Skip to main content
SpringerLink
Log in

Invariant subgrid modelling in large-eddy simulation of heat convection turbulence

  • Original Article
  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

Symmetries have an important role in turbulence. To some extent, they contain the physics of the equations (conservation laws, etc.), and it is essential that turbulence models respect them. However, as observed by Oberlack (Annual Research Briefs. Stanford University, Stanford 1997) and next by Razafindralandy and Hamdouni (Direct and Large-Eddy Simulation 6: Proceedings of the 6th International ERCOFTAC Workshop on Direct and Large-Eddy Simulation. Springer, Heidelberg, 2006) in the case of an isothermal fluid, only few subgrid stress tensor models preserve the symmetries of the Navier–Stokes equations. In this communication, we present the symmetries of the equations of a non-isothermal fluid flow and analyze some common subgrid stress tensor and flux models under the point of view of these symmetries.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bardina, J., Ferziger, J., Reynolds, W.: Improved turbulence models based on large eddy simulation of homogeneous, incompressible, turbulent flows. Tech. Rep. Report TF-19, Stanford University, Stanford (1983)

  2. Cannone, M.: Ondelettes, paraproduits et Navier-Stokes. Diderot Editeur, Arts et Sciences (1995)

  3. Cantwell B. (1978). Similarity transformations for the two-dimensional, unsteady, stream-function equation. J. Fluid Mech. 85: 257–271

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. Eidson T. (1985). Numerical simulation of the turbulent Rayleigh–Bénard problem using subgrid modelling. J. Fluid Mech. 158: 245–268

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. Fureby C., Tabor G. (1997). Mathematical and physical constraints on large-eddy simulations. Theor. Comput. Fluid Dyn. 9(2): 85–102

    Article  MATH  MathSciNet  Google Scholar 

  6. Fushchych W., Popowych R. (1994). Symmetry reduction and exact solutions of the Navier–Stokes equations I. J. Nonlin. Math. Phys. 1(1): 75–113

    Article  MATH  MathSciNet  Google Scholar 

  7. Hereman C. (1994). Review of symbolic software for the computation of Lie symmetries of differential equations. Euromath Bull. 1(2): 45–79

    MATH  MathSciNet  Google Scholar 

  8. Horiuti K. (1989). The role of the bardina model in large eddy simulation of turbulent channel flow. Phys. Fluids A 1(2): 426–428

    Article  ADS  Google Scholar 

  9. Ibragimov, N.: CRC handbook of Lie group analysis of differential equations, vol 1 Symmetries, exact solutions and conservation laws. CRC Press,West Palm Beach (1994)

  10. Ibragimov, N.: CRC handbook of Lie group analysis of differential equations, vol 3 New trends in theorical developments and computational methods. CRC Press, West Palm Beach (1996)

  11. Keating, A., Piomelli, U., Bremhorst, K., Nesic, S.: Large-eddy simulation of heat transfer downstream of a backward-facing step. J. Turbulence 5(20) (2004)

  12. Kim P., Olver P. (2004). Geometric integration via multi-space. Regular Chaotic Dyn. 9(3): 213–226

    Article  MATH  MathSciNet  Google Scholar 

  13. Lilly D. (1992). A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A4(3): 633–635

    ADS  MathSciNet  Google Scholar 

  14. Lindgren B., Österlund J., Johansson A. (2004). Evaluation of scaling laws derived from lie group symmetry methods in zero-pressure-gradient turbulent boundary layers. J. Fluid Mech. 502: 127–152

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. Nœther, E.: Invariante Variationsprobleme. In: Königliche Gesellschaft der Wissenschaften, pp. 235–257 (1918)

  16. Oberlack, M.: Invariant modeling in large-eddy simulation of turbulence. In: Annual Research Briefs. Stanford University, Stanford (1997)

  17. Oberlack M. (1999). Symmetries, invariance and scaling-laws in inhomogeneous turbulent shear flows. Flow Turbulence Combust. 62(2): 111–135

