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On the Eddy Viscosity Associated with the Subgrid Stresses

  • A. CimarelliEmail author
  • A. Abbà
  • M. Germano
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 25)

Abstract

Thanks to its simplicity and robustness, the models based on the eddy viscosity concept represent the most common procedure to introduce the effect of the unresolved scales in the equations of motion for the Large Eddy Simulation (LES) approach. Indeed, the subgrid scale (sgs) viscosity approach allows from an energetic point of view to respect the dissipative nature of turbulence.

References

  1. 1.
    Abbà, A., Cercignani, C., Valdettaro, L.: Analysis of subgrid scale models. Comput. Math. Appl. 46, 521–535 (2003)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Abbà, A., Bonaventura, L., Nini, M., Restelli, M.: Dynamic models for large eddy simulation of compressible flows with a high order DG method. Comput. Fluids 122, 209–222 (2015).  https://doi.org/10.1016/j.compfluid.2015.08.021MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Abbà, A., Campaniello, D., Nini, M.: Filter size definition in anisotropic subgrid models for large eddy simulation on irregular grids. J. Turbul. 18(6), 589–610 (2017).  https://doi.org/10.1080/14685248.2017.1312001MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bardina, J., Ferziger, J., Reynolds, W.: Improved subgrid scale models for large eddy simulation. AIAA Paper 801357 (1980)Google Scholar
  5. 5.
    Carati, D., Cabot, W.: Anisotropic eddy viscosity models. In: Proceedings of the Summer Program - Center for Turbulence Research, pp. 249–259 (1996)Google Scholar
  6. 6.
    Cimarelli, A., De Angelis, E.: Anisotropic dynamics and subgrid energy transfer in wall-turbulence. Phys. Fluids 24, 015102 (2012)CrossRefGoogle Scholar
  7. 7.
    Clark, R.A., Ferziger, J.H., Reynolds, W.C.: Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1–16 (1979)CrossRefGoogle Scholar
  8. 8.
    Colosqui, C., Oberai, A.: Generalized Smagorinsky model in physical space. Comput. Fluids 37, 207217 (2008)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Gallerano, F., Napoli, E.: A dynamic subgrid-scale tensorial eddy viscosity model. Contin. Mech. Thermodyn. 11, 114 (1999)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Germano, M.: A proposal for a redefinition of the turbulent stresses in the filtered Navier-Stokes equations. Phys. Fluids 29, 2323–2324 (1986)CrossRefGoogle Scholar
  11. 11.
    Germano, M.: Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336 (1992)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Germano, M.: A direct relation between the filtered subgrid stress and the second order structure function. Phys. Fluids 19, 038102 (2007)CrossRefGoogle Scholar
  13. 13.
    Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1765 (1991)CrossRefGoogle Scholar
  14. 14.
    Horiuty, K.: A proper velocity scale for modelling subgrid-scale eddy viscosities in large eddy simulation. Phys. Fluids A 5(1), 146–157 (1993)CrossRefGoogle Scholar
  15. 15.
    Leonard, A.: Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18, 237–248 (1974)CrossRefGoogle Scholar
  16. 16.
    Piomelli, U., Amirreza, R., Geurts, B.J.: A grid-independent length scale for large-eddy simulations. J. Fluid Mech. 766, 499–527 (2015)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Scotti, A., Meneveau, C., Lilly, D.: Generalized Smagorinsky model for anisotropic grids. Phys. Fluids 5(9), 23062308 (1993)CrossRefGoogle Scholar
  18. 18.
    Smagorinsky, J.: General circulation experiments with the primitive equations. Mon. Weather Rev. 91(3), 99–164 (1963)CrossRefGoogle Scholar
  19. 19.
    Vreman, B., Geurts, B., Kuerten, H: Subgrid-modelling in LES of compressible flows. In: Proceedings of the First ERFOCTAC Workshop on Direct and Large Eddy Simulation. Guildford (1994)Google Scholar
  20. 20.
    Vreman, B., Geurts, B., Kuerten, H.: Large-eddy simulation of the temporal mixing layer using the Clark model. Theoret. Comput. Fluid Dyn. 8, 309–324 (1996)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Industriale e Scienze MatematicheUniversità Politecnica delle MarcheAnconaItaly
  2. 2.Department of Aerospace Science and TechnologyPolitecnico di MilanoMilanItaly
  3. 3.Department of Civil and Environmental EngineeringDuke UniversityDurhamUSA

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