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A Boundary Element Analysis for Thermal Convection Problems

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Viscous Flow Applications

Part of the book series: Topics in Boundary Element Research ((TBOU,volume 5))

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Abstract

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.

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References

  1. Lewis, R.W. and Morgan, K. (Eds.), “Numerical Methods in Thermal Problems,” Vol. 4, Pineridge Press, Swansea, 1985.

    MATH  Google Scholar 

  2. Taylor, C. et. al. (Eds.), “Numerical Methods in Laminar and Turbulent Flow,” Vol. 4 Pineridge Press, Swansea, 1985.

    Google Scholar 

  3. Bristeau, M.O. et. al. (Eds.), Proc. 6th Int. Symp. on Finite Element Methods in Flow Problems, Antibes, France, 1986.

    Google Scholar 

  4. A. Sa, Da. Costa, et. al. (Eds.), “Finite Elements in Water Resources,” Vol. 6, C.M. Publications, 1986.

    Google Scholar 

  5. Brebbia, C.A., “The Boundary Element Method for Engineers,” Pentech Press, London, 1978.

    Google Scholar 

  6. Brebbia, C.A., Telles, J.C.F., and Wrobel, L.C., “Boundary Element Techniques,” Springer-Verlag, Berin, 1984.

    MATH  Google Scholar 

  7. Brebbia, C.A. et. al. (Eds.), “Boundary Elements IX,” C.M. Publications, 1987.

    Google Scholar 

  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).

    Article  MATH  Google Scholar 

  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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Roache, P.J., “Computational Fluid Dynamics,” Hermosa Publishers Inc., 1976.

    Google Scholar 

  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).

    Article  ADS  MATH  Google Scholar 

  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. 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. 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).

    Article  Google Scholar 

  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).

    Article  MathSciNet  MATH  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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. Kitagawa, K., Wrobel, L.C., Brebbia, C.A. and Tanaka, M., “A Boundary Element Formulation for Natural Convection Problems,” Int. J. Num. M.th. Fluids, 8, 139–144 (1988).

    Article  MATH  Google Scholar 

  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. 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. 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. 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 

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Kitagawa, K., Brebbia, C.A., Tanaka, M. (1989). A Boundary Element Analysis for Thermal Convection Problems. In: Brebbia, C.A. (eds) Viscous Flow Applications. Topics in Boundary Element Research, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83683-1_5

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  • DOI: https://doi.org/10.1007/978-3-642-83683-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83685-5

  • Online ISBN: 978-3-642-83683-1

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