On Monotonically Integrated Large Eddy Simulation of Turbulent Flows Based on FCT Algorithms

  • Fernando F. Grinstein
  • Christer Fureby
Part of the Scientific Computation book series (SCIENTCOMP)


Non-classical Large Eddy Simulation (LES) approaches based on using the unfiltered flow equations instead of the filtered ones have been the subject of considerable interest during the last decade. In the Monotonically Integrated LES (MILES) approach, flux-limiting schemes are used to emulate the characteristic turbulent flow features in the high-wavenumber end of the inertial subrange region. Mathematical and physical aspects of implicit SGS modeling using non-linear flux-limiters are addressed using the modified LES-equation formalism. FCT based MILES performance is demonstrated in selected case studies including (1) canonical flows (homogeneous isotropic turbulence and turbulent channel flows), (2) complex free and wall-bounded flows (rectangular jets and flow past a prolate spheroid), (3) very-complex flows at the frontiers of current unsteady flow simulation capabilities (submarine hydrodynamics).


Large Eddy Simulation Direct Numerical Simulation Prolate Spheroid Turbulent Channel Flow Direct Numerical Simulation Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was completed while one of us (FFG) was the 2003–2004 Orson Anderson Distinguished Visiting Scholar at the Los Alamos National Laboratory, on Sabbatical leave from the Naval Research Laboratory in Washington DC. Support from the Office of Naval Research through the Naval Research Laboratory 6.1 Computational Physics task area is also greatly appreciated.


