A Boundary Element Analysis for Thermal Convection Problems

  • K. Kitagawa
  • C. A. Brebbia
  • M. Tanaka
Part of the Topics in Boundary Element Research book series (TBOU, volume 5)


In recent years, the rapid development of computers has been utilized for applying numerical analyses to solve a variety of problems in the scientific and engineering fields. Especially, the numerical analysis of fluid flow problems has become recognized as a new subject called Numerical fluid mechanics or Computational fluid mechanics.


Singular Point Boundary Element Rayleigh Number Penalty Function Boundary Element 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.


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  1. 1.
    Lewis, R.W. and Morgan, K. (Eds.), “Numerical Methods in Thermal Problems,” Vol. 4, Pineridge Press, Swansea, 1985.MATHGoogle Scholar
  2. 2.
    Taylor, C. et. al. (Eds.), “Numerical Methods in Laminar and Turbulent Flow,” Vol. 4 Pineridge Press, Swansea, 1985.Google Scholar
  3. 3.
    Bristeau, M.O. et. al. (Eds.), Proc. 6th Int. Symp. on Finite Element Methods in Flow Problems, Antibes, France, 1986.Google Scholar
  4. 4.
    A. Sa, Da. Costa, et. al. (Eds.), “Finite Elements in Water Resources,” Vol. 6, C.M. Publications, 1986.Google Scholar
  5. 5.
    Brebbia, C.A., “The Boundary Element Method for Engineers,” Pentech Press, London, 1978.Google Scholar
  6. 6.
    Brebbia, C.A., Telles, J.C.F., and Wrobel, L.C., “Boundary Element Techniques,” Springer-Verlag, Berin, 1984.MATHGoogle Scholar
  7. 7.
    Brebbia, C.A. et. al. (Eds.), “Boundary Elements IX,” C.M. Publications, 1987.Google Scholar
  8. 8.
    Wu, J.C., and Thompson, J.F., “Numerical solution of Time-Dependent Incompressible NavierStokes Equations Using an Integro-Differential Formulation,” J. Computational Fluids, 1, 197–215 (1973).MATHCrossRefGoogle Scholar
  9. 9.
    Wu, J.C., Rizk, Y.M., and Sankar, N.L., “Boundary Element Methods,” Vol. 3 (Banerjee, P.K. and Mukherjee, S. Eds.), Applied Science Publishers, pp. 136–169, 1984.Google Scholar
  10. 10.
    Brebbia, C.A. and Wrobel, L.C., “Viscous Flow Problems by the Boundary Element Method, Computational Techniques for Fluid Flow (Taylor, C. et. al. Eds.), pp. 1–21, Pineridge Press, Swansea, 1984.Google Scholar
  11. 11.
    Skerget, P., Alujevic, A. and Brebbia, C.A., “The Solution of Navier-Stokes Equations in Terms of Vorticity-Velocity Variables by Boundary Elements,” Proc. 6th Int. BEM Conf. in Engineering (Brebbia, C.A. Ed.), pp. 4/41–4/56, C.M. Publications, 1984.Google Scholar
  12. 12.
    Skerget, P., Alujevic, A. and Brebbia, C.A., “Analysis of Laminar Flows with Separation Using BEM,” Proc. 7th Int. BEM Conf. in Engineering (Brebbia, C.A. et. al. Eds.), pp. 9/23–9/36, C.M. Publications, 1985.Google Scholar
  13. 13.
    Skerget, P., Alujevic, A., Kuhn, G. and Brebbia, C.A., “Natural Convection Flow Problems by BEM,” BEM IX (Brebbia, C.A. et. al. Eds.), Vol. 3, pp. 401–417, C.M. Publications, 1987.Google Scholar
  14. 14.
    Onishi, K., Kuroki, T. and Tanaka, M., “Boundary Element Method for Laminar Viscous Flow and Convective Diffusion Problems,” Topics in Boundary Element Research, Vol. 2, pp. 209–229, Springer-Verlag, 1985.Google Scholar
  15. 15.
    Bush, M.B. and Tanner, R.I., “Numerical Solution of Viscous Flows Using Integral Equation Methods,” Int. J. Num. Meth. Fluids, 71–92 (1983).Google Scholar
  16. 16.
    Kakuda, K. and Tosaka, N., “Boundary Element Analysis of the Unsteady Viscous Flows,” Proc. 1st Japan National Symposium on BEM (Ed. M. Tanaka) 241–246, 1984 (in Japanese).Google Scholar
  17. 17.
    Kuroki, T., Onishi, K. and Tosaka, N., “Thermal Fluid Flow with Velocity Evaluation Using Boundary Elements and Penalty Function Method,” Proc. 7th Int. BEM Conf. in Enginerring, pp. 2/107–2/114, C.M. Publications, 1985.Google Scholar
  18. 18.
