Advertisement

An Adaptive-Smoothing Multigrid Method for the Navier-Stokes Equations

  • Dimitris Drikakis
  • Oleg Iliev
  • Daniela Vassileva
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 14)

Abstract

The paper presents the development and investigation of an adaptive-smoothing (AS) procedure in conjunction with a full multigrid (FMG) — full approximation storage (FAS) method. The latter has been developed by the authors [1] for solving the incompressible Navier-Stokes equations, in conjunction with the artificial-compressibility method and a characteristic-based discretisation scheme, and forms here the basis for investigating the AS approach. The principle of adaptive-smoothing is to exploit the non-uniform convergence behaviour of the numerical solution during the iterations in order to reduce the size of the computational domain and, thus, reduce the total computing time. The results show that significant acceleration of the multigrid flow computations can be achieved by using adaptive-smoothing.

Keywords

Fine Grid Multigrid Method Curve Channel Steady State Problem Adaptivity Criterion 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Drikakis, D., Iliev, O.P., Vassileva, D.P.: A nonlinear multigrid method for the three-dimensional incompressible Navier-Stokes equations. J. Comput. Phys. 146 (1998) 310–321CrossRefGoogle Scholar
  2. 2.
    Brandt, A.: A multilevel adaptive solutions of boundary value problems. Math. Comput. 31 (1977) 333–390zbMATHCrossRefGoogle Scholar
  3. 3.
    Rüde, U.: Fully adaptive multigrid methods. SIAM J. Numer. Anal 30 (1993) 230–248zbMATHCrossRefGoogle Scholar
  4. 4.
    Drikakis, D., Tsangaris, S.: Local solution acceleration method for the Euler and Navier-Stokes equations. AIAA J. 30 (1992) 340–348zbMATHCrossRefGoogle Scholar
  5. 5.
    Southwell, R.: Relaxation methods in engineering science - a treatise in approximate computation. Oxford University Press (1940)Google Scholar
  6. 6.
    Drikakis, D.: A parallel multiblock characteristic-based method for three-dimensional incompressible flows. Advances in Eng. Software 26 (1996) 111–119Google Scholar
  7. 7.
    Jameson, A.: Solution of the Euler Equations for 2-D Transonic Flow by a Multigrid Method. Appl. Math. and Comput. 13 (1983) 327–356MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Dimitris Drikakis
    • 1
  • Oleg Iliev
    • 2
  • Daniela Vassileva
    • 3
  1. 1.Department of EngineeringQueen Mary and Westfield College, University of LondonLondonUK
  2. 2.Institute for Industrial Mathematics (ITWM)KaiserslauternGermany
  3. 3.Institute of Mathematics and InformaticsBulgarian Academy of ScienceSofiaBulgaria

Personalised recommendations