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The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 1: Theory and Model Description


The article gives an overview of the Scale-Adaptive Simulation (SAS) method developed by the authors during the last years. The motivation for the formulation of the SAS method is given and a detailed explanation of the underlying ideas is presented. The derivation of the high-Reynolds number form of the equations as well as the calibration of the constants is provided. The concept of SAS is explained using several generic examples and test cases. In a companion article, the model is applied to more complex industrial-type applications.

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  1. Baldwin, B.S., Barth, T.J.: A one-equation turbulence transport model for aerodynamic flows. AIAA Paper 92-0439 (1992)

  2. Coles, D., Wadcock, A.J.: Flying hot-wire study of flow past an NACA 4412 airfoil at maximum lift. AIAA J. 17(4), 312–329 (1979)

    Article  ADS  Google Scholar 

  3. Comte-Bellot, G., Corrsin, S.: Simple Eulerian time correlation of full- and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence. J. Fluid Mech. 48(Part 2), 273–337 (1971)

    Article  ADS  Google Scholar 

  4. Craft, T.J., Launder, B.E., Suga, K.: Development and application of a cubic eddy-viscosity model of turbulence. Int. J. Heat Fluid Flow 17(2), 108–115 (1996)

    Article  Google Scholar 

  5. Davidson, L.: Evaluation of the SST–SAS model: channel flow, asymmetric diffuser and axi-symmetric hill. In: Proceedings European Conference on Comp. Fluid Dyn. ECCOMAS CFD (2006)

  6. Egorov, Y., Menter, F.R.: Development and application of SST–SAS model in the DESIDER project. In: Advances in Hybrid RANS–LES Modelling. Notes on Num. Fluid Mech. Multidiscip. Des., vol. 97, Springer (2008)

  7. Egorov, Y., Menter, F.R., Cokljat, D.: The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 2: application to complex flows. Flow Turbul. Combust. (2010). doi:10.1007/s10494-010-9265-4

    MATH  Google Scholar 

  8. Fröhlich, J., Mellen, C.P., Rodi, W., Temmerman, L., Leschziner, M.: Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J. Fluid Mech. 526, 19–66 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. Fröhlich, J., von Terzi, D.: Hybrid LES/RANS methods for simulation of turbulent flows. Prog. Aerosp. Sci. 44(5), 349–377 (2008)

    Article  Google Scholar 

  10. Gatski, T.B., Speziale, C.G.: On explicit algebraic stress models for complex turbulent flows. J. Fluid Mech. 254, 59–78 (1993)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. Kim, S.E.: Large Eddy simulation using unstructured meshes and dynamic subgrid-scale turbulence models. AIAA Paper no. 2004-2548 (2004)

  12. Launder, B.E., Spalding, D.B.: The numerical computation of turbulent flows. Comput. Methods. Appl. Mech. Eng. 3, 269–289 (1974)

    Article  MATH  Google Scholar 

  13. Launder, B.E., Reece, G.J., Rodi, W.: Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68, 537 (1975)

    Article  MATH  ADS  Google Scholar 

  14. Menter, F.R.: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32(8), 1598–1605 (1994)

    Article  ADS  Google Scholar 

  15. Menter, F.R.: Eddy viscosity transport equations and their relation to the k–ε model. NASA-TM-108854 (1994)

  16. Menter, F.R.: Eddy viscosity transport equations and their relation to the k–ε model. J. Fluids Eng. 119, 876–884 (1997)

    Article  Google Scholar 

  17. Menter, F.R, Kuntz, M., Bender R.: A scale-adaptive simulation model for turbulent flow predictions. AIAA Paper 2003-0767 (2003)

  18. Menter, F.R., Egorov, Y.: Re-visiting the turbulent scale equation. In: Proc. IUTAM Symp. One Hundred Years of Boundary Layer Research. Springer, Göttingen (2004)

    Google Scholar 

  19. Menter, F.R., Egorov, Y.: A scale-adaptive simulation model using two-equation models. AIAA Paper 2005-1095, Reno/NV (2005)

  20. Menter, F.R., Egorov, Y.: Turbulence models based on the length-scale equation. In: Fourth International Symposium on Turbulent Shear Flow Phenomena, Williamsburg, 2005—Paper TSFP4-268 (2005)

  21. Menter, F.R., Egorov, Y.: SAS turbulence modelling of technical flows. In: DLES 6—6th ERCOFTAC Workshop on Direct and Large Eddy Simulation September, Poitiers (2005)

