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Efficient Simulation of Incompressible Viscous Flows on Parallel Computers

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Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NONUFM,volume 48))

Summary

A parallel multigrid method for the prediction of laminar and turbulent flows in complex geometries is described. Geometrical complexity is handled by a block structuring technique, which also constitutes the base for the parallelization of the method by grid partitioning. Automatic load balancing is implemented through a special mapping procedure. High numerical efficiency is obtained by a global nonlinear multigrid method with a pressure-correction smoother also ensuring only slight deteriotation of the convergence rate with increasing processor numbers. By various numerical experiments the method is investigated with respect to its numerical and parallel efficiency. The results illustrate that the high performance of the underlying sequential multigrid algorithm can be largely retained in the parallel implementation and that the proposed method is well suited for solving complex flow problems on parallel computers with high efficiency.

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References

  1. L. Bai, K. Mitra, M. Fiebig, and A. Kost. A multigrid method for predicting periodically fully developed flow. Int. J. Num. Meth. in Fluids, 18:843–852, 1994.

    Article  MATH  Google Scholar 

  2. B. Basara, F. Durst, and M. Schäfer. A Parallel Multigrid Method for the Prediction of Turbulent Flows with Reynolds Stress Closure. In Parallel Computational Fluid Dynamics 95, Elsevier, Amsterdam, 1996, in press.

    Google Scholar 

  3. U. Bückle, F. Durst, B. Howe, and A. Melling. Investigation of a floating element flowmeter. Flow Meas. Instrum., 4:215–225, 1992.

    Article  Google Scholar 

  4. U. Bückle, Y. Katoh, M. Schäfer, K. Suzuki, and K. Takashiba. The Application of Modern Numerical Tools to the Investigation of Transport Phenomena Related to Czochralski Crystal Growth Processes. In Proc. Int. Symp. on Heat and Mass Transfer, Kyoto, 1994.

    Google Scholar 

  5. I. Demirdžić and M. Perić. Finite volume method for prediction of fluid flow in arbitrary shaped domains with moving boundaries. Int. J. Num. Meth. in Fluids, 10: 771–790, 1990.

    Article  MATH  Google Scholar 

  6. F. Durst, L. Kadinski, and M. Schäfer. A Multigrid Solver for Fluid Flow and Mass Transfer Coupled with Grey-Body Surface Radiation for the Numerical Simulation of Chemical Vapor Deposition Processes. J. Cryst. Growth, 146:202–208, 1995.

    Article  Google Scholar 

  7. F. Durst and M. Schäfer. A Parallel Blockstructured Multigrid Method for the Prediction of Incompressible Flows. Int. J. for Num. Meth. in Fluids, 22:1–17, 1996.

    Article  Google Scholar 

  8. W. Hackbusch. Multi-Grid Methods and Applications. Springer, Berlin, 1985.

    MATH  Google Scholar 

  9. C. Hirsch. Numerical Computation of Internal and External Flows. Wiley, Chichester, 1988.

    MATH  Google Scholar 

  10. M. Hortmann, M. Peric, and G. Scheuerer. Finite volume multigrid prediction of laminar natural convection: Benchmark solutions. Int. J. Num. Meth. in Fluids, 11:189–207, 1990.

    Article  MATH  Google Scholar 

  11. M. Hortmann, M. Pophal, M. Schäfer, and K. Wechsler. Computation of Heat Transfer with Methods of High Performance Scientific Computing. In B. Hertzberger and G. Serazzi, editors, High-Performance Computing and Networking, V. 919 of Lecture Notes in Computer Science, pp. 293–299, Springer, Berlin, 1995.

    Chapter  Google Scholar 

  12. M. Hortmann and M. Schäfer. Numerical prediction of laminar flow in plane, bifurcating channels. Comput. Fluid Mech., 2:65–82, 1994.

    Google Scholar 

  13. P. Khosla and S. Rubin. A Diagonally Dominant Second-Order Accurate Implicit Scheme. Computers and Fluids, 2:207–209, 1974.

    Article  MATH  Google Scholar 

  14. B. Launder and B. Spalding. The numerical computation of turbulent flows. Comp. Meth. Appl Mech. Eng., 3:269–289, 1974.

