Advertisement

Scale Separation for Implicit Large Eddy Simulation

  • X. Y. Hu
  • N. A. Adams
Conference paper

Introduction

Unlike standard large eddy simulation (LES) (for a review of LES for incompressible and compressible turbulence refer e.g. to [18, 7]), implicit LES (ILES) does not require an explicitly computed sub-grid scale (SGS) closure, but rather employs an inherent, usually nonlinear, regularization mechanism due to the nonlinear truncation error of the convective-flux discretization scheme as implicit SGS model. As finite-volume discretizations imply a top-hat filtered solution, regularized finitevolume reconstruction schemes were among the first ILES approaches, such as the flux-corrected transport (FCT) method [4], the piecewise parabolic method (PPM) [5]. Although ILES is attractive due to its relative simplicity, numerical robustness and easy implementation, it often exhibits inferior performance to explicit LES [8] if the discretization scheme is not constructed properly. Some schemes, such as PPM, FCT, MUSCL [16] and WENO [3] methods, work reasonably well for ILES by being able to recover a Kolmogorov-range for high-Reynolds-number turbulence up to k max /2, where k max is the Nyquist wavenumber of the underlying grid [9, 10, 21]. These promising results have led to further efforts on the physically-consistent design of discretization schemes for ILES. Physical consistency implies the correct and resolution-independent reproduction of the subgrid-scale (SGS) energy transfer mechanism of isotropic turbulence. Based on this notion the adaptive local deconvolution method (ALDM) has been developed [1, 11]. Approaches for decreasing excessive model dissipation for the solenoidal velocity field include the low-Mach number switch of [22], and the dilatation switch and shock sensor of [15].

Keywords

Large Eddy Simulation Discretization Scheme Isotropic Turbulence Subgrid Scale WENO Scheme 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adams, N.A., Hickel, S., Franz, S.: Implicit subgrid-scale modeling by adaptive deconvolution. J. Comput. Phys. 200(2), 412–431 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Adams, N.A., Shariff, K.: A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems. J. Comput. Phys. 127, 27–51 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Balsara, D.S., Shu, C.W.: Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. J. Comput. Phys. 160(2), 405–452 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Boris, J.P., Grinstein, F.F., Oran, E.S., Kolbe, R.L.: New insights into large eddy simulation. Fluid Dynamics Research 10(4-6), 199–228 (1992)CrossRefGoogle Scholar
  5. 5.
    Colella, P., Woodward, P.R.: The Piecewise Parabolic Method (PPM) for gas-dynamical simulations. J. Comput. Phys. 54(1), 174–201 (1984)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Cook, A.W.: Artificial fluid properties for large-eddy simulation of compressible turbulent mixing. Physics of Fluids 19, 055103 (2007)CrossRefGoogle Scholar
  7. 7.
    Garnier, E., Adams, N.A., Sagaut, P.: Large Eddy Simulation for Compressible Flows. Springer (2009)Google Scholar
  8. 8.
    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(2), 273–311 (1999)zbMATHCrossRefGoogle Scholar
  9. 9.
    Grinstein, F.F., Fureby, C.: Recent progress on flux-limiting based implicit Large Eddy Simulation. In: European Conference on Computational Fluid Dynamics, ECCOMAS CFD (2006)Google Scholar
  10. 10.
    Grinstein, F.F., Margolin, L.G., Rider, W.: Implicit large eddy simulation: computing turbulent fluid dynamics. Cambridge University Press, Cambridge (2007)zbMATHCrossRefGoogle Scholar
  11. 11.
    Hickel, S., Adams, N.A., Domaradzki, J.A.: An adaptive local deconvolution method for implicit LES. J. Comput. Phys. 213(1), 413–436 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Hu, X.Y., Wang, Q., Adams, N.A.: An adaptive central-upwind weighted essentially non-oscillatory scheme. J. Comput. Phys. 229(23), 8952–8965 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Jiang, G.S., Shu, C.W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys 126, 202–228 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Johnsen, E., Larsson, J., Bhagatwala, A.V., Cabot, W.H., Moin, P., Olson, B.J., Rawat, P.S., Shankar, S.K., Sjögreen, B., Yee, H.C., et al.: Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves. J. Comput. Phys. 229(4), 1213–1237 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Kawai, S., Shankar, S.K., Lele, S.K.: Assessment of localized artificial diffusivity scheme for large-eddy simulation of compressible turbulent flows. J. Comput. Phys. 229(5), 1739–1762 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Kim, K.H., Kim, C.: Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows: Part II: Multi-dimensional limiting process. Journal of Computational Physics 208(2), 570–615 (2005)zbMATHCrossRefGoogle Scholar
  17. 17.
    Lesieur, M., Ossia, S.: 3D isotropic turbulence at very high Reynolds numbers: EDQNM study. Journal of Turbulence 1(7), 1–25 (2000)Google Scholar
  18. 18.
    Sagaut, P.: Large eddy simulation for incompressible flows: an introduction. Springer (2006)Google Scholar
  19. 19.
    Shu, C.W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes, II. J. Comput. Phys. 83(1), 32–78 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Skrbek, L., Stalp, S.R.: On the decay of homogeneous isotropic turbulence. Physics of Fluids 12, 1997 (2000)CrossRefGoogle Scholar
  21. 21.
    Thornber, B., Mosedale, A., Drikakis, D.: On the implicit large eddy simulations of homogeneous decaying turbulence. J. Comput. Phys. 226(2), 1902–1929 (2007)zbMATHCrossRefGoogle Scholar
  22. 22.
    Thornber, B., Mosedale, A., Drikakis, D., Youngs, D., Williams, R.J.R.: An improved reconstruction method for compressible flows with low Mach number features. J. Comput. Phys. 227(10), 4873–4894 (2008)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • X. Y. Hu
    • 1
  • N. A. Adams
    • 1
  1. 1.Institute of Aerodynamics and Fluid MechanicsTechnical Univeristy of MunichGermany

Personalised recommendations