한국해양공학회지 (Journal of Ocean Engineering and Technology)

  • 제23권5호
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  • Pages.1-8
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  • 2009
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  • 1225-0767(pISSN)
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  • 2287-6715(eISSN)
한국해양공학회 (Korean Society of Ocean Engineers)
권호 표지

Hermite 유동함수법에 의한 자연대류 유동 계산

Computations of Natural Convection Flow Using Hermite Stream Function Method

  • Kim, Jin-Whan (Department of Mechanical Engineering, Dong-Eui University)
  • 발행 : 2009.10.31
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초록

This paper is a continuation of the recent development on Hermite-based divergence free element method and deals with a non-isothermal fluid flow thru the buoyancy driven flow in a square enclosure with temperature difference across the two sides. The basis functions for the velocity field consist of the Hermite function and its curl while the basis functions for the temperature field consists of the Hermite function and its gradients. Hence, the number of degrees of freedom at a node becomes 6, which are the stream function, two velocities, the temperature and its x and y derivatives. This paper presents numerical results for Ra = 105, and compares with those from a stabilized finite element method developed by Illinca et al. (2000). The comparison has been done on 32 by 32 uniform elements and the degree of approximation of elements used for the stabilized finite element are linear (Deg. 1) and quadratic (Deg. 2). The numerical results from both methods show well agreements with those of De vahl Davi (1983).

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참고문헌

  1. 김진환 (2005). "유동계산을 위한 다단계 부분 구조법에 대한 연구", 한국전산유체공학회, 제10권, 제2호, pp 38-47
  2. 김진환 (2007). "Hermite 유동함수를 이용한 비압축성 유동 계산", 한국전산유체공학회, 제12권, 제1호, pp 35-42
  3. Botella, O. and Peyret, R. (1998). "Benchmark Spectral Results on the Lid-Driven Cavity Flow", Computers & Fluids, Vol 27, pp 421-433 https://doi.org/10.1016/S0045-7930(98)00002-4
  4. Clay Mathematics Institute (2000), Cambridge, MA, U.S.A., http://www.claymath.org/millennium/
  5. Christon, M.A., Gresho, P.M. and Sutton, S.B. (2002). "Computational Predictability of Time-dependent Natural Convection Flows in Enclosures (Including a Benchmark Solution)", Int. J. for Numer. Methods in Fluids, Vol 40, pp 953-980 https://doi.org/10.1002/fld.395
  6. De Vahl Davis, G. (1983). "Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution", Int. J. for Numer. Nethods in Fluids, Vol 3, pp 249-264 https://doi.org/10.1002/fld.1650030305
  7. Ghia, U., Ghia, K.N. and Shin, C.T. (1982). "High-Re Solutions for Incompressible Flow Using the Navier- Stokes Equations and a Multigrid Method", J. of Comp. Physics, Vol 48, pp 387-411 https://doi.org/10.1016/0021-9991(82)90058-4
  8. Griffiths, D.F. (1981). "An Approximately Divergence-Free 9-Node Velocity Element (with Variationa) for Incompressible Flows", Int. J. for Numer. Meth. in Fluids, Vol 1, pp 323-346 https://doi.org/10.1002/fld.1650010405
  9. Holdeman, J.T. (2004). "I. Some Lagrange Interpolation Functions for Solenoidal and Irrotational Vector Fields", manuscript, http://j.t.holdeman.home.att.net
  10. Holdeman, J.T. (2004). "II. Some Hermite Interpolation Functions for Solenoidal and Irrotational Vector Fields", manuscript, http://j.t.holdeman.home.att.net
  11. Ilinca, F., Hetu, J.F. and Pelletier, D. (2000). 'On Stabilized Finite Element Formulations for Incompressible Advective-Diffusive Transport and Fluid Flow Problems', Comput. Methods Appl. Mech. Engrg., Vol 188, pp 235-255 https://doi.org/10.1016/S0045-7825(99)00150-4
  12. Lapidus, L. and Pinder, G.F. (1982). Numerical Solution of Partial Differential Equations in Sciences and Engineering, John Wiley & Sons, Inc
  13. Pozikidis, C. (1977). Introduction to Theoretical and Computational Fluid Dynamics, Oxford University Press
  14. Shu, C. and Wee, K.H.A. (2002). "Numerical Simulation of Natural Convection in a Square Cavity by SIMPLEGeneralized Differential Quadrature Method", Computers & Fluids, Vol 31, pp 209-226 https://doi.org/10.1016/S0045-7930(01)00024-X