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Development and Application of a Finite Volume Method for the Prediction of Complex Flows

  • Ž. Lilek
  • M. Perić
  • V. Seidl
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NONUFM, volume 48)

Summary

In this paper the development and application of a finite volume method for the prediction of compressible and incompressible, laminar and turbulent, steady and unsteady flows in complex geometries is presented. The method uses quadrilateral (2D) or hexaedral (3D) control volumes, block-structured grids (which may not fit at block interfaces) and a colocated (cell-centered) arrangement of variables on the grid. The conservation equations for mass, momentum, energy, turbulent kinetic energy and its dissipation rate are solved iteratively in a sequential manner. Discretization methods up to fourth order were tested, but second order centered approximations, together with local grid refinement, were found to be the best compromise between accuracy, efficiency and ease of implementation. The efficiency is increased by using multigrid methods and parallel computing. Results of several example calculations are presented to demonstrate the efficiency and accuracy of the method.

Keywords

Mach Number Finite Volume Method Outer Iteration Multigrid Method Inviscid Flow 
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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References

  1. [1]
    Burmeister, J., AND Hackbusch, W. On a time and space parallel multi-grid method including remarks on filtering techniques. In Notes on Numerical Fluid Mechanics (1996), E. H. Hirschel, Ed., Vieweg, Braunschweig. In print.Google Scholar
  2. [2]
    Demirdžic, I., Lilek, Ž., AND Perić, M. Fluid flow and heat transfer test problems for non-orthogonal grids: Bench-mark solutions. International Journal for Numerical Methods in Fluids 15 (1992), 329–354.CrossRefGoogle Scholar
  3. [3]
    Demirdžić, I., lilek, Ž., AND Perić, M. A collocated finite volume method for predicting flows at all speeds. International Journal for Numerical Methods in Fluids 16 (1993), 1029–1050.zbMATHCrossRefGoogle Scholar
  4. [4]
    Demirdžić, I., AND Perić, M. Space conservation law in finite volume calculations of fluid flow. International Journal for Numerical Methods in Fluids 8 (1988), 1037–1050.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    Demirdžić, I., AND Perić, M. Finite volume method for prediction of fluid flow in arbitrary shaped domains with moving boundary. International Journal for Numerical Methods in Fluids 10 (1990), 771–790.zbMATHCrossRefGoogle Scholar
  6. [6]
    Drikakis, D. Private communication, Lehrstuhl für Strömungsmechanik, Universität Erlangen, 1992.Google Scholar
  7. [7]
    Durst, F., Schäfer, M., AND Wechsler, K. Efficient simulation of incompressible viscous flows on parallel computers. In Notes on Numerical Fluid Mechanics (1996), E. H. Hirschel, Ed., Vieweg, Braunschweig. In print.Google Scholar
  8. [8]
    Hackbusch, W.Multi-Grid Methods and Applications. Springer Series in Computational Mathemathics. Springer-Verlag, 1985.Google Scholar
  9. [9]
    Hortman, M., Perić, M., AND Scheuerer, G. Finite volume multigrid prediction of laminar natural convection: Bench-mark solutions. International Journal for Numerical Methods in Fluids 11 (1990), 189–207.CrossRefGoogle Scholar
  10. [10]
    Horton, G. TIPSI — a time-parallel SIMPLE-based method for the incompressible Navier-Stokes equations. In Proceedings of the Parallel CFD 1991, Stuttgart 1991 (1991), K. R. et al., Ed., Elsevier Science Publisher B.V.Google Scholar
  11. [11]
    ITTC. Cooperative Experiments on Wigley Parabolic Models in Japan, 17th ITTC resistance Comittee Report, 1993.Google Scholar
  12. [12]
    Lilek, Ž. Ein Berechnungsverfahren für dreidimensionale, viskose Strömungen mit freien Oberflächen. Institut für Schiffbau der Universität Hamburg, Bericht Nr. 553, ISBN 3-89220-553-1.Google Scholar
  13. [13]
    Lilek, Ž., AND Perić, M. A fourth-order finite volume method with colocated variable arrangement. Computers & Fluids 24, 3 (1995), 239–252.zbMATHCrossRefGoogle Scholar
  14. [14]
    Mason, M. L., Putnam, L. E., AND Re, R. The effect of throat contouring on two-dimensional converging-diverging nozzle at static conditions. NASA Techn. Paper No. 1704 (1980).Google Scholar
  15. [15]
    Miyata, H., Zhu, M., AND Watanabe, O. Numerical study on a viscous flow with free-surface waves about a ship in steady straight course by a finite-volume method. Journal of Ship Research 36, 4 (1992), 332–345.Google Scholar
  16. [16]
    Patankar, S. V., AND Spalding, D. B. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. International J. Heat Mass Transfer 15 (1972), 1787–1806.zbMATHCrossRefGoogle Scholar
  17. [17]
    Perić, M.A finite volume method for the prediction of three-dimensional flow in complex ducts. PhD thesis, University of London, 1985.Google Scholar
  18. [18]
    Perić, M., AND Schreck, E. Analysis of efficiency of implicit CFD methods on MIMD computers. In Parallel CFD’ 95, Pasadena (june 1995).Google Scholar
  19. [19]
    Rubin, S. G., AND Khosla, P. K. A diagonally dominant second-order accurate implicit scheme. Computers & Fluids 2 (1974), 207.zbMATHCrossRefGoogle Scholar
  20. [20]
    Schreck, E., AND Perić, M. Computation of fluid flow with a parallel multigrid solver. International Journal for Numerical Methods in Fluids 16 (1993), 303–327.zbMATHCrossRefGoogle Scholar
  21. [21]
    Seidl, V., Perić, M., AND Schmidt, S. Space-and time-parallel Navier-Stokes solver for 3D block-adaptive cartesian grids. In Parallel Computational Fluid Dynamics — Implementation and Results Using Parallel Computers (1996), P. Fox, Ed., Elsevier Science B.V.Google Scholar
  22. [22]
    Van den Vorst, H.A. BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 13 (1992), 631–644.zbMATHCrossRefGoogle Scholar
  23. [23]
    Vilsmeier, R., AND Hänel, D. Computational aspects of flow simulation on 3-D, unstructured, adaptive grids. In Notes on Numerical Fluid Mechanics (1996), E. H. Hirschel, Ed., Vieweg, Braunschweig. In print.Google Scholar
  24. [24]
    Wagner, S., Ed. Computational Fluid Dynamics on Parallel Systems (1995), Vieweg, Braunschweig.zbMATHGoogle Scholar
  25. [25]
    Yang, K., AND Ferziger, J. H. Large-eddy-simulation of turbulent flow using a dynamic subgrid-scale model. AIAA Journal 31, 8 (1993), 1406–1413.zbMATHCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Ž. Lilek
    • 1
  • M. Perić
    • 1
  • V. Seidl
    • 1
  1. 1.Institut für SchiffbauUniversität HamburgHamburgGermany

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