Science China Physics, Mechanics & Astronomy

, Volume 57, Issue 12, pp 2188–2193 | Cite as

Recent understanding on the subgrid-scale modeling of large-eddy simulation in physical space



In the last 50 years, the methodology of large-eddy simulation (LES) has been greatly developed, while lots of different subgridscale (SGS) models have appeared. However, the understanding of the procedure of SGS modeling is still not clear. The present contribution aims at reviewing the recent SGS models and, more importantly, expressing our recent understanding on the SGS modeling of LES in physical space. Taking the Kolmogorov equation for filtered quantities (KEF) as an example, it is argued that the KEF alone is not enough to be a closure method. Three physical laws are then introduced to complete this closure procedure and are expected to inspire the future researches of SGS modeling.


large-eddy simulation subgrid-scale modeling Kolmogorov equation 


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  1. 1.
    Sagaut P. Large Eddy Simulation for Imcompressible Flows. Berlin: Springer, 2006Google Scholar
  2. 2.
    Lesieur M. Turbulence in Fluids. Dordrecht: Kluwer Academic, 1997CrossRefMATHGoogle Scholar
  3. 3.
    Spalart P R. Detached-eddy simulation. Annu Rev Fluid Mech, 2009, 41: 181–202ADSCrossRefGoogle Scholar
  4. 4.
    Xiao Z X, Chen H X, Zhang Y F, et al. Study of delayed-detached eddy simulation with weakly nonlinear turbulence model. J Aircraft, 2006, 43(5): 1377–1385CrossRefGoogle Scholar
  5. 5.
    Xiao Z X, Liu J, Huang J B, et al. Numerical dissipation effects on massive separation around tandem cylinders. AIAA J, 2012, 50(5): 1119–1136ADSCrossRefGoogle Scholar
  6. 6.
    Batten P, Goldberg U, Chakravarthy S. LNS—an approach towards embedded LES. AIAA Paper, 2002, AIAA-2012-427Google Scholar
  7. 7.
    Lesieur M, Metais O. New trends in large-eddy simulations of turbulence. Annu Rev Fluid Mech, 1996, 28: 45–82ADSCrossRefMathSciNetGoogle Scholar
  8. 8.
    Vreman B, Geurts B, Kuerten H. Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer. Int J Numer Methods Fluids, 1996, 22(4): 297–311CrossRefMATHGoogle Scholar
  9. 9.
    Meneveau C, Katz J. Scale-invariance and turbulence models for largeeddy simulation. Annu Rev Fluid Mech, 2000, 32: 1–32ADSCrossRefMathSciNetGoogle Scholar
  10. 10.
    Breuer M. A challenging test case for large eddy simulation: High Reynolds number circular cylinder flow. Int J Heat Fluid Flow, 2000, 21(5): 648–654CrossRefGoogle Scholar
  11. 11.
    Hinz D F, Kim T Y, Riley J J, et al. A priori testing of alpha regularisation models as subgrid-scale closures for large-eddy simulations. J Turbul, 2013, 14(6): 1–20CrossRefMathSciNetGoogle Scholar
  12. 12.
    Park N, Yoo J Y, Choi H. Toward improved consistency of a priori tests with a posteriori tests in large eddy simulation. Phys Fluids, 2005, 17: 015103ADSCrossRefGoogle Scholar
  13. 13.
    Smagorinsky J. General circulation experiments with primitive equation. Mon Weather Rev, 1963, 91: 99ADSCrossRefGoogle Scholar
  14. 14.
    Germano M, Piomelli U, Moin P, et al. A dynamic subgrid-scale eddy viscosity model. Phys Fluids A, 1991, 3(7): 1760–1765ADSCrossRefMATHGoogle Scholar
  15. 15.
    Métais O, Lesieur M. Spectral large-eddy simulation of isotropic and stably stratified turbulence. J Fluid Mech, 1992, 239: 157–194ADSCrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Bardina J, Ferziger J, Reynolds W C. Improved subgrid-scale models for large-eddy simulation. AIAA Paper, 1980, AIAA-80-1357Google Scholar
  17. 17.
    Yu C P, Hong R K, Xiao Z L, et al. Subgrid-scale eddy viscosity model for helical turbulence. Phys Fluids, 2013, 25(9): 095101ADSCrossRefGoogle Scholar
  18. 18.
    Verma A, Park N, Mahesh K. A hybrid subgrid-scale model constrained by reynolds stress. Phys Fluids, 2013, 25(11): 110805ADSCrossRefGoogle Scholar
  19. 19.
