Skip to main content

Abstract

This chapter is devoted to analyze the numerical performances of the models and numerical techniques that we have studied in the preceding chapters. It is intended to provide a starting guide to the numerical discretization of VMS models for students and researchers interested in the computation of turbulent flows. With this purpose we test the practical performances of the VMS models, in some relevant benchmark turbulent flows.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Albensoeder, S., Kuhlmann, H.C., Rath, H.J.: Three-dimensional centrifugal-flow instabilities in the lid-driven cavity problem. Phys. Fluids 13, 121–135 (2001)

    Article  Google Scholar 

  2. Armali, B.F., Durst, F., Pereira, J.C., Schönung, B.: Experimental and numerical study of backward-facing step flow. J. Fluid Mech. 127, 473–496 (1983)

    Article  Google Scholar 

  3. Auteri, F., Parolini, N., Quartapelle, L.: Numerical investigation on the stability of singular driven cavity flow. J Comput. Phys. 183, 1–25 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bazilevs, Y., Calo, V.M., Cottrell, J.A., Hughes, T. J.R., Reali, A., Scovazzi, G.: Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flow. Comp. Methods Appl. Mech. Eng. 197, 173–201 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Braack, M., Burman, E., John, V., Lube, G.: Stabilized finite element methods for the generalized Oseen problem. Comput. Methods Appl. Mech. Eng. 196, 853–866 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Berselli, L.C., Iliescu, T., Layton, W.J.: Mathematics of Large Eddy Simulation of Turbulent Flows. Springer, Berlin (2006)

    MATH  Google Scholar 

  7. Carati, D., Winckelmans, G.S., Jeanmart, H.: On the modeling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation. J. Fluid Mech. 441, 119 (2001)

    MATH  Google Scholar 

  8. Chacón Rebollo, T.: A term by term stabilzation algorithm for finite element solution of incompressible flow problems. Numer. Math. 79, 283–319 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  9. Chacón-Rebollo, T., Gómez-Mármol, M., Rubino, S.: Derivation of the Smagorinsky Model from a Galerkin Discretization. Mascot11 Proc.: IMACS Series in Comp. Appl. Math. 17, 61–70 (2013)

    Google Scholar 

  10. Chacón-Rebollo, T., Gómez-Mármol, M., Rubino, S.: Numerical analysis of a finite element projection-based VMS turbulence model with wall laws. Submitted to Appl. Numer. Math.

    Google Scholar 

  11. 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)

    Article  MATH  Google Scholar 

  12. Codina, R.: Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Comput. Methods. Appl. Mech. Eng. 91, 4295–4321 (2002)

    Article  MathSciNet  Google Scholar 

  13. Codina, R.: Comparison of some finite element methods for solving the diffusion-convection-reaction equation. Comput. Methods Appl. Mech. Eng. 156, 185–210 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  14. Dubois, T., Jauberteau, F., Temam, R.: Dynamic Multilevel Methods and the Numerical Simulation of Turbulence. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  15. Erturk, E.: Discussions on driven cavity flow. Int. J. Numer. Meth. Fluids 60, 275–294 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  16. Erturk, E.: Numerical solutions of 2-D steady incompressible flow over a backward-facing step, Part I: High Reynolds number solutions. Comput. Fluids 37, 633–655 (2008)

    MATH  Google Scholar 

  17. Fortin, M.: Finite element solution of the Navier-Stokes equations. Acta Numer. 239–284 (1993)

    Google Scholar 

  18. Galdi, G.P., Layton, W.J.: Approximation of the larger eddies in fluid motion II: a model for space-filtered flow. M3AS- Math. Mod. Meth. Appl. Sci. 10 (3), 343–350 (2000)

    Google Scholar 

  19. Ghia, U., Ghia, K.N. Shin, C.T.: High-re solutions for incompressible flow using the navier-stokes equations and a multigrid method. J. Comput. Physics 48, 387–411 (1982)

