Advertisement

Computational Results

  • Koichi Kitagawa
Part of the Lecture Notes in Engineering book series (LNENG, volume 55)

Abstract

The numerical evaluation of derivatives involved in the convective terms is discussed in the following section. The results obtained by using the finite difference schemes (both upwind and central approximations) and the boundary integral equations are compared in the Hagen-Poiseuille flow problem and the square cavity flow problem [1]. Next, the effect of the self-adaptive coordinate transformation technique is examined for the case of quasi-singular boundary integrations [2].

Keywords

Singular Point Rayleigh Number Internal Node Finite Difference Scheme Boundary Node 
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.
    Kitagawa, K., Brebbia, C.A., Wrobel, L.C. and Tanaka, M., Boundary Element Analysis of Viscous Flow by Penalty Function Formulation, Engineering Analysis, Vol. 3, No. 4, pp. 194–200, (1986).CrossRefGoogle Scholar
  2. 2.
    Kitagawa, K., Brebbia, C.A., Wrobel, L.C. and Tanaka, M., A Boundary Element Analysis of Natural Convection Problems, Proc. of the 4th Japan National Symposium on BEM (Kobayashi, S. ed.), pp. 161–166, (1987), in Japanese.Google Scholar
  3. 3.
    Kitagawa, K., Wrobel, L.C., Brebbía, C.A. and Tanaka, M., Modelling Thermal Transport Problems Using the Boundary Element Method, Proceedings of the International Conference on Development and Application of Computer Techniques to Environmental Studies, pp. 715–731, C.M. Publications, (1986).Google Scholar
  4. 4.
    Kitagawa, K., Wrobel, L.C., Brebbia, C.A. and Tanaka, M., A Boundary Element Formulation for Natural Convection Problems, Int. J. for Numer. Meth. in Fluids, Vol. 8, pp. 139–149, (1988).Google Scholar
  5. 5.
    Kitagawa, K., Brebbia, C.A., Wrobel, L.C. and Tanaka, M., Viscous Flow Analysis Including Thernal Convection, Proc. of the 9th BEM Conf. on BEM in Engineering (Brebbía, C.A. et al eds.), pp. 459–476, C.M. Publications, (1987).Google Scholar
  6. 6.
    Tanaka, M., Kitagawa, K., Brebbia, C.A. and Wrobel, L.C., A Boundary Element Investigation of Natural Convection Problems, Proc. of the 7th Int. Conf. on Computational Methods in Water Resources, C.M. Publications, Southampton, (1988).Google Scholar
  7. 7.
    Kitagawa, K., Brebbia, C.A., Tanaka, M. and Wrobel, L.C., A Boundary Element Analysis of Natural Convection Problems by Penalty Function Formulation, Proc. of the 10th Int. Conf. on BEM in Engineering (Brebbia, C.A. et al eds.), C.M. Publications, (1988).Google Scholar
  8. 8.
    Batchelor, G.K., An Introduction to Fluid Dynamics, Cambridge Univ. Press., (1967).Google Scholar
  9. 9.
    Thomasset, F., Implementation of Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, New York, (1981).Google Scholar
  10. 10.
    Burggraf, O.R., Analytical and numerical studies of the structure of steady separated flows, J. Fluid Mech., Vol. 24, pp. 113–151, (1966).CrossRefGoogle Scholar
  11. 11.
    Bercovier, M. and Engelman, M., A finite element for the numerical solution of viscous incompressible flows, J. Compy. Physics., Vol. 30, pp. 181–201, (1979).CrossRefGoogle Scholar
  12. 12.
    Borrel, M., Resolution des equations de Navier-Stokes par une methode delements finis, Technical note Onera no. 1977 /8, (1977).Google Scholar
  13. 13.
    Campion-Renson, A. and Crochet, M.J. On the stream function vorticity finite element solutions of Navier-Stokes equations, Int. J. Num. Meth. Enq., Vol. 12, pp. 1809–1818, (1978).Google Scholar
  14. 14.
    Hughes, T.J.R., Liu, W.K. and Brooks, A. Finite Element Analysis of Incompressible Viscous Flows by the Penalty Function Formulation, J. Comp. Phys., Vol. 30, pp. 1–60, (1979).CrossRefGoogle Scholar
  15. 15.
    Telles, J.C.F., A Self-adaptive Coordinate Transformation for Efficient Numerical Evaluation of General Boundary Element Integrals, Int. J. of Num. Meth. In Engng., Vol. 24, pp. 959, (1987).Google Scholar
  16. 16.
    Denham, M.K. and Patrick, M.A., Laminar Flow Over a Downstream-Facing Step in a Two-Dimensional Flow Channel, Transcript of the Institute of Chemical Engineers, Vol. 52, pp. 361–367, (1974).Google Scholar
  17. 17.
    Hutton, A.G. and Smith, R.M., The Prediction of Laminar Flow Over a Downstream-Facing Step by the Finite Element Method, CEGB Report No. RD/B/N3660, (1979).Google Scholar
  18. 18.
    Davis, G.V. and Jones, I.P., Natural Convection in a Square Cavity; A Comparison Exercise, Numerical Methods in Thermal Problems. Vol. 2, (Lewis, R.W., Morgan, K. and Sherefler, B. A. eds.), pp. 552–572, (1981).Google Scholar
  19. 19.
    Jones, I.P. and Thomson, C.P. (eds.) Numerical Solutions for a Comparison Problem on Natural Convection in an Enclosed Cavity, AERE-R9955, HMSO, (1981).Google Scholar
  20. 20.
    Kuhn, T.H. and Goldstein, R.J., An Experimental and Theoretical Study of Natural Convection in the Annulus between Horizontal Concentric Cylinders, J. Fluid Mechanics, Vol. 74, pp. 695–716, (1976).CrossRefGoogle Scholar
  21. 22.
    Heinrich, J.C. and Zienkiewicz, 0.C., finite element modelling of steady state circulation in shallow water and Navier-Stokes equation using a penalty function approach, Univ. College of Swanseam, (1977).Google Scholar
  22. 23.
    Lee, R.L., Gresho, P.M. and Sani, R.L., Smoothing techniques for certain primitive variable solution of the Navier-Stokes equation, Int. J. Numer. Meth. Engng., Vol. 14, pp. 1785–1804, (1979).CrossRefGoogle Scholar
  23. 24.
    Hughes, T.J.R., Liu, W.K., and Brooks, A., Finite Element Analysis of Incompressible Viscous Flows by the Penalty Function Formulaltion, J. Comp. Phys., Vol. 30, No. 1, pp. 1–60, (1979).CrossRefGoogle Scholar
  24. 25.
    Oden, J.T. and Jacquotte, 0., A stable second-order accurate, finite element scheme for the analysis of two-dimensional incompressible viscous flow, Proc. of 4th Int. Symp. on FEM in Flow Problems (Kawai, T. ed.), pp. 19–25, Tokyo Univ. Press, (1982).Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1990

Authors and Affiliations

  • Koichi Kitagawa
    • 1
  1. 1.Consumer Products Engineering Lab.Toshiba Corp.Yokohama, 235Japan

Personalised recommendations