Engineering (iMMC), Université catholique de Louvain (UCL)Louvain-la-NeuveBelgium

Personalised recommendations