Advertisement

Analysis of Truncation Errors and Design of Physically Optimized Discretizations

  • Stefan Hickel
  • Nikolaus A. Adams
Part of the Ercoftac Series book series (ERCO, volume 12)

Abstract

Further development of Large Eddy Simulation (LES) faces as major obstacle the strong coupling between subgrid-scale (SGS) model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and certain flow configurations the truncation error itself can act as implicit SGS model. In this paper, we explore how implicit SGS models can be derived systematically and propose a procedure for design, analysis, and optimization of nonlinear discretizations. Implicit LES can be made rigorous by requiring that the numerical dissipation approximates the SGS dissipation obtained from the analysis of nonlinear interactions in turbulence.

Keywords

Truncation error Optimization Subgrid-scale modeling Implicit LES 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adams NA, Hickel S, Franz S (2004) Implicit subgrid-scale modeling by adaptive deconvolution. J Comp Phys 200:412–431MATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Back T, Fogel D, Michalewicz Z (1997) Handbook of Evolutionary Computation. University Oxford Press.Google Scholar
  3. 3.
    Chollet J-P (1984) Two-point closures as a subgrid-scale modeling tool for large-eddy simulations. In: Durst F and Launder B (eds) Turbulent Shear Flows IV, Heidelberg:62–72. Springer, BerlinGoogle Scholar
  4. 4.
    Domaradzki JA, Adams NA (2002) Direct modeling of subgrid scales of turbulence in large-eddy simulations. J Turb 3, Art no 24ADSGoogle Scholar
  5. 5.
    Domaradzki JA, Radhakrishnan S (2005). Eddy viscosities in implicit large eddy simulations of decaying high Reynolds number turbulence with and without rotation. Fluid Dyn Res 36:385–406MATHCrossRefADSGoogle Scholar
  6. 6.
    Domaradzki JA., Xiao Z, Smolarkiewicz PK (2003). Effective eddy viscosities in implicit large eddy simulations of turbulent flows. Phys Fluids 15:3890–3893CrossRefADSGoogle Scholar
  7. 7.
    Fureby C, Tabor G, Weller HG, Gosman AD (1997). A comparative study of subgrid scale models in homogeneous isotropic turbulence. Phys Fluids 9:1416–1429MATHCrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Garnier E, Mossi M, Sagaut P, Comte P, Deville M (1999) On the use of shock-capturing schemes for large-eddy simulation. J Comput Phys 153:273–311MATHCrossRefADSGoogle Scholar
  9. 9.
    Ghosal S (1996) An analysis of numerical errors in large-eddy simulations of turbulence. J Comput Phys 125:187–206MATHCrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Grinstein F, Margolin L, Rider W (eds) (2007) Implicit large eddy simulation: computing turbulent flow dynamics. Cambridge University PressGoogle Scholar
  11. 11.
    Harten A, Engquist B, Osher S, Chakravarthy S (1987) Uniformly high order accurate essentially non-oscillatory schemes, III. J Comput Phys 71:231–303MATHCrossRefADSMathSciNetGoogle Scholar
  12. 12.
    Heisenberg W (1948) Zur statistischen Theorie der Turbulenz. Z Phys A 124:628–657MATHMathSciNetGoogle Scholar
  13. 13.
    Hickel S, Adams NA (2007) On implicit subgrid-scale modeling in wall-bounded flows. Phys Fluids 19, Art no 105106CrossRefADSGoogle Scholar
  14. 14.
    Hickel S, Adams NA, Domaradzki JA (2006) An adaptive local deconvolution method for implicit LES. J Comput Phys 213:413–436MATHCrossRefADSMathSciNetGoogle Scholar
  15. 15.
    Hickel S, Adams NA, Mansour NN (2007) Implicit subgrid-scale modeling for large-eddy simulation of passive-scalar mixing. Phys Fluids 19, Art no 095102CrossRefADSGoogle Scholar
  16. 16.
    Leonard A (1974) Energy cascade in large eddy simulations of turbulent fluid flows. Adv Geophys 18A:237–248ADSGoogle Scholar
  17. 17.
    Lesieur M (1997) Turbulence in Fluids, third edn. Kluwer, DordrechtMATHGoogle Scholar
  18. 18.
    LeVeque RJ (1992) Numerical methods for conservation laws Birkhäuser, BaselGoogle Scholar
  19. 19.
    Sagaut P (2005) Large-Eddy Simulation for Incompressible Flows, third edn. Springer, BerlinGoogle Scholar
  20. 20.
    Schumann U (1975) Subgrid scale model for finite-difference simulations of turbulence in plane channels and annuli. J Comput Phys 18:376–404MATHCrossRefADSMathSciNetGoogle Scholar
  21. 21.
    Spalart PR (1988) Direct simulation of a turbulent boundary layer up to Re_θ = 1410. J Fluid Mech 187:61–98MATHCrossRefADSGoogle Scholar
  22. 22.
    Stolz S, Adams NA (1999) An approximate deconvolution procedure for large-eddy simulation. Phys Fluids 11:1699–1701CrossRefADSMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Stefan Hickel
    • 1
  • Nikolaus A. Adams
    • 1
  1. 1.Institute of AerodynamicsTechnische Universität MünchenMünchenGermany

Personalised recommendations