    Jin G D, He G W. A nonlinear model for the subgrid timescale experienced by heavy particles in large eddy simulation of isotropic turbulence with a stochastic differential equation. New J Phys, 2013, 15: 035011CrossRefGoogle Scholar
  20. 20.
    Jin G D, He G W, Wang L P. Large-eddy simulation of turbulentcollision of heavy particles in isotropic turbulence. Phys Fluids, 2010, 22(5): 055106ADSCrossRefMathSciNetGoogle Scholar
  21. 21.
    Jin G D, He G W, Wang L P, et al. Subgrid scale fluid velocity time scales seen by inertial particles in large eddy simulation of particleladen turbulence. Int J Multiphase Flow, 2010, 36(5): 432–437CrossRefMathSciNetGoogle Scholar
  22. 22.
    Horiuti K, Tamaki T. Nonequilibrium energy spectrum in the subgridscale one-equation model in large-eddy simulation. Phys Fluids, 2013, 25(12): 125104ADSCrossRefGoogle Scholar
  23. 23.
    Park G I, Moin P. An improved dynamic non-equilibrium wall-model for large eddy simulation. Phys Fluids, 2014, 26(1): 015108ADSCrossRefGoogle Scholar
  24. 24.
    Ghorbaniasl G, Agnihotri V, Lacor C. A self-adjusting flow dependent formulation for the classical Smagorinsky model coefficient. Phys Fluids, 2013, 25(5): 055102ADSCrossRefGoogle Scholar
  25. 25.
    Fang L. A new dynamic formula for determining the coefficient of smagorinsky model. Theor Appl Mech Lett, 2011, 1(3): 032002ADSCrossRefGoogle Scholar
  26. 26.
    Ryu S, Iaccarino G. A subgrid-scale eddy-viscosity model based on the volumetric strain-streching. Phys Fluids, 2014, 26(6): 065107ADSCrossRefGoogle Scholar
  27. 27.
    Rasam A, Brethouwer G, Johansson A V. A stochastic extension of the explicit algebraic subgrid-scale models. Phys Fluids, 2014, 26(5): 055113ADSCrossRefGoogle Scholar
  28. 28.
    Fang L, Li B, Lu L P. Scaling law of resolved-scale isotropic turbulence and its application in large-eddy simulation. Acta Mech Sin, 2014, 30(3): 339–350ADSCrossRefGoogle Scholar
  29. 29.
    Rasthofer U, Burton G C, Wall W A, et al. Multifractal subgrid-scale modeling within a variational multiscale method for large-eddy simulation of passive-scalar mixing in turbulent flow at low and high schmidt numbers. Phys Fluids, 2014, 26(5): 055108ADSCrossRefGoogle Scholar
  30. 30.
    Balarac G, Le Sommer J, Meunier X, et al. A dynamic reglarized gradient model of the subgrid-scale scalar flux for large-eddy simulations. Phys Fluids, 2014, 25(7): 075107ADSCrossRefGoogle Scholar
  31. 31.
    Fauconnier D, Dick E. Analytical and numerical study of resolution criteria in large-eddy simulation. Phys Fluids, 2014, 26(6): 065104ADSCrossRefGoogle Scholar
  32. 32.
    Pope S. Turbulent Flows. Cambridge: Cambridge University Press, 2000CrossRefMATHGoogle Scholar
  33. 33.
    Fang L, Bos W J T, Shao L, et al. Time-reversibility of Navier-Stokes turbulence and its implication for subgrid scale models. J Turbul, 2012, 13: 1–14CrossRefMathSciNetGoogle Scholar
  34. 34.
    Fang L. Applying the Kolmogorov Equation to the Problem of Subgrid Modeling for Large-Eddy Simulation of Turbulence. Dissertation for Doctoral Degree. Lyon: Ecole centrale de Lyon, 2009Google Scholar
  35. 35.
    Fang L, Shao L, Bertoglio J P, et al. The rapid-slow decomposition of the subgrid flux in inhomogeneous scalar turbulence. J Turbul, 2011, 12(8): 1–23MathSciNetGoogle Scholar
  36. 36.
    Leonard A. Energy cascade in large-eddy simulations of turbulent flows. Adv Geophys, 1974, A18: 237ADSGoogle Scholar
  37. 37.
    Brun C, Friedrich R, da Silva C B. A non-linear SGS model based on the spatial velocity increment. Theor Comput Fluid Dyn, 2006, 20: 1–21CrossRefMATHGoogle Scholar
  38. 38.
    Geurts B J, Holm D. Regularization modeling for large-eddy simulations of turbulence. J Comput Phys, 2003, 15: L13–L16MathSciNetGoogle Scholar
  39. 39.
    Kolmogorov A N. The local structure of turbulence in incompressible viscous fluid for very large reynolds number. Proc Math Phys Sci, 1941, 30: 301–305Google Scholar
  40. 40.
    Shi Y P, Xiao Z L, Chen S Y. Constrained subgrid-scale stress model for large eddy simulation. Phys Fluids, 2008, 20(1): 011701ADSCrossRefGoogle Scholar