    Article  MATH  Google Scholar 

  18. Oberlack M., Cabot W., Pettersson Reif B., Weller T. (2006). Group analysis, direct numerical simulation and modelling of a turbulent channel flow with streamwise rotation. J. Fluid Mech. 562: 355–381

    Article  MathSciNet  Google Scholar 

  19. Olver P. (1986). Applications of Lie groups to differential equations. Graduate texts in mathematics. Springer, Heidelberg

    MATH  Google Scholar 

  20. Olver P. (2001). Geometric foundations of numerical algorithms and symmetry. Appli Algebra Eng. Commun. Comput. 11(5): 417–436

    Article  MATH  MathSciNet  Google Scholar 

  21. Peng, S.H., Davidson, L.: Comparison of subgrid-scale models in LES for turbulent convection flow with heat transfer. In: 2nd EF Conference in Turbulent Heat Transfer, vol. 1, pp. 5.25–5.35 (1998)

  22. Pukhnachev, V.: Invariant solution of Navier–Stokes equations describing motions with free boundary. Doklady Akademii Nauk SSSR, pp. 202–302 (1972)

  23. Razafindralandy, D., Hamdouni, A.: Consequences of symmetries on the analysis and construction of turbulence models. In: Symmetry, Integrability and Geometry: Methods and Applications vol. 2, Paper 052 (2006)

  24. Razafindralandy, D., Hamdouni, A.: Symmetry invariant subgrid models. In: Lamballais Friedrich, G.M. (ed.) Direct and Large-Eddy Simulation 6: Proceedings of the Sixth International ERCOFTAC Workshop on Direct and Large-Eddy Simulation. Springer, Heidelberg (2006)

  25. Razafindralandy D., Hamdouni A., Béghein C. (2007). A class of subgrid-scale models preserving the symmetry group of Navier–Stokes equations. Commun. Nonlin. Sci. Numer. Simul. 12(3): 243–253

    Article  MATH  Google Scholar 

  26. Razafindralandy, D., Hamdouni, A., Oberlack, M.: Analysis and development of subgrid turbulence models preserving the symmetry properties of the Navier–Stokes equations. To appear in Eur. J. Mech.B

  27. Speziale C. (1981). Some interesting properties of two-dimensional turbulence. Phys. Fluids 24: 1425–1427

    Article  MATH  ADS  Google Scholar 

  28. Ünal G. (1994). Application of equivalence transformations to inertial subrange of turbulence. Lie Group Appl. 1(1): 232–240

    MATH  Google Scholar 

  29. Vu K., Carminati J. (2000). Symbolic computation and differential equations: Lie symmetries. J. Symbolic Comput. 29(2): 95–116

    MATH  MathSciNet  Google Scholar 

  30. Wang L. (1997). Frame-indifferent and positive-denite Reynolds stress-strain relation. J. Fluid Mech. 352: 341–358

    Article  MATH  ADS  Google Scholar 

  31. Wang, L.: Physics-preserving turbulent closure models: SGS flux vectors of mass and energy. In: 3rd AFOSR International Conference on Direct Numerical Simulation and Large Eddy Simulation (TAICDL) (2001)

  32. Winckelmans, G., Wray, A., Vasilyev, O.: Testing of a new mixed model for LES: the Leonard model supplemented by a dynamic Smagorinsky term. In: Summer Program, pp. 367–388. Center for Turbulence Research, NASA Ames/Standford University (1998)

Download references

Author information

Authors and Affiliations

  1. LEPTAB, Avenue Michel Crépeau, 17042, La Rochelle Cedex 1, France

    Dina Razafindralandy & Aziz Hamdouni

Authors
  1. Dina Razafindralandy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aziz Hamdouni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dina Razafindralandy.

Additional information

Communicated by M.Y. Hussaini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Razafindralandy, D., Hamdouni, A. Invariant subgrid modelling in large-eddy simulation of heat convection turbulence. Theor. Comput. Fluid Dyn. 21, 231–244 (2007). https://doi.org/10.1007/s00162-007-0046-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-007-0046-1

Keywords

PACS

Search

Navigation