    Tosaka, N. and Kakuda, K., “Numerical Solutions of Steady Incompressible Viscous Flow Problems by the Integral Equation Method,” Proc. 4th Int. Conf. on Numerical Methods for Engineers, pp. 211–222, C.M. Publications, 1986.Google Scholar
  19. 19.
    Tosaka, N. and Kakuda, K., “Numerical Simulations for Incompressible Viscous Flow Problems Using the Integral Equation Methods,” Boundary Elements VIII, Vol. 2, pp. 813–822, C.M. Publications, 1986.Google Scholar
  20. 20.
    Tosaka, N. and Fukushima, N., “Integral Equation Analysis of Laminar Natural Convection Problem,” Boundary Elements VIII, pp. 803–812, C.M. Publications, 1986.Google Scholar
  21. 21.
    Tanaka, M. and Kitagawa, K., “Boundary Element Analysis of Viscous Flow by Penalty Function Method,” Proc. 2nd Japan National Symp. on Boundary Element Methods, pp. 227–232, 1985 (in Japanese).Google Scholar
  22. 22.
    Roache, P.J., “Computational Fluid Dynamics,” Hermosa Publishers Inc., 1976.Google Scholar
  23. 23.
    Leonard, B. P., “A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation,” Computer Method in Applied Mechnics and Engineering, 19, 59–98 (1979).ADSMATHCrossRefGoogle Scholar
  24. 24.
    Leonard, B. P., “A Survey of Finite Differences with Upwinding for Numerical Modelling of the Incompressible Convective Diffusion Equation,” Computational Techniques in Transient and Turbulent Flow, Vol. 2, Pineridge Press, Swansea, 1981.Google Scholar
  25. 25.
    Kawamura, T., Takami, H. and Kawahara, K., “New-Higher Order Upwind for Incompressible Navier Stokes Equations,” Proc. 9th Int. Conf. Numerical Method in Fluid Dynamics, 1984.Google Scholar
  26. 26.
    Heinrich, J.C., Huyakorn, P.S., Zienkiewicz, O.C. and Mitchell, A.R., “An Upwind Finite Element Scheme for Two-dimensional Convective Transport Equation,” Int. J. Num. Meth. Eng., 10, 131–143 (1977).CrossRefGoogle Scholar
  27. 27.
    Kelly, D.W., Nakazawa, S., Zienkiewicz, O.C. and Heinrich, J.C., “A Note on Upwinding and Anisotropic Balancing Dissipation in Finite Element Approximations to Convective Diffusion Problems,” Int. J. Num. Meth. Eng. 15, 1705–1711 (1980).MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Kitagawa, K., Brebbia, C.A., Wrobel, L.C. and Tanaka, M., “Boundary Element Analysis of Viscous Flow by Penalty Function Formulation,” Engineering Analysis, 3, 194–200 (1986).ADSCrossRefGoogle Scholar
  29. 29.
    Kitagawa, K., Wrobel, L.C., Brebbia, C.A. and Tanaka, M., Modelling Thermal Transport Problems Using the Boundary Element Method,“ Proc. Int. Conf. Development and Application of Computer Techniques to Enviromental Studies, pp. 715–731, C.M. Publications, 1986.Google Scholar
  30. 30.
    Kitagawa, K., Wrobel, L.C., Brebbia, C.A. and Tanaka, M., “A Boundary Element Formulation for Natural Convection Problems,” Int. J. Num. Fluids, 8, 139–144 (1988).MATHCrossRefGoogle Scholar
  31. 31.
    Telles, J.C.F., “A Self-adaptive Coordinate Transformation for Efficient Numerical Evaluation of General Boundary Element Integrals,” Int. J. Num. Meth. in Eng. 24, 1959 (1987).Google Scholar
  32. 32.
    Kitagawa, K., Brebbia, C.A., Wrobel, L.C. and Tanaka, M., “A Boundary Element Analysis of Natural Convection Problems,” Proc. 4th Japan National Symp. on Boundary Element Methods, pp. 161–166, 1987.Google Scholar
  33. 33.
    Oden, J.T. and Jacquotte, “A Stable Second-order Accurate Finite Element Scheme for the Analysis of Two-dimensional Incompressible Viscous Flow,” Proc. 4th Int. Symp. on Finite Element Methods in Flow problems, pp. 19–25, Tokyo Univ. Press, Tokyo, 1982.Google Scholar
  34. 34.
    Davis, G.V. and Jones, I.P., “Natural Convection in a Square Cavity — A Comparison Exercise, Numerical Methods in Thermal Problems,” Vol. 2, (Eds. Lewis, R.W. and Morgan K.), pp. 552–572, Pineridge Press, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • K. Kitagawa
  • C. A. Brebbia
  • M. Tanaka

There are no affiliations available

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