  41. 41.
    Fang L, Ge M W, Wu J Z. Comment on “a self-adjusting flow dependent formulation for the classical Smagorinsky model coefficient”. Phys Fluids, 2013, 25(9): 099101ADSCrossRefGoogle Scholar
  42. 42.
    Meneveau C. Statistics of turbulence subgrid-scale stresses: Necessary conditions and experimental tests. Phys Fluids, 1994, 6(2): 815–833ADSCrossRefMATHMathSciNetGoogle Scholar
  43. 43.
    Cui G X, Zhou H B, Zhang Z S, et al. A new dynamic subgrid eddy viscosity model with application to turbulent channel flow. Phys Fluids, 2004, 16(8): 2835–2842ADSCrossRefGoogle Scholar
  44. 44.
    Shao L, Zhang Z S, Cui G X, et al. Subgrid modeling of anisotropic rotating homogeneous turbulence. Phys Fluids, 2005, 17(11): 115106ADSCrossRefGoogle Scholar
  45. 45.
    Fang L, Boudet J, Shao L. Les échanges inter-echelles en simulation des grandes échelles. In: 18e Congrés Français de Mécanique, 2007Google Scholar
  46. 46.
    Fang L, Shao L, Bertoglio J P, et al. An improved velocity increment model based on Kolmogorov equation of filtered velocity. Phys Fluids, 2009, 21(6): 065108ADSCrossRefGoogle Scholar
  47. 47.
    Cui G X, Xu C X, Fang L, et al. A new subgrid eddy-viscosity model for large-eddy simulation of anisotropic turbulence. J Fluid Mech, 2007, 582: 377–397ADSCrossRefMATHMathSciNetGoogle Scholar
  48. 48.
    Benzi R, Ciliberto S, Baudet C, et al. On the scaling of threedimensional homogeneous and isotropic turbulence. Physica D, 1995, 80: 385–398ADSCrossRefMATHMathSciNetGoogle Scholar
  49. 49.
    Fang L, Bos W J T, Zhou X Z, et al. Corrections to the scaling of the second-order structure function in isotropic turbulence. Acta Mech Sin, 2010, 26(2): 151–157ADSCrossRefMATHMathSciNetGoogle Scholar
  50. 50.
    Bos W J T, Chevillard J, Scott J, et al. Reynolds number effects on the velocity increment skewness in isotropic turbulence. Phys Fluids, 2012, 24: 015108ADSCrossRefGoogle Scholar
  51. 51.
    Kolmogorov A N. A refinement of previous hypotheses concerning the local structure of turbulence. J Fluid Mech, 1962, 13: 82–85ADSCrossRefMATHMathSciNetGoogle Scholar
  52. 52.
    She Z S, Leveque E. Universal scaling law in fully developed turbulence. Phys Rev Lett, 1994, 72: 336–339ADSCrossRefGoogle Scholar
  53. 53.
    Pumir A, Shraiman B I. Lagrangian particle approach to large eddy simulations of hydrodynamic turbulence. J Stat Phys, 2003, 113: 693–700CrossRefMATHMathSciNetGoogle Scholar
  54. 54.
    Marusic I, Mathis R, Hutchins N. Predictive model for wall-bounded turbulent flow. Science, 2010, 329: 193–196ADSCrossRefMATHMathSciNetGoogle Scholar
  55. 55.
    Yao S Y, Fang L, Lv J M, et al. Multiscale three-point velocity increment correlation in turbulent flows. Phys Lett A, 2014, 378(11–12): 886–891ADSCrossRefMATHGoogle Scholar
  56. 56.
    He GW, Rubinstein R, Wang L P. Effects of subgrid-scale modeling on time correlations in large eddy simulation. Phys Fluids, 2002, 14(7): 2186–2193ADSCrossRefGoogle Scholar
  57. 57.
    He G W, Zhang J B. Elliptic model for space-time correlation in turbulent shear flows. Phys Rev E, 2006, 73(5): 055303ADSCrossRefGoogle Scholar
  58. 58.
    Zhao X, He G W. Space-time correlations of fluctuating velocities in turbulent shear flows. Phys Rev E, 2009, 79(4): 046316ADSCrossRefGoogle Scholar
  59. 59.
    He G W, Wang M, Lele S K. On the computation of space-time correlations by large-eddy simulation. Phys Fluids, 2004, 16(11): 3859–3867ADSCrossRefGoogle Scholar
  60. 60.
    Yang Y, He G W, Wang L P. Effects of subgrid-scale modeling on Lagrangian statistics in large-eddy simulation. J Turbul, 2008, 9: 1–24MathSciNetGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Laboratory of Mathematics and Physics, Ecole Centrale de PékinBeijing University of Aeronautics and AstronauticsBeijingChina
  2. 2.Laboratoire de Mécaniques des Fluides et d’AcoustiqueEcole Centrale de LyonEcullyFrance

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