A Comparison of Smoothers and Numbering Strategies for Laminar Flow Around a Cylinder

  • Henrik Rentz-Reichert
  • Gabriel Wittum
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NONUFM, volume 48)


We introduce several multigrid smoothers for the incompressible Navier-Stokes equations in 2 space dimensions on unstructured grids and compare their performance for the DFG-bench markproblem of laminar flow around a cylinder depending on the kinematic viscosity. We further employ a streamwise numbering strategy of the unknowns and compare it to the hierarchical ordering the refinement module creates as well as to standard lexicographic numbering.


Unstructured Grid Numbering Strategy Increase Reynolds Number Multi Grid Method Approximate Inverse 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [ABF]
    Arnold, D.N., Brezzi, F., Fortin M.: A stable finite element for the Stokes equations, Calcolo, 21 (1984) 337–344.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [BW]
    Bey, J., Wittum, G.: Downwind Numbering: A Robust Multigrid Method for Convection-Diffusion Problems on Unstructerd Grids, Preprint 1995/2, ICA, Universität Stuttgart.Google Scholar
  3. [BD]
    Brandt, A., Dinar, N.: Multigrid solutions to elliptic flow problems. ICASE Report 79-15 (1979).Google Scholar
  4. [DJRST]
    Dorok, O., John, V., Risch, U., Schieweck, F., Tobiska, L.: Parallel Finite Element Methods for the Incompressible Navier-Stokes Equations. In this publication.Google Scholar
  5. [DSW]
    Durst, F., Schäfer, M., Wechsler, K.: Efficient Simulation of Incompressible Viscous Flows on Parallel Computers. In this publication.Google Scholar
  6. [LPS]
    Lilek, Z., Peric, M., Seidl, V.: Development and Application of a Finite Volume Method for the Prediction of Complex Flows. In this publication.Google Scholar
  7. [PS]
    Patankar, S. V, Spalding, D.B.: A calculation procedure for heat and mass transfer in threedimensional parabolic flows. Int. J. Heat Mass Transfer 15 (1972), 1787–1806.zbMATHCrossRefGoogle Scholar
  8. [Ra]
    Raw, M.J.: A New Control-Volume-Based Finite Element Procedure for the Numerical Solution of the Fluid Flow and Scalar Transport Equations, Ph.D. thesis, University of Waterloo, Ontario, Canada, 1985.Google Scholar
  9. [RW1]
    Reichert, H. (now Rentz-Reichert), Wittum, G.: Solving the Navier-Stokes Equations on Unstructured Grids. NNFM, Vol. 38, p. 321–333, Vieweg, Braunschweig 1993.Google Scholar
  10. [RW2]
    Reichert, H. (now Rentz-Reichert), Wittum, G.: Robust Multigrid Methods for the Incompressible Navier-Stokes-Equations. NNFM, Vol. 49, p. 216–228, Vieweg, Braunschweig 1995.Google Scholar
  11. [SR]
    Schneider, G.E., Raw, M.J.: Control volume finite-element method for heat transfer and fluid-flow using co-located variables. Numer.Heat.Transf. 11 (1988) 363.Google Scholar
  12. [Wil]
    Wittum, G.: On the Robustness of ILU-Smoothing. SISSC 10 (1989) 699–717.MathSciNetzbMATHGoogle Scholar
  13. [Wi2]
    Wittum, G.: Spektralverschobene Iterationen, Preprint 1995/4, ICA, Universität Stuttgart.Google Scholar
  14. [Wi3]
    Wittum, G.: Distributive Iterationen für indefinite Systeme. Ph. D. Thesis, Univ. Kiel, 1986.Google Scholar
  15. [VH]
    Vilsmeier, R., Hänel, D.: Computational Aspects of Flow Simulation on 3-D, Unstructured, Adaptive Grids. In this publication.Google Scholar

Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1996

Authors and Affiliations

  • Henrik Rentz-Reichert
    • 1
  • Gabriel Wittum
    • 1
  1. 1.Institut für Computeranwendungen IIIUniversität StuttgartStuttgartGermany

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