A finite element variational multiscale method for computations of turbulent flow over an aerofoil

Article
  • 160 Downloads

Abstract

Numerical simulation of turbulent flows over different aerofoil configurations are presented in this paper. The incompressible fluid flow is described by the time-dependent incompressible Navier–Stokes equations. Further, a finite element variational multiscale method is used to simulate the turbulent flows. Computation over a cylinder and different variants of aerofoils are presented. The obtained numerical results demonstrate the capabilities of variational multiscale methods.

Keywords

Turbulent flows Incompressible Navier–Stokes Multiscale method Finite elements 

References

  1. 1.
    Davidson, P.A.: Turbulence: An Introduction for Scientists and Engineers. Oxford University Press, Oxford (2004)Google Scholar
  2. 2.
    Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)CrossRefMATHGoogle Scholar
  3. 3.
    Chen, H.C., Patel, V.C., Ju, S.: Solutions of Reynolds-averaged Navier–Stokes equations for three-dimensional incompressible flows. J. Comput. Phys. 88, 305–336 (1990)CrossRefMATHGoogle Scholar
  4. 4.
    Fischer, P., Iliescu, T.: Large eddy simulation of turbulent channel flows by the rational les model. Phys. Fluids 15, 3036–3047 (2003)CrossRefGoogle Scholar
  5. 5.
    Guermond, J.L., Oden, J.T., Prudhomme, S.: Mathematical perspectives on large eddy simulation models for turbulent flows. J. Math. Fluid Mech. 6, 194–248 (2004)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Rogallo, R.S., Moin, P.: Numerical simulation of turbulent flows. Ann. Rev. Fluid Mech 16, 99–137 (1984)CrossRefGoogle Scholar
  7. 7.
    Sagaut, P.: Large Eddy Simulation for Incompressible Flows, 2nd edn. Springer, Berlin (2002)CrossRefMATHGoogle Scholar
  8. 8.
    Hughes, T.J.R.: Multiscale phenomena: green’s functions, the dirichlet to neumann formulation, subgrid scale models, bubbles and origins of stabilized methods. Comput. Methods Appl. Mech. Eng. 127, 387–401 (1995)CrossRefGoogle Scholar
  9. 9.
    Hughes, T.J.R., Feijoo, G.R., Mazzei, L., Quincy, J.B.: The variational multiscale method—a paradigm for computational mechanics. Comput. Methods Appl. Mech. Eng. 166, 3–24 (1998)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Collis, S.S.: Monitoring unresolved scales in multiscale turbulence modelling. Phys. Fluids 13(6), 1800–1806 (2001)CrossRefGoogle Scholar
  11. 11.
    Gamnitizer, P., Gravemeier, V., Wall, W.A.: Advances in variational multiscale methods for turbulent flows. In: de Borst, R., Ramm, E. (eds.) Multiscale Methods in Computational Mechanics. Lecture Notes in Applied and Computational Mechanics, pp. 39–52. Springer, Berlin (2011)Google Scholar
  12. 12.
    Gravemeier, V.: The variational multiscale methods for laminar and turbulent incompressible flows. Phd thesis, Institute of Structural Mechanics, University of Stuttgart (2003)Google Scholar
  13. 13.
    John, V.: On large eddy simulation and variational multiscale methods in the numerical simulation of turbulent incompressible flows. Appl. Math. 51(4), 321–353 (2006)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    John, V., Kaya, S., Layton, W.J.: A two-level variational multiscale method for convection-dominated convection diffusion equations. Comput. Methods Appl. Mech. Eng. 195, 4594–4603 (2006)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    John, V., Layton, W.J.: Subgrid scale eddy viscosity models and variational multiscale methods. Technical report TR-MATH 03–05. University of Pittsburgh (2003)Google Scholar
  16. 16.
    John, V., Kaya, S.: Finite element error analysis of a variational multiscale method for Navier–Stokes equations. Adv. Comp. Math. 28, 43–61 (2008)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    John, V.: Large Eddy Simulation of Turbulent Incompressible Flows. Analytical and Numerical Results for a Class of LES Models. Lecture Notes in Computational Science and Engineering. Springer, Berlin (2004)CrossRefMATHGoogle Scholar
  18. 18.
    Gamnitizer, P., Gravemeier, V., Wall, W.A.: Time-dependent subgrid scales in residual-based large eddy simulation. Comput. Methods Appl. Mech. Eng. 199, 819–827 (2010)CrossRefGoogle Scholar
  19. 19.
    Hughes, T.J.R., Mazzei, L., Jensen, K.E.: Large eddy simulation and variational multiscale methods. Comput. Vis. Sci. 3, 47–59 (2000)CrossRefGoogle Scholar
  20. 20.
    Hughes, T.J.R., Oberai, A.A., Mazzei, L.: Large eddy simulation of turbulent channel flows by the variational multiscale method. Phys. Fluids 13(6), 1784–1799 (2001)CrossRefGoogle Scholar
  21. 21.
    Gravemeier, V., Wall, W.A., Ramm, E.: A three level finite element method for instationary incompressible Navier–Stokes equations. Comput. Methods Appl. Mech. Eng. 193, 1323–1366 (2004)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Gravemeier, V., Wall, W.A., Ramm, E.: Large eddy simulation of turbulent incompressible flows by a three-level finite element method. Int. J. Numer. Methods Fluids 48, 1067–1099 (2005)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Masud, A., Calderer, R.: A variational multiscale method for incompressible turbulent flows: bubble functions and fine scale fields. Comput. Methods Appl. Mech. Eng. 200, 2577–2593 (2011)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    John, V., Kaya, S.: A finite element variational multiscale method for the Navier–Stokes equation. SIAM J. Sci. Comput. 26(5), 1485–1503 (2005)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Gravemeier, V.: Scale-seperating operators for variational multiscale large eddy simulation of turbulent flows. J. Comput. Phys. 212, 400–435 (2006)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Indian Institute of Technology Madras 2015

Authors and Affiliations

  1. 1.Numerical Mathematics and Scientific Computing, SERCIndian Institute of ScienceBangaloreIndia

Personalised recommendations