    Article  MATH  Google Scholar 

  15. F. Lien and M. Leschziner. Multigrid Acceleration for Recirculating Laminar and Turbulent Flows Computed with a Non-Orthogonal, Collocated Finite-Volume Scheme. Comp. Meth. Appl Mech. Eng., 118:351–371, 1994.

    Article  MATH  Google Scholar 

  16. Ž. Lilek, M. Perić, and V. Seidl. Development and Application of a Finite Volume Method for the Prediction of Complex Flows. In this publication.

    Google Scholar 

  17. S. Patankar and B. Spalding. A calculation procedure for heat, mass and momentum transfer in three dimensional parabolic flows. Int. J. Heat Mass Transf:, 15:1787–1806, 1972.

    Article  MATH  Google Scholar 

  18. R. Pelz, A. Ecer, and J. Häuser (editors). Parallel Computational Fluid Dynamics’ 92. North-Holland, Amsterdam, 1993.

    MATH  Google Scholar 

  19. M. Peric. A Finite Volume Method for the Prediction of Three-Dimensional Fluid Flow in Complex Ducts. PhD Thesis, University of London, 1985.

    Google Scholar 

  20. M. Peric. Analysis of pressure-velocity coupling on nonorthogonal grids. Num. Heat Transf., Part B, 17:63–82, 1990.

    Article  MATH  Google Scholar 

  21. M. Peric, R. Kessler, and G. Scheuerer. Comparison of finie-volume numerical methods with staggered and colocated grids. Computers and Fluids, 16:389–403, 1988.

    Article  MATH  Google Scholar 

  22. M. Peric and E. Schreck. Computation of fluid flow with a parallel multigrid solver. Int. J. Num. Meth. in Fluids, 16:303–327, 1993.

    Article  MATH  Google Scholar 

  23. K. Reinsch, W. Schmidt, A. Ecer, J. Häuser, and J. Periaux (editors). Parallel Computational Fluid Dynamics’ 91. North-Holland, Amsterdam, 1992.

    MATH  Google Scholar 

  24. C. Rhie and W. Chow. Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA Journal, 21:1525–1532, 1983.

    Article  MATH  Google Scholar 

  25. M. Schäfer, E. Schreck, and K. Wechsler. An Efficient Parallel Solution Technique for the Incompressible Navier-Stokes Equations. In F.-K. Hebeker, R. Rannacher, and G. Wittum, editors, Numerical Methods for the Navier-Stokes Equations, V. 47 of Notes on Numerical Fluid Mechanics, pp. 228–238, Vieweg, Braunschweig, 1994.

    Google Scholar 

  26. M. Schäfer and S. Turek. Benchmark Computations of Laminar Flow Around a Cylinder. In this publication.

    Google Scholar 

  27. H. Stone. Iterative solution of implicit approximations of multi-dimensional partial differential equations. SIAM J. Num. Anal., 5:530–558, 1968.

    Article  MATH  Google Scholar 

  28. K. Wechsler, I. Rangelow, Z. Borkowicz, F. Durst, L. Kadinski, and M. Schäfer. Experimental and Numerical Study of the Effects of Neutral Transport and Chemical Kinetics on Plasma Etching System CF4/Si. In Proc. Int. Symp. Plasma Etching, pp. 909–914, 1993.

    Google Scholar 

  29. D. Wilcox. Turbulence Modeling for CFD. DCW Industries, La Canada, 1993.

    Google Scholar 

  30. G. Wittum. On the Convergence of Multi-Grid Methods with Transforming Smoothers. Num. Math., 57:15–38, 1990.

    Article  MathSciNet  MATH  Google Scholar 

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

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Durst, F., Schäfer, M., Wechsler, K. (1996). Efficient Simulation of Incompressible Viscous Flows on Parallel Computers. In: Hirschel, E.H. (eds) Flow Simulation with High-Performance Computers II. Notes on Numerical Fluid Mechanics (NNFM), vol 48. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89849-4_7

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  • DOI: https://doi.org/10.1007/978-3-322-89849-4_7

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-322-89851-7

  • Online ISBN: 978-3-322-89849-4

  • eBook Packages: Springer Book Archive

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