Skip to main content
SpringerLink
Log in

A Computational Comparison of Two FEM Solvers for Nonlinear Incompressible Flow

  • Conference paper
Challenges in Scientific Computing - CISC 2002

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 35))

Abstract

In this comparative study, we examine the influence of two different FEM discretization techniques (conforming Q2/Pinonconforming Q1/Qo Stokes element) and solution procedures (nonlinear Newton variants and multigrid vs. Krylov-space solvers for the linear subproblems) onto the approximation properties and particularly the total efficiency of corresponding CFD simulation tools. We discuss algorithmic details and give numerical results for laminar incompressible flow examples including non-Newtonian behavior ofpower law type.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Baranger and K. Najib. Analyse numerique des écoulements quasi-newtoniens dont la viscosity obeit la loi puissance ou la loi de carreau.Numer. Math., 58:3549, 1990.

    Article  MathSciNet  Google Scholar 

  2. R. Bramley and X. Wang. SPLIB:A library of iterative methods for sparse linear systems. Department of Computer Science, Indiana University,Bloomington,IN,1997.http://www.cs.indiana.edu/ftp/bramley/splib.tar.gz/ftp/bramley/splib.tar.gz

    Google Scholar 

  3. C. S. Brenner. Korn’s inequalities for piecewise H1vector fields.IMI Preprint Series, 5:1–21, 2002.

    Google Scholar 

  4. P. Hansbo and M. G. Larson. A simple nonconforming bilinear element for the elasticity problem. InCIMNEBarcelona, Spain, 2001.

    Google Scholar 

  5. J. Hron, J. Málek, J. Neéas, and K. R. Rajagopal. Numerical simulations and global existence of solutions of two dimensional flows of fluids with pressure and shear dependent viscosities.Math. Comp. Sim., 2002. to appear.

    Google Scholar 

  6. D. Kuzmin, M. Möller, and S. Turek. Multidimensional fem-fct schemes for arbitrary time-stepping.J. Comp. Phys., 2002. (to appear).

    Google Scholar 

  7. A. Ouazzi, R. Schmachtel, and S. Turek. Multigrid methods for stabilized nonconforming finite elements for incompressible flow involving the deformation tensor formulation.J. Numer. Math.10:235–248, 2002.

    MathSciNet  MATH  Google Scholar 

  8. A. Prohl and M. Rúziéka. On fully implicit space-time discretization for motions of incompressible fluids with shear-dependent viscosity: the case p < 2. SIAMJ. Numer. Anal.39:214–249, 2001.

    Article  MATH  Google Scholar 

  9. R. Rannacher and S. Turek. A simple nonconforming quadrilateral stokes element.Numer. Meth. Part. Diff. Equ.8:97–111, 1992.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. D. Schaeffer. Instability in the evolution equations describing incompressible granular flow.J. Diff. Eq.66:19–50, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Schäfer and S. Turek. Benchmark computations of laminar flow around cylinder. In E.H. Hirschel, editorFlow Simulation with High-Performance Computers II, volume 52 of Notes on Numerical Fluid Mechanicspages 547–566. Vieweg, 1996.

    Chapter  Google Scholar 

  13. R. Schmachtel.Robuste lineare und nichtlineare Lösungsverfahren für die inkompressiblen Navier-Stokes-Gleichungen. PhD thesis, University of Dortmund, 2002. (to be published).

    Google Scholar 

  14. S. Turek.Efficient solvers for incompressible flow problems: An algorithmic and computational approachvolume 6 ofLNCSE.Springer, Berlin, 1999.

    Google Scholar 

  15. S. Turek et al. FEATFLOW -Finite element software for the incompressible Navier-Stokes equations: User Manual, Release1.2, 1999.http://www.featflow.de

    Google Scholar 

  16. S. Turek and S. Kilian.The Virtual Album of Fluid Motion.Multimedia DVD. Springer, 2002.http://www.featflow.de/album

    Google Scholar 

  17. H. A. van der Vorst. Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems.SIAM J. Sci. Stat. Comput.13(2):631–644, 1992.

    Article  MATH  Google Scholar 

  18. S. P. Vanka. Implicit multigrid solutions of navier-stokes equations in primitive variables.J. Comp. Phys.65:138–158, 1985.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics, University of Dortmund, Vogelpothsweg 87, Dortmund, 44227, Germany

    Jaroslav Hron, Abderrahim Ouazzi & Stefan Turek

Authors
  1. Jaroslav Hron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abderrahim Ouazzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stefan Turek
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Weierstrass-Institut für AngewandteAnalysis und Stochastik, Mohrenstr. 39, Berlin, 10117, Germany

    Eberhard Bänsch

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hron, J., Ouazzi, A., Turek, S. (2003). A Computational Comparison of Two FEM Solvers for Nonlinear Incompressible Flow. In: Bänsch, E. (eds) Challenges in Scientific Computing - CISC 2002. Lecture Notes in Computational Science and Engineering, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19014-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-19014-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62406-3

  • Online ISBN: 978-3-642-19014-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation