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Approximate Wall Boundary Conditions in the Large-Eddy Simulation of High Reynolds Number Flow

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Abstract

The near-wall regions of high Reynolds numbers turbulent flows must be modelled to treat many practical engineering and aeronautical applications. In this review we examine results from simulations of both attached and separated flows on coarse grids in which the near-wall regions are not resolved and are instead represented by approximate wall boundary conditions. The simulations use the dynamic Smagorinsky subgrid-scale model and a second-order finite-difference method. Typical results are found to be mixed, with acceptable results found in many cases in the core of the flow far from the walls, provided there is adequate numerical resolution, but with poorer results generally found near the wall. Deficiencies in this approach are caused in part by both inaccuracies in subgrid-scale modelling and numerical errors in the low-order finite-difference method on coarse near-wall grids, which should be taken into account when constructing models and performing large-eddy simulation on coarse grids. A promising new method for developing wall models from optimal control theory is also discussed.

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References

  1. AGARD, A selection of test cases for the validation of large-eddy simulations of turbulent flows. Advisory Report 345, NATO (1998), Chap. 5, pp. 109-128.

  2. Akselvoll, K. and Moin, P., Large eddy simulation of turbulent confined coannular jets and turbulent flow over a backward facing step. Technical Report TF-63, Department of Mechanical Engineering, Stanford, CA (1995).

    Google Scholar 

  3. Arnal, M. and Friedrich, R., Large-eddy simulation of a turbulent flow with separation. In: Durst, F., Friedrich, R., Launder, B.E., Schmidt, F.W., Schumann, U. and Whitelaw, J.H. (eds), Selected Papers from the Eighth Symposium on Turbulent Shear Flows. Springer-Verlag, New York (1993) pp. 169-187.

    Google Scholar 

  4. Baggett, J.S., Jiménez, J. and Kravchenko, A.G., Resolution requirements in large-eddy simulations of shear flows. In: Annual Research Briefs. Center for Turbulence Research, Stanford, CA (1997) pp. 51-66.

    Google Scholar 

  5. Baggett, J.S., Some modeling requirements for wall models in large eddy simulation. In: Annual Research Briefs. Center for Turbulence Research, Stanford, CA (1997) pp. 123-134.

    Google Scholar 

  6. Baggett, J.S., On the feasibility of merging LES with RANS for the near-wall region of attached turbulent flows. In: Annual Research Briefs. Center for Turbulence Research, Stanford, CA (1998) pp. 267-277.

    Google Scholar 

  7. Bagwell, T.G., Adrian, R.J., Moser, R.D. and Kim, J., Improved approximation of wall shear stress boundary conditions for large eddy simulation. In: So, R.M.C., Speziale, C.B. and Launder, B.E. (eds), Near-Wall Turbulent Flows. Elsevier Science, New York (1993) pp. 265-276.

    Google Scholar 

  8. Balaras, E. and Benocci, C., Subgrid scale models in finite difference simulations of complex wall flows. In: AGARD CP-551 (1994) pp. 2.1-2.6.

  9. Balaras, E., Benocci, C. and Piomelli, U., Two-layer approximate boundary conditions for large-eddy simulations. AIAA J. 34 (1996) 1111-1119.

    MATH  ADS  Google Scholar 

  10. Bewley, T.R. and Moin, P., Optimal and robust approaches for linear and nonlinear regulation problems in fluid mechanics. AIAA Paper 97-1872 (1997).

  11. Cabot, W., Large-eddy simulations with wall models. In: Annual Research Briefs. Center for Turbulence Research, Stanford, CA (1995) pp. 41-50.

    Google Scholar 

  12. Cabot, W., Near-wall models in large eddy simulations of flow behind a backward-facing step. In: Annual Research Briefs. Center for Turbulence Research, Stanford, CA (1996) pp. 199-210.

    Google Scholar 

  13. Cabot, W., Wall models in large eddy simulation of separated flow. In: Annual Research Briefs. Center for Turbulence Research, Stanford, CA (1997) pp. 97-106.