  1. 1.
    Sagaut, P.: Large Eddy Simulation for Incompressible Flows. Springer, New York (2002) zbMATHGoogle Scholar
  2. 2.
    Liu, S., Meneveau, C., Katz, J.: On the properties of similarity subgridscale models as deduced from measurements in a turbulent jet. J. Fluid Mech. 275, 83 (1994) ADSCrossRefGoogle Scholar
  3. 3.
    Bardina, J.: Improved turbulence models based on large eddy simulation of homogeneous incompressible turbulent flows. Ph.D. Thesis, Stanford University (1983) Google Scholar
  4. 4.
    Adams, N.A., Stolz, S.: Deconvolution methods for subgrid-scale approximation in LES. In: Geurts, B.J. (ed.) Modern Simulation Strategies for Turbulent Flows, p. 21. Edwards, Philadelphia (2001) Google Scholar
  5. 5.
    Spalart, P.R., Jou, W.H., Strelets, M., Allmaras, S.R.: Comments on the feasibility of LES for wings, and on hybrid RANS/LES approach. In: Advances in DNS/LES, First AFOSR International Conference in DNS/LES. Greyden Press, Columbus (1997) Google Scholar
  6. 6.
    Boris, J.P.: On large eddy simulation using subgrid turbulence models. In: Lumley, J.L. (ed.) Whither Turbulence? Turbulence at the Crossroads, p. 344. Springer, New York (1989) Google Scholar
  7. 7.
    Boris, J.P., Grinstein, F.F., Oran, E.S., Kolbe, R.J.: New insights into large eddy simulations. Fluid Dyn. Res. 10, 199 (1992) ADSCrossRefGoogle Scholar
  8. 8.
    J. Fluids Eng. 124(4) (2002). Alternative LES and Hybrid RANS/LES, edited by F.F. Grinstein and G.E. Karniadakis, pp. 821–942 Google Scholar
  9. 9.
    Int. J. Numer. Methods Fluids 39(9) (2002). Special Issue edited by D. Drikakis, pp. 763–864 Google Scholar
  10. 10.
    von Neumann, J., Richtmyer, R.D.: A method for the numerical calculation of hydrodynamic shocks. J. Appl. Phys. 21, 232 (1950) MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. 11.
    Smagorinsky, J.: The beginnings of numerical weather prediction and general circulation modeling: early recollections. Adv. Geophys. 25, 3 (1983) ADSCrossRefGoogle Scholar
  12. 12.
    Grinstein, F.F., Margolin, L.G., Rider, W.J. (eds.): Implicit Large Eddy Simulation: Computing Turbulent Flow Dynamics, 2nd edn. Cambridge University Press, New York (2010) Google Scholar
  13. 13.
    Fureby, C., Grinstein, F.F.: Monotonically integrated large eddy simulation of free shear flows. AIAA J. 37, 544 (1999) ADSCrossRefGoogle Scholar
  14. 14.
    Fureby, C., Grinstein, F.F.: Large eddy simulation of high Reynolds number free and wall bounded flows. J. Comput. Phys. 181, 68 (2002) MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. 15.
    Schumann, U.: Subgrid scale model for finite difference simulation of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376 (1975) MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. 16.
    Carati, D., Winckelmans, G.S., Jeanmart, H.: Exact expansions for filtered scales modeling with a wide class of LES filters. In: Voke, P.R., Sandham, N.D., Kleiser, L. (eds.) Direct and Large Eddy Simulation III, pp. 213–224. Kluwer Academic, Dordrecht (1999) Google Scholar
  17. 17.
    Godunov, S.K.: Reminiscences about difference schemes. J. Comput. Phys. 153, 6–25 (1999) MathSciNetADSzbMATHCrossRefGoogle Scholar
  18. 18.
    Margolin, L.G., Rider, W.J.: A rationale for implicit turbulence modeling. Int. J. Numer. Methods Fluids 39, 821 (2002) MathSciNetADSzbMATHCrossRefGoogle Scholar
  19. 19.
    Jimenez, J., Wray, A., Saffman, P., Rogallo, R.: The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65 (1993) MathSciNetADSzbMATHCrossRefGoogle Scholar
  20. 20.
    Shao, L., Sarkar, S., Pantano, C.: On the relationship between the mean flow and subgrid stresses in large eddy simulation of turbulent shear flows. Phys. Fluids 11, 1229 (1999) ADSzbMATHCrossRefGoogle Scholar
  21. 21.
    Borue, V., Orszag, S.A.: Local energy flux and subgrid-scale statistics in three dimensional turbulence. J. Fluid Mech. 366, 1 (1998) MathSciNetADSzbMATHCrossRefGoogle Scholar
  22. 22.
    Patnaik, G., Boris, J.P., Grinstein, F.F., Iselin, J.P.: Large scale urban simulations with FCT, Chap. 4 in this volume; see also Chap. 17 in Ref. [12] (2004) Google Scholar
  23. 23.
    Hirsch, C.: Numerical Computation of Internal and External Flows. Wiley, New York (1999) Google Scholar
  24. 24.
    Albada, G.D., van Leer, B., van Roberts, W.W.: A comparative study of computational methods in cosmic gas dynamics. Astron. Astrophys. 108, 76 (1982) ADSzbMATHGoogle Scholar
  25. 25.
