THE NUMERICAL SOLUTION OF THE UNSTEADY NATURAL CONVECTION FLOW IN A SQUARE CAVITY AT HIGH RAYLEIGH NUMBER USING SADI METHOD

Applied Mathematics and Mechanics (English Edition) ›› 1987, Vol. 8 ›› Issue (3): 219-228.

THE NUMERICAL SOLUTION OF THE UNSTEADY NATURAL CONVECTION FLOW IN A SQUARE CAVITY AT HIGH RAYLEIGH NUMBER USING SADI METHOD

王璞¹, R. Kahawita²

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

收稿日期:1986-02-20 出版日期:1987-03-18 发布日期:1987-03-18

THE NUMERICAL SOLUTION OF THE UNSTEADY NATURAL CONVECTION FLOW IN A SQUARE CAVITY AT HIGH RAYLEIGH NUMBER USING SADI METHOD

Wang Pu¹, R. Kahawita ²

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

Received:1986-02-20 Online:1987-03-18 Published:1987-03-18

摘要/Abstract

摘要： 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.}}

关键词: nonautonomous equation, approximate inertial manifold, spectral gap condition

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.}}

Key words: nonautonomous equation, approximate inertial manifold, spectral gap condition

王璞;R. Kahawita. THE NUMERICAL SOLUTION OF THE UNSTEADY NATURAL CONVECTION FLOW IN A SQUARE CAVITY AT HIGH RAYLEIGH NUMBER USING SADI METHOD[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(3): 219-228.

Wang Pu;R. Kahawita . THE NUMERICAL SOLUTION OF THE UNSTEADY NATURAL CONVECTION FLOW IN A SQUARE CAVITY AT HIGH RAYLEIGH NUMBER USING SADI METHