Abstract
We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations. The wall model operates directly on the Cartesian computational mesh without the need for a dual boundary-conforming mesh. The combination of wall model and implicit LES is investigated in detail for turbulent channel flow at friction Reynolds numbers from Re τ = 395 up to Re τ =100,000 on very coarse meshes. The TBLE wall model with implicit LES gives results of better quality than current explicit LES based on eddy viscosity subgrid-scale models with similar wall models. A straightforward formulation of the wall model performs well at moderately large Reynolds numbers. A logarithmic-layer mismatch, observed only at very large Reynolds numbers, is removed by introducing a new structure-based damping function. The performance of the overall approach is assessed for two generic configurations with flow separation: the backward-facing step at Re h = 5,000 and the periodic hill at Re H = 10,595 and Re H = 37,000 on very coarse meshes. The results confirm the observations made for the channel flow with respect to the good prediction quality and indicate that the combination of implicit LES, immersed-interface method, and TBLE-based wall modeling is a viable approach for simulating complex aerodynamic flows at high Reynolds numbers. They also reflect the limitations of TBLE-based wall models.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Adams E.W., Johnstont J.P.: Flow structure in the near-wall zone of a turbulent separated flow. AIAA J. 26(8), 932–939 (1988)
del Alamo J.C., Jiménez J., Zandonade P., Moser R.D.: Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144 (2004)
Baggett, J.S.: Some modeling requirements for wall models in large eddy simulation. CTR Annu. Res. Briefs 123–134 (1997)
Baggett, J.S., Jiménez, J., Kravchenko, A.: Resolution requirements in large-eddy simulation of shear flows. CTR Annu. Res. Briefs 51–66 (1997)
Balaras, E., Benocci, C.: Subgrid-scale models in finite-difference simulations of complex wall bounded flows AGARD 2.1–2.5 (1994)
Balaras E., Benocci C., Piomelli U.: Two-layer approximate boundary conditions for large-eddy simulations. AIAA J. 34, 1111–1119 (1996)
Baldwin, B.S., Lomax, H.: Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows. AIAA paper (78-257) (1978)
Bhattacharya, A., Das, A., Moser, R.D.: A filtered-wall formulation for large-eddy simulation of wall-bounded turbulence. Phys. Fluids 20, 115104-1–115104-16 (2008)
Brasseur, J., Wei, T.: Designing large-eddy simulation of the turbulent boundary layer to capture law-of-the-wall scaling. Phys. Fluids 22, 021303-1–021303-21 (2010)
Breuer M., Jaffrézic B., Arora K.: Hybrid LES-RANS technique based on a one-equation near-wall model. J. Theor. Comput. Fluid Dyn. 22, 157–187 (2008)
Breuer M., Kniazev B., Abel M.: Development of wall models for LES of separated flows using statistical evaluations. Comput. Fluids 36, 817–837 (2007)
Cabot, W.H.: Wall models in large eddy simulation of separated flow. CTR Annu. Res. Briefs 97–106 (1997)
Cabot W.H., Moin P.: Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flows. Flow Turbul. Combust. 63, 269–291 (1999)
Choi J.I., Oberoi R.C., Edwards J.R., Rosati J.A.: An immersed boundary method for complex incompressible flows. J. Comput. Phys. 224, 757–784 (2007)
Cristallo A., Verzicco R.: Combined immersed boundary/large-eddy-simulations of incompressible three dimensional complex flows. Flow Turbul. Combust. 77, 3–26 (2006)
Deardorff J.W.: A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453–465 (1970)
Fadlun E.A., Verzicco R., Orlandi P., Mohd-Yusof J.: Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 35–60 (2000)
Fröhlich J., Mellen C.P., Rodi W., Temmerman L., Leschziner M.A.: Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J. Fluid Mech. 526, 19–66 (2005)
Fröhlich J., von Terzi D.: Hybrid LES/RANS methods for the simulation of turbulent flows. Prog. Aerosp. Sci. 44, 349–377 (2008)
Fureby C., Grinstein F.F.: Large eddy simulation of high-Reynolds number free and wall-bounded flows. J. Comput. Phys. 181, 68–97 (2002)
Garnier E., Mossi M., Sagaut P., Deville M.: On the use of shock-capturing schemes for large-eddy simulation. J. Comput. Phys. 153, 273–311 (1999)
Grinstein F.F., Fureby C.: From canonical to complex flows: Recent progress on monotonically integrated LES. Comp. Sci. Eng. 6, 36–49 (2004)
Grinstein F.F., Margolin L.G., Rider W.J.: Implicit Large Eddy Simulation. Cambridge University Press, Cambridge (2007)