    Google Scholar 

  14. Cabot, W., Jiménez, J. and Baggett, J.S., On wakes and near-wall behavior in coarse large-eddy simulation of channel flow with wall models and second-order finite-difference methods. In: Annual Research Briefs. Center for Turbulence Research, Stanford, CA (1999) pp. 343-354.

    Google Scholar 

  15. Choi, H. and Moin, P., Effects of the computational time step on numerical simulation of turbulent flow. J. Comput. Phys. 113 (1994) 1-4.

    Article  MATH  ADS  Google Scholar 

  16. Dean, R.B., A single formula for the complete velocity profile in a turbulent boundary layer. ASME J. Fluids Engrg. 98 (1976) 723-727.

    Google Scholar 

  17. Deardorff, J.W., A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41 (1970) 453-480.

    Article  MATH  ADS  Google Scholar 

  18. Durbin, P.A., Near-wall turbulence closure without “damping functions”. Theoret. Comput. Fluid Dynam. 3 (1991) 1-13.

    MATH  ADS  Google Scholar 

  19. Germano, M., Piomelli, U., Moin, P. and Cabot, W.H., A dynamic subgrid-scale eddy viscosity model. Phys. Fluids 3 (1991) 1760-1765. Erratum: Phys. Fluids 3 (1991), 3128.

    Article  MATH  ADS  Google Scholar 

  20. Ghosal, S., An analysis of numerical errors in large-eddy simulations of turbulence. J. Comput. Phys. 125 (1996) 187-206.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. Ghosal, S. and Moin, P., The basic equations for the large eddy simulation of turbulent flows in complex geometry. J. Comput. Phys. 118 (1995) 24-37.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  22. Grötzbach, G., Direct numerical and large eddy simulation of turbulent channel flows. In: Cheremisinoff, N.P. (ed.), Encyclopedia of Fluid Mechanics Gulf Publishers, Houston (1987) Chap. 34, pp. 1337-1391.

    Google Scholar 

  23. Harlow, F.H. and Welch, J.E., Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8 (1965) 2182-2189.

    Article  ADS  Google Scholar 

  24. Hoffmann, G. and Benocci, C., Approximate wall boundary conditions for large eddy simulations. In: Benzi, R. (ed.), Advances in Turbulence V, Kluwer Academic Publishers, Dordrecht (1995), pp. 222-228.

    Google Scholar 

  25. Kim, J. and Moin, P., Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 177 (1987) 133-166.

    MATH  ADS  Google Scholar 

  26. Kravchenko, A.G. and Moin, P., On the effects of numerical errors in large-eddy simulations of turbulent flows. J. Comput. Phys. 59 (1985) 308-323.

    Article  MathSciNet  ADS  Google Scholar 

  27. Kravchenko, A.G., Moin, P. and Moser, R., Zonal embedded grids for numerical simulations of wall-bounded turbulent flows. J. Comput. Phys. 127 (1996) 412-423.

    Article  MATH  ADS  Google Scholar 

  28. Jiménez, J. and Moser, R.D., LES: Where we are and what we can expect. AIAA Paper 98-2891 (1998).

  29. Jiménez, J. and Vasco, C., Approximate lateral boundary conditions for turbulent simulations. In: Moin, P. and Reynolds, W.C. (eds), Studying Turbulence Using Numerical Simulation VII. Center for Turbulence Research, Stanford, CA (1998) pp. 399-412.

    Google Scholar 

  30. Le, H., Moin, P. and Kim, J., Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330 (1997) 349-374.

    Article  MATH  ADS  Google Scholar 

  31. Lilly, D., A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4 (1992) 633-635.

    Article  ADS  Google Scholar 

  32. Lund, T.S. and Kaltenbach, H.-J., Experiments with explicit filtering for LES using a finite-difference method. In: Annual Research Briefs. Center for Turbulence Research, Stanford, CA (1995) pp. 91-105.

    Google Scholar 

  33. Mason, P.J. and Callen, N.S., On the magnitude of the subgrid-scale eddy coefficient in large-eddy simulations of turbulent channel flow. J. Fluid Mech. 162 (1986) 439-462.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  34. Mason, P.J. and Thomson, D.J., Stochastic backscatter in large-eddy simulations of boundary layers. J. Fluid Mech. 242 (1992) 51-78.

