Numerical Simulation of Complex Fluid Flows on MIMD Computers

  • M. Perić
  • M. Schäfer
  • E. Schreck
Part of the Lecture Notes in Computer Science book series (LNCS, volume 732)


The paper analyses the efficiency of parallel computation of incompressible fluid flows using a fully implicit finite volume multigrid method. The parallelization is achieved via domain decomposition, which is chosen for its suitability in complex geometries when blockstructured or unstrucutured grids are employed. Numerical efficiency (increase of computing effort to reach converged solution) and parallel efficiency (increase of runtime due to local and global communication) are analysed for a typical recirculating flow induced by buoyancy. Good efficiencies are found and the possibilities for further improvement by avoiding some global communication or by simultaneous computation and communication are indicated.


Coarse Grid Domain Decomposition Outer Iteration Fine Grid Multigrid Method 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. Bastian and G. Horton: “Parallelization of robust multi-grid methods: ILU factorization and frequency decomposition method”, in W. Hackbusch and R. Rannacher (eds.), Notes on Numerical Fluid Mechanics, Vol. 30, Vieweg, Braunschweig, 1989, pp. 24–36.Google Scholar
  2. 2.
    I. Demirdäie and M. Perié:“Finite volume method for prediction of fluid flow in arbitrarily shaped domains with moving boundaries”, Int. J. Num. Methods in Fluids, 10, 771–790 (1990).Google Scholar
  3. 3.
    I. Demirdzie, 2. Lilek and M. Perié: “Fluid flow and heat transfer test problems for non-orthogonal grids: benchmark solutions”, Int. J. Num. Methods in Fluids, 15, 329–354 (1992).CrossRefGoogle Scholar
  4. 4.
    M. Hestens and E. Stiefel: “Methods of conjugate gradients for solving linear systems”, Nat. Bur. Standards J. Res., 49, 409–436 (1952).CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    M. Hortmann, M. Perié and G. Scheurer: “Finite volume multigrid prediction of laminar natural convection: bench-mark solutions”, Int. J. Numer. Methods Fluids, 11, 189–207 (1990).CrossRefMATHGoogle Scholar
  6. 6.
    S. V. Patankar and D. B. Spalding: “A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows”, Int. J. Heat Mass Transfer, 15, 1787–1806 (1972).CrossRefMATHGoogle Scholar
  7. 7.
    M. Perié, M. Schäfer and E. Schreck: “Computation of fluid flow with a parallel multi-grid solver”, in K.G. Reinsch et al. (Eds.), Proc. Int. Conference on “Parallel Computational Fluid Dynamics”, Elsevier, Amsterdam, 1991.Google Scholar
  8. 8.
    E. Schreck and M. Perié: “Computation of fluid flow with a parallel multi-grid solver”, Int. J. Num. Methods in Fluids, 16, 303–327 (1993).CrossRefGoogle Scholar
  9. 9.
    H.L. Stone: “Iterative solution of implicit approximations of multi-dimensional partional differential equations”, SIAM J. Numer. Anal., 5, 530–558 (1968).CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • M. Perić
    • 1
  • M. Schäfer
    • 1
  • E. Schreck
    • 1
  1. 1.Lehrstuhl für StrömungsmechanikUniversität Erlangen-NürnbergErlangenGermany

Personalised recommendations