用SADI方法求解方形空腔中具有高Rayleigh数的非定常自然对流问题

王璞; 阿.卡哈维塔

用SADI方法求解方形空腔中具有高Rayleigh数的非定常自然对流问题

王璞¹,
阿.卡哈维塔²

1.
中国兰州大学;
2.
加拿大蒙特利尔工学院

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出版历程
- 收稿日期: 1986-02-20
- 刊出日期: 1987-03-15

The Numerical Solution of the Unsteady Natural Convection Flow in a Square Cavity at High Rayleigh Number Using SADI Method

Wang Pu¹,
R. Kahawita²

1.
Lanzhou University, Lanzhou;
2.
Ecole Polytechnique de Montreal, Canada

摘要

摘要: 本文用三次样条积分计算了在方形空腔中具有高Rayleigh数Ra=10⁷和Ra=2×10⁷的非定常自然对流问题。二维N-S方程和能量方程是在非均匀网格中用两个交替方向的三次样条公式进行计算的。文中简要讨论了过渡流动的主要特征,所得结果与理论予估值^[1,2]吻合很好。Ra=10⁷时的稳态结果与近期文献中的结果一致。

Abstract: The unsteady natural convection flow in a square cavity at high Rayleigh number Ra=10⁷ and 2×10⁷ has been computed using cubic spline integration. The required solutions to thetwo dimensional Navier-Stokes and energy equations have been obtained using two alternate numerical formulations on non-uniform grids. The main features of the transient flow have been briefly discussed. The results obtained by using the present method are in good agreement-with the theoretical predictions^[1,2]. The steady state results have been compared with accurate solutions presented recently for Ra=10⁷.

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参考文献(13)

[1]	Patterson, J.and J.Imberger, unsteady natural convection in a rectangular cavity, J.Fluid Mech., 100(1980), 65-86.
[2]	9 J.S.L ee and L.Z.Jiang,A boundary integral formulation and 2D fundamental solution for piezo-electric media,Mech.Res.Comm.,21(2)(1994),47-54.
[3]	Rubin, S.G.and R.A.Graves, Viscous flows solutions with a cubic spline approximation, Computer and Fluids, 3(1975), 1-36.
[4]	Rubin, S.G.and P.K.Khosla, Higher order numerical solutions using cubic splines, AIAA JOurnal, 14(1976), 851-858.
[5]	Wang, P.and R.Kahawita, Numerical integration of partial differential equations using cubic splines, Int.J Computer Math., 13(1983), 271-286.
[6]	王璞,R, Kahawita, Burgers方程的立方样条数值解法,空气动力学学报,2 (1984), 11-18.
[7]	王璞,样条Las-Wandroff格式和样条跳蛙格式,空气动力学学报,3 (1985),90-95.
[8]	Wang, P.and R.Kahawita, A two-dimensional model of estuarine circulation using cubic splines, Can.J.Civil Eng., 10(1983), 116-124.
[9]	De Vahl Davis, G., Natural convection of air, a square cavity:an accurate numerical solution, Report FMT/1, University of N.S.W., Kensington, Australia(1981).
[10]	Lauriat, G., Accurate solutions of natural convection flow in square cavities at high raleigh numbers with a cubic spline approximation, ASME Winter Annual Meeting, Phoenix, Arizona(1982).
[11]	Wang, P.and R.Kahawita, The numerical solution of the natural convection flow in a square cavity, Proc.of 4th Int.Conf.on Mathematical Modelling in Sciencc and Technology, Zurich, Aug.24-26(1983), 640-645.
[12]	王璞,方形空腔中关于Ra=10⁷的非定常自然对流的样条数值模拟,力学学报(待发表).
[13]	Upson, C.D., P.M.Greho, and R.L.Lee, Finite element simulations of thermally induced convection in anenclosed cavity, Report UCID 18602, Lawrence Livermore Laboratory, Mars(1980).