  22. Menter, F.R., Egorov, Y., Rusch D.: Steady and unsteady flow modelling using the \(k-\sqrt k L\) model. In: Hanjalic, K., Nagano, Y., Jakirlic, S. (eds.) Proc. Turbulence, Heat and Mass Transfer, vol. 5 (2006)

  23. Menter, F.R., Egorov, Y.: Formulation of the Scale-Adaptive Simulation (SAS) model during the DESIDER Project. In: Haase, W., Braza, M., Revell, A. (eds.) Notes on Num. Fluid Mech. and Multidisc. Design, vol. 103, Springer (2009)

  24. Menter, F.R., Garbaruk A., Smirnov P.: Scale adaptive simulation with artificial forcing. In: Proc. 3rd Symposium on Hybrid RANS–LES Methods (2009)

  25. Moffatt, H.K.: Turbulence and stochastic processes: Kolmogorov’s ideas 50 years on. In: Hunt, J.C.R., Phillips, O.M., Williams, D. (eds.) Proceedings of the Royal Society, London, A, vol. 434, 1991, pp. 1–240 (1991)

  26. Nicoud, F., Ducros, F.: Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 62, 183–200 (1999)

    Article  MATH  Google Scholar 

  27. Pope, S.B.: A more general effective-viscosity hypothesis. J. Fluid Mech. 72, 331–340 (1975)

    Article  MATH  ADS  Google Scholar 

  28. Rodi, W.: A new algebraic relation for calculating the Reynolds stresses. Z. Angew. Math. Mech. 56, 219–221 (1976)

    Article  MathSciNet  Google Scholar 

  29. Rodi, W.: Turbulence modelling for boundary layer calculations. In: Proc. IUTAM Symp. One Hundred Years of Boundary Layer Research, Göttingen, Springer (2004)

  30. Rodi, W., Mansour, N.N.: Low Reynolds number modelling with the aid of direct numerical simulation data. J. Fluid Mech. 250, 509–529 (1993)

    Article  MATH  ADS  Google Scholar 

  31. Rotta, J.C.: Statistische theorie nicht-homogener turbulenz I und II. Z. Phys. 129, 547–572; 131, 51–77 (1951)

    Google Scholar 

  32. Rotta, J.C.: Über eine methode zur Berechnung turbulenter Scherströmungen, aerodynamische Versuchsanstalt Göttingen. Rep. 69 A14 (1968)

  33. Rotta, J.C.: Turbulente Strömumgen. BG Teubner Stuttgart (1972)

  34. Sagaut, P., Deck, S., Terracol, M.: Multiscale and Multiresolution Approaches in Turbulence. Imperial College Press, London (2006)

    Book  Google Scholar 

  35. Spalart, P.R., Allmaras, S.R.: A one-equation turbulence model for aerodynamic flows. La Recherche Aerospatiale n 1, 5–21 (1994)

    Google Scholar 

  36. Spalart, P.R.: Strategies for turbulence modelling and simulations. Int. J. Heat Fluid Flow. 21, 2 (2000)

    Article  Google Scholar 

  37. Spalart, P.R., Jou, W., Strelets, M., Allmaras, S.: Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In: Advances in DNS/LES, 1st AFOSR Int. Conf. on DNS/LES (1997)

  38. Sjunnesson, A., Henriksson, R., Lofstrom C.: CARS measurements and visualization of reacting flows in bluff body stabilized flame. AIAA Paper. 92-3650 (1992)

  39. Strelets, M.: Detached Eddy simulation of massively separated flows. AIAA Paper 2001-879 (2001)

  40. Temmerman, L., Leschziner, M.A.: Large eddy simulation of separated flow in a streamwise periodic channel constriction. In: Proceedings, 2nd Symp. on Turbulence and Shear-Flow Phenomena, Stockholm (2001)

  41. Tennekes, H., Lumley, J.L.: A First Course in Turbulence. MIT Press, London (1992)

    Google Scholar 

  42. Travin, A., Shur, M., Spalart, P.R., Strelets, M.: On URANS solutions with LES-like behaviour. In: Proc. ECCOMAS 2004, Jyväskylä (2004)

  43. Wallin, S., Johansson, A.V.: An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows. J. Fluid Mech. 403, 89–132 (2000)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  44. Wilcox, D.C.: Turbulence Modeling for CFD. DCW Industries Inc., 2. Edition (1998)

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Menter, F.R., Egorov, Y. The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 1: Theory and Model Description. Flow Turbulence Combust 85, 113–138 (2010).

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  • Turbulence model
  • Scale-adaptive simulation
  • SAS
  • Hybrid RANS–LES