    Article  MATH  ADS  Google Scholar 

  35. Nakayama, A., Maeda, K. and Noda, H., Instantaneous and filtered velocity profiles in smooth and rough boundary layers. Preprint (1999).

  36. Nicoud, F., Winckelmans, G., Carati, D., Baggett, J. and Cabot, W., Boundary conditions for LES away from the wall. In: Moin, P. and Reynolds, W.C. (eds), Studying Turbulence Using Numerical Simulation VII. Center for Turbulence Research, Stanford, CA (1998) pp. 413-422.

    Google Scholar 

  37. Nicoud, F. and Baggett, J., On the use of the optimal control theory for deriving wall models for LES. In: Annual Research Briefs. Center for Turbulence Research, Stanford, CA (1999) pp. 329-341.

    Google Scholar 

  38. Nicoud, F., Baggett, J., Moin, P. and Cabot, W., LES wall-modeling based on optimal control theory. Phys. Fluids (2000) submitted.

  39. Perry, A.E., Henbest, S.M. and Chong, M.S., A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165 (1986) 163-199.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  40. Piomelli, U., Ferziger, J., Moin, P. and Kim, J., New approximate boundary conditions for large eddy simulations of wall-bounded flows. Phys. Fluids 1 (1989) 1061-1068.

    Article  ADS  Google Scholar 

  41. Porté-Agel, F., Meneveau, C. and Parlange, M.B., A scale-dependent dynamic model for large-eddy simulation: Application to a neutral atmospheric boundary. J. Fluid Mech. (2000) submitted.

  42. Schumann, U., Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18 (1975) 376-404.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  43. Smagorinsky, J., General circulation experiments with the primitive equations. I. The basic experiment. Mon. Weather Rev. 91 (1963) 499-164.

    Google Scholar 

  44. Sullivan, P.P., McWilliams, J.C. and Moeng, C.-H., A grid nesting method for large-eddy simulation of planetary boundary-layer flows. Boundary-Layer Met. 80 (1996) 167-202.

    Article  ADS  Google Scholar 

  45. Vasilyev, O.V., Lund, T.S. and Moin, P., A general class of commutative filters for LES in complex geometries. J. Comput. Phys. 146 (1998) 82-104.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  46. Wang, M., LES with wall model for trailing-edge aeroacoustics. In: Annual Research Briefs. Center for Turbulence Research, Stanford, CA (1999) pp. 355-364.

    Google Scholar 

  47. Werner, H. and Wengle, H., Large-eddy simulation of turbulent flow over and around a cube in a plate channel. In: Durst, F., Friedrich, R., Launder, B.E., Schmidt, F.W., Schumann, U. and Whitelaw, J.H. (eds), Selected Papers from the Eighth Symposium on Turbulent Shear Flows. Springer-Verlag, New York (1993) pp. 155-168.

    Google Scholar 

  48. Wu, X. and Squires, K.D., Prediction of the three-dimensional turbulent boundary layer over a swept bump. AIAA J. 36 (1998) 505-514.

    Article  ADS  Google Scholar 

  49. Zagarola, M.V. and Smits, A.J., Scaling of the mean velocity profile for turbulent pipe flow. Phys. Rev. Lett. 78 (1997) 239-242.

    Article  ADS  Google Scholar 

  50. Zang, Y., Street, R.L. and Koseff, J.R., A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows. Phys. Fluids A 5 (1993) 3186-3196.

    Article  ADS  Google Scholar 

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  1. Center for Turbulence Research, Stanford University, Bldg. 500, 488 Escondido Mall, Stanford, CA, 94305-3030, U.S.A.

    W. Cabot & P. Moin

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  1. W. Cabot
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  2. P. Moin
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Cabot, W., Moin, P. Approximate Wall Boundary Conditions in the Large-Eddy Simulation of High Reynolds Number Flow. Flow, Turbulence and Combustion 63, 269–291 (2000). https://doi.org/10.1023/A:1009958917113

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