Skip to main content

Multigrid for the steady-state incompressible Navier-Stokes equations: A survey

  • Invited Lectures
  • Conference paper
  • First Online:
11th International Conference on Numerical Methods in Fluid Dynamics

Part of the book series: Lecture Notes in Physics ((LNP,volume 323))

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdalass, E.M.: Resolution performante du probleme de Stokes par mini-elements, maillages auto-adaptatifs et methodes multigrilles — applications. Ph.D. Thesis, Ecole Centrale de Lyon, 1987

    Google Scholar 

  2. Barcus, M.; Peric, M.; Scheuerer, G.: A control volume based full multigrid procedure for the prediction of two-dimensional, laminar, incompressible flows. Proceedings of the 7th GAMM-Conference on Numerical Methods in Fluid Mechanics, Louvain-la-Neuve, Belgium, Vieweg-Verlag, 1987

    Google Scholar 

  3. Brandt, A.: Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics. Monograph, GMD-Studien 85, 1984

    Google Scholar 

  4. Brandt, A.; Dinar, N.: Multigrid solutions to elliptic flow problems. In “Numerical Methods for PDE” (Parter, S.V., ed.), Academic Press, 1984

    Google Scholar 

  5. Brezzi, F.; Pitkäranta, J.: On the stabilization of finite-element approximations of the Stokes equations. In “Efficient Solutions of Elliptic Systems” (Hackbusch, W., ed.), Notes on Numerical Fluid Mechanics 10, Vieweg-Verlag, 1984, pp.11–19

    Google Scholar 

  6. Fuchs, L.; Zhao, H.S.: Solution of three-dimensional viscous incompressible flows by a multigrid method. Int. J. Numer. Methods in Fluids 4, 1984, pp. 539–555

    Google Scholar 

  7. Fuchs, L.: Multigrid schemes for incompressible flows. In “Efficient Solution of Elliptic Systems” (Hackbusch, W., ed.), Notes on Numerical Fluid Mechanics 10, Vieweg Verlag, 1984, pp. 38–51

    Google Scholar 

  8. Linden, J.; Steckel, B.; Stüben, K.: Parallel multigrid solution of the Navier-Stokes equations on general 2D-domains. To appear in: Parallel Computing 1988, North Holland (in press

    Google Scholar 

  9. Lonsdale, G.: Solution of a rotating Navier-Stokes problem by a nonlinear multigrid algorithm. J. Comp. Phys. 74, 1988, pp. 177–190

    Google Scholar 

  10. Niestegge, A.; Witsch, K.: Analysis of a multigrid Stokes solver. To be submitted to AMC

    Google Scholar 

  11. Patankar, S.V.: Numerical heat transfer and fluid flow. Hemisphere, Washington DC-New York, 1980

    Google Scholar 

  12. Peric, M.: A finite volume method for the prediction of three-dimensional fluid flow in complex ducts. Ph.D. Thesis, Mech. Eng. Dept., Imperial College, London, 1985

    Google Scholar 

  13. Shaw, G.J.; Sivalagonathan, S.: On the smoothing properties of the SIMPLE pressurecorrection algorithm. Int. J. Numer. Methods Fluids 8, 1988, pp.441–461

    Google Scholar 

  14. Solchenbach, K.; Trottenberg, U.: On the multigrid acceleration approach in computational fluid dynamics. GMD-Arbeitspapier 251, 1987

    Google Scholar 

  15. Stüben, K.; Linden, J.: Multigrid methods: An overview with emphasis on grid generation processes. Proceedings “Numerical Grid Generation in Computational Fluid Dynamics” (Häuser, J.; Taylor, C., eds.), Pineridge Press, Swansea, 1986, pp. 483–509

    Google Scholar 

  16. Stüben, K; Trottenberg, U.: Multigrid methods: Fundamental algorithms, model problem analysis and applications. In “Multigrid Methods” (Hackbusch, W.; Trottenberg, U., eds.), Lecture Notes in Mathematics 960, Springer-Verlag, 1982, pp. 1–176

    Google Scholar 

  17. Vanka, S.P.: Block-implicit multigrid solution of Navier-Stokes equations in primitive variables. J. Comp. Phys. 65, 1986, pp.138–156

    Google Scholar 

  18. Wittum, G.: Distributive Iterationen für indefinite Systeme als Glätter in Mehrgitterverfahren am Beispiel der Stokes-und Navier-Stokes-Gleichungen mit Schwerpunkt auf unvollständigen Zerlegungen. Dissertation, University of Kiel, 1986

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

D. L. Dwoyer M. Y. Hussaini R. G. Voigt

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Linden, J., Lonsdale, G., Steckel, B., Stüben, K. (1989). Multigrid for the steady-state incompressible Navier-Stokes equations: A survey. In: Dwoyer, D.L., Hussaini, M.Y., Voigt, R.G. (eds) 11th International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51048-6_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-51048-6_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51048-2

  • Online ISBN: 978-3-540-46141-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics