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COMPUTATIONS OF NATURAL CONVECTION FLOW WITHIN A SQUARE CAVITY BY HERMITE STREAM FUNCTION METHOD  

Kim, J.W. (동의대학교 기계공학과)
Publication Information
Journal of computational fluids engineering / v.14, no.4, 2009 , pp. 67-77 More about this Journal
Abstract
This paper is a continuation of a recent development on the Hermite-based divergence-free element method and deals with a non-isothermal fluid flow driven by the buoyancy force in a square cavity with temperature difference across the two sides. Two Hermite functions are considered for numerical computations in this paper. One is a cubic function and the other is a quartic function. The degrees-of-freedom of the cubic Hermite function are stream function and its first and second derivatives for the velocity field, and temperature and its first derivatives for the temperature field. The degrees-of-freedom of the quartic Hermite function include two second derivatives and one cross derivative of the stream function in addition to the degrees-of-freedom of the cubic stream function. This paper presents a brief review on the Hermite based divergence-free basis functions and its finite element formulations for the buoyancy driven flow. The present algorithm does not employ any upwinding or a stabilization term. However, numerical values and contour graphs for major flow variables showed good agreements with those by De Vahl Davis[6].
Keywords
Natural Convection; Divergence-free Element; Vector Potential; Solenoidal Basis Function; Irrotational Basis Function;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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1 1977, Pozrikidis, C., Introduction to Theoretical and Computational Fluid Dynamics, Oxford University Press
2 2002, Christon, M.A., Gresho, P.M. and Sutton, S.B., "Computational Predictability of Time-dependent Natural Convection Flows in Enclosures(including a benchmark solution)," International Journal for Numerical Methods in Fluids, Vol.40, pp.953-980   DOI   ScienceOn
3 1982, Lapidus, L. and Pinder, G.F., Numerical solution of Partial Differential Equations in Sciences and Engineering, John Wiley & Sons, Inc
4 2008, 김진환, "이차원 비압축성 유동 계산을 위한 Hermite 겹 3차 유동함수법," 한국전산유체공학회지, 제13권, 제4호, pp.13-23
5 1994, Reddy, J.N. and Gartling, D.K., The Finite Element Method in Heat Transfer and Fluid Dynamics, CRC Press, Inc
6 2002, Shu, C. and Wee, K.H.A., "Numerical Simulation of Natural Convection in A Square Cavity by SIMPLE-generalized Differential Quadrature Method," Computers & Fluids, Vol.31, pp.209-226   DOI   ScienceOn
7 1973, Gopalacharyulu, S., "A Higher Order Conforming Rectangular Plate Element," International Journal for Numerical Methods in Engineering, Vol.6, pp.305-308   DOI
8 2007, 김진환, "Hermite 유동함수를 이용한 비압축성 유동 계산," 한국전산유체공학회지, 제12권, 제1호, pp.35-42   과학기술학회마을
9 2002, Holdeman, J.T., "Recent Advances in the Finite Element Method for Incompressible Flow," USNCTAM14 Conference, Blacksburg, VA
10 1983, De Vahl Davis, G., "Natural Convection of Air in A Square Cavity: A Bench mark Numerical Solution," International Journal for Numerical Methods in Fluids, Vol.3, pp.249-264   DOI   ScienceOn
11 1981, Griffiths, D.F., "An Approximately Divergence-free 9-Node Velocity Element (with variationa) for Incompressible flows," International Journal for Numerical Methods in Fluids, Vol.1, pp.347-364   DOI
12 1984, Bejan, A., Convection Heat Transfer, John Wiley & Sons, Inc
13 1991, Le Quere, P., "Accurate Solutions to the Square Thermally Driven Cavity at High Rayleigh Number," Computers & Fluids, Vol.20, pp.29-41   DOI   ScienceOn