    Jasak, H., Weller, H.G., Gosman, A.D.: High resolution NVD differencing scheme for arbitrarily unstructured meshes. Int. J. Numer. Methods Fluids 31, 431 (1999) ADSzbMATHCrossRefGoogle Scholar
  26. 26.
    Boris, J.P., Book, D.L.: Flux corrected transport I, SHASTA, a fluid transport algorithm that works. J. Comput. Phys. 11, 38 (1973) ADSzbMATHCrossRefGoogle Scholar
  27. 27.
    Colella, P., Woodward, P.: The piecewise parabolic method (PPM) for gas dynamic simulations. J. Comput. Phys. 54, 174 (1984) MathSciNetADSzbMATHCrossRefGoogle Scholar
  28. 28.
    Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to Re τ=590. Phys. Fluids 11, 943 (1999) ADSzbMATHCrossRefGoogle Scholar
  29. 29.
    Porter, D.H., Pouquet, A., Woodward, P.R.: Kolmogorov-like spectra in decaying three-dimensional supersonic flows. Phys. Fluids 6, 2133 (1994) ADSzbMATHCrossRefGoogle Scholar
  30. 30.
    Garnier, E., Mossi, M., Sagaut, P., Comte, P., Deville, M.: On the use of shock-capturing schemes for large eddy simulation. J. Comput. Phys. 153, 273 (2000) ADSCrossRefGoogle Scholar
  31. 31.
    Okong’o, N., Knight, D.D., Zhou, G.: Large eddy simulations using an unstructured grid compressible Navier-Stokes algorithm. Int. J. Comput. Fluid Dyn. 13, 303 (2000) MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Eswaran, V., Pope, S.B.: An examination of forcing in direct numerical simulation of turbulence. Comput. Fluids 16, 257 (1988) ADSzbMATHCrossRefGoogle Scholar
  33. 33.
    Fureby, C., Tabor, G., Weller, H., Gosman, D.: A comparative study of sub grid scale models in isotropic homogeneous turbulence. Phys. Fluids 9, 1416 (1997) MathSciNetADSzbMATHCrossRefGoogle Scholar
  34. 34.
    Kim, W.-W., Menon, S.: A new incompressible solver for large-eddy simulations. Int. J. Numer. Methods Fluids 31, 983 (1999) ADSzbMATHCrossRefGoogle Scholar
  35. 35.
    Driscoll, R.J., Kennedy, L.A.: A model for the turbulent energy spectrum. Phys. Fluids 26, 1228 (1983) ADSzbMATHCrossRefGoogle Scholar
  36. 36.
    Wei, T., Willmarth, W.W.: Reynolds number effects on the structure of a turbulent channel flow. J. Fluid Mech. 204, 57 (1989) ADSCrossRefGoogle Scholar
  37. 37.
    Nikitin, N.V., Nicoud, F., Wasistho, B., Squires, K.D., Spalart, P.R.: An approach to wall modeling in large eddy simulations. Phys. Fluids 12, 1629 (2000) ADSCrossRefGoogle Scholar
  38. 38.
    Fureby, C., Alin, N., Wikström, N., Menon, S., Persson, L., Svanstedt, N.: On large eddy simulations of high Re-number wall bounded flows. AIAA J. 42, 457–468 (2004) ADSCrossRefGoogle Scholar
  39. 39.
    Grinstein, F.F., Oran, E.S., Boris, J.P.: Pressure field, feedback and global instabilities of subsonic spatially developing mixing layers. Phys. Fluids 3(10), 2401–2409 (1991) ADSzbMATHCrossRefGoogle Scholar
  40. 40.
    Grinstein, F.F., DeVore, C.R.: On global instabilities in countercurrent jets. Phys. Fluids 14(3), 1095–1100 (2002) MathSciNetADSzbMATHCrossRefGoogle Scholar
  41. 41.
    Grinstein, F.F.: Vortex dynamics and entrainment in regular free jets. J. Fluid Mech. 437, 69–101 (2001) ADSzbMATHCrossRefGoogle Scholar
  42. 42.
    Grinstein, F.F.: On integrating large eddy simulation and laboratory turbulent flow experiments. Philos. Trans. R. Soc. Lond. A 367(1899), 2931–2945 (2009) MathSciNetADSzbMATHCrossRefGoogle Scholar
  43. 43.
    Hussain, F., Husain, H.S.: Elliptic jets. Part I. Characteristics of unexcited and excited jets. J. Fluid Mech. 208, 257–320 (1989) ADSCrossRefGoogle Scholar
  44. 44.
    Wetzel, T.G., Simpson, R.L., Chesnakas, C.J.: Measurement of three-dimensional crossflow separation. AIAA J. 36, 557–564 (1998) ADSCrossRefGoogle Scholar
  45. 45.
    Alin, N., Svennberg, U., Fureby, C.: Large eddy simulation of flows past simplified submarine hulls. In: Proc. 8th Int’l Conf. Numerical Ship Hydrodynamics, Busan, Korea, pp. 208–222 (2003) Google Scholar
  46. 46.
    Groves, N.C., Huang, T.T., Chang, M.S.: Geometric characteristics of DARPA SUBOFF models. Report DTRC/SHD-1298-01, David Taylor Research Ctr. (1989) Google Scholar
  47. 47.
    Huang, T.T., et al.: Measurements of flows over an axisymmetric body with various appendages (DARPA SUBOFF experiments). In: Proc. 19th Symp. Naval Hydrodynamics, Seoul, Korea (1992) Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.X-Computational Physics DivisionLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Dept. of Weapons and ProtectionThe Swedish Defence Research Agency—FOIStockholmSweden

Personalised recommendations