    Article  MATH  Google Scholar 

  20. Gravemeier, V.: The variational multiscale method for laminar and turbulent incompressible flow, PhD Thesis, Report No. 40, Institute of Structural Mechanics, University of Stuttgart (2003)

    Google Scholar 

  21. Gravemeier, V., Wall, W., Ramm, E.: A three-level finite element method for the in stationary incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 193, 1323–1366 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  22. Gravemeier, V., Wall, W., Ramm, E.: Large eddy simulation of turbulent incompressible flows by a three-level finite element method. Int. J. Numer. Meth. Fluids 48, 1067–1099 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  23. Gresho, P.M., Sani, R.L.: Incompressible Flow and the Finite Element Method. Wiley, New York (2000)

    MATH  Google Scholar 

  24. Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 29(7), 2323–2324 (1986)

    Article  MATH  Google Scholar 

  25. Hecht, F., Pironneau, O.: Freefem++. http://www.freefem.org.

  26. Henao, C.A.A., Coutinho, A.L.G.A., Franca, L.P.: A stabilized method for transient transport equations. Comput. Mech. 46(1), 199–204 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  27. Iliescu, T., Fischer, P.F.: Large eddy simulation of turbulent channel flows by the rational large eddy simulation model. Phys. Fluids 15, 3036–3047 (2003)

    Article  Google Scholar 

  28. Iliescu, J., John, V., Layton, W.J., Matthies, G., Tobiska, L.: A numerical study of a class of LES models. Int. J. Comp. Fluid Dyn. 17, 75–85 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  29. Jansen, K.E., Whiting, C.H., Hulbert, G.M.: A generalized-a method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comp. Methods Appl. Mech. Eng. 190, 305–319 (1999)

    Article  MathSciNet  Google Scholar 

  30. John, V.: Reference values for drag and lift of a two-dimensional time dependent flow around a cylinder. Int. J. Numer. Methods Fluids 44, 777–788 (2004)

    Article  MATH  Google Scholar 

  31. John, V., Kindle, A: Numerical study of finite element variational multiscale methods for turbulent flow simulations. Comput. Methods Appl. Mech. Eng. 199, 841–852 (2010)

    MATH  Google Scholar 

  32. Moin, P.: Advances in large eddy simulation methodology for complex flows. Int. J. Heat Fluid Flow 23, 710–720 (2002)

    Article  Google Scholar 

  33. Moin, P., Kim, J.: Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377 (1982)

    Article  MATH  Google Scholar 

  34. Moser, R., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to Re τ  = 590. Phys. Fluids 11, 943–945 (1999)

    Article  MATH  Google Scholar 

  35. Oswald, P.: On a BPX preconditioner for P 1 elements. Computing 51, 125–133 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  36. Prasad, A.K., Koseff, J.R.: Reynolds number and end-wall effects on a lid-driven cavity flow. Phys. Fluids A 1(2), 208–218 (1989)

    Article  Google Scholar 

  37. Peng, Y-H, Shiau, Y-H, Hwang, R.R.: Transition in a 2-D lid-driven cavity flow. Comput. Fluids 32, 337–352 (2003)

    Article  MATH  Google Scholar 

  38. Saad, Y., Schultz, M.H.: GMRES-A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856–869 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  39. Sagaut, P.: Large Eddy Simulation for Incompressible Flows. Springer, Belin (2002)

    Book  MATH  Google Scholar 

  40. Schlichting, H.: Boundary Layer Theory, 8th. edn. Springer, NewYork (2000)

    Google Scholar 

  41. Tiesinga, G., Wubs, F.W., Veldman, A.E.P.: Bifurcation analysis of incompressible flow in a driven cavity by the Newton–Picard method. J. Comput. Appl. Math. 140, 751–772 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  42. Zang, Y., Street, R.L., Koseff, J.R.: A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows. Phys. Fluids A 5(12), 3186–3196 (1993)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Chacón Rebollo, T., Lewandowski, R. (2014). Numerical Experiments. In: Mathematical and Numerical Foundations of Turbulence Models and Applications. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-0455-6_13

Download citation

Publish with us

Policies and ethics