Hickel, S., Adams, N.A.: On implicit subgrid-scale modeling in wall-bounded flows. Phys. Fluids 19, 105106-1–105106-13 (2007). doi:10.1063/1.2773765
Hickel S., Adams N.A.: A proposed simplification of the adaptive local deconvolution method. Eur. Ser. Appl. Ind. Math. 16, 66–76 (2007). doi:10.1051/proc:2007008
Hickel S., Adams N.A.: Implicit LES applied to zero-pressure-gradient and adverse-pressure-gradient boundary-layer turbulence. Int. J. Heat Fluid Flow 29(3), 626–639 (2008). doi:10.1016/j.ijheatfluidflow.2008.03.008
Hickel S., Adams N.A., Domaradzki J.A.: An adaptive local deconvolution method for implicit LES. J. Comput. Phys. 213, 413–436 (2006). doi:10.1016/j.jcp.2005.08.017
Hoyas, S., Jiménez, J.: Scaling of the velocity fluctuations in turbulent channels up to Re τ = 2003. Phys. Fluids 18, 011702-1–011702-4 (2006)
Hutchins, N., Marusic, I. (2007) Large-scale influences in near-wall turbulence. Philos. Trans. R. Soc. A 365, 647–664
Jovic, S.: An Experimental Study of a Separated/Reattached Flow Behind a Backward-Facing Step. Re h = 37,000. NASA TM 110384 (1996)
Jovic, S., Driver, D.M.: Backward-Facing Step Measurements at Low Reynolds Number, Re h = 5000. NASA TM 108807 (1994)
Kang S., Iaccarino G., Ham F., Moin P.: Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method. J. Comput. Phys. 228, 6753–6772 (2009)
Kobayashi H., Ham F., Wu X.: Application of a local SGS model based on coherent structures to complex geometries. Int. J. Heat Fluid Flow 29(3), 640–653 (2008)
Le H., Moin P., Kim J.: Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349–74 (1997)
Meyer M., Devesa A., Hickel S., Hu X.Y., Adams N.A.: A conservative immersed interface method for large-eddy simulation of incompressible flows. J. Comput. Phys. 18, 6300–6317 (2010). doi:10.1016/j.jcp.2010.04.040
Meyer M., Hickel S., Adams N.A.: Assessment of implicit large-eddy simulation with a conservative immersed-interface method for turbulent cylinder flow. Int. J. Heat Fluid Flow. 31, 368–377 (2010). doi:10.1007/978-3-642-13872-0_12
Mittal R., Iaccarino G.: Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261 (2005)
Moser R.D., Kim J., Mansour N.N.: Direct numerical simulation of turbulent channel flow up to Re τ = 590. Phys. Fluids 11(4), 943–945 (1999)
Nicoud F., Baggett J.S., Moin P., Cabot W.: Large eddy simulation wall-modeling based on suboptimal control theory and linear stochastic estimation. Phys. Fluids 13(10), 2968–2984 (2001)
Piomelli U.: Wall-layer models for large eddy simulations. Prog. Aerosp. Sci. 44, 437–446 (2008)
Piomelli U., Balaras E.: Wall-layer models for large-eddy simulation. Annu. Rev. Fluid Mech. 34, 349–374 (2002)
Piomelli U., Moin P., Ferziger J.H., Kim J.: New approximate boundary conditions for large-eddy simulations of wall-bounded flows. Phys. Fluids A 1, 1061–1068 (1989)
Rapp, C., Breuer, M., Manhart, M., Peller, N.: 2D Periodic Hill Flow. http://qnet.cfms.org.uk (2010)
Roman, F., Armenio, V., Fröhlich, J.: A simple wall-layer model for large eddy simulation with immersed boundary method. Phys. Fluids 12, 101701-1–101701-4 (2009)
Schumann U.: Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376–404 (1975)
Stolz S., Adams N.A.: An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids 11(4), 1699–1701 (1999)
Temmerman L., Leschziner M.A., Mellen C.P., Fröhlich J.: Investigation of wall-function approximations and subgrid-scale models in large-eddy simulation of separated flow in a channel with periodic constrictions. Int. J. Heat Fluid Flow 24, 157–180 (2003)
Tessicini, F., Iaccarino, G., Wang, M., Verzicco, R.: Wall modeling for large-eddy simulation using an immersed-boundary method. CTR Annu. Res. Briefs 181–187 (2002)
̆Sarić, S., Jakirlić, S., Breuer, M., Jaffrézic, B., Deng, G., Chikhaoni, O.: Evaluation of detached-eddy simulations for predicting the flow over periodic hills. In: Cancès, E., Gerbeau, J.F. (eds.) ESAIM Proceedings CEMRACS 2005: Computational aeroacoustics and computational fluid dynamics in turbulent flows. Marseille, France (July 18–August 26, 2005)
Wang M., Moin P.: Dynamic wall modeling for large-eddy simulation of complex turbulent flows. Phys. Fluids 14(7), 2044–2051 (2002)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by S. Sarkar.
Rights and permissions
About this article
Cite this article
Chen, Z.L., Hickel, S., Devesa, A. et al. Wall modeling for implicit large-eddy simulation and immersed-interface methods. Theor. Comput. Fluid Dyn. 28, 1–21 (2014). https://doi.org/10.1007/s00162-012-0286-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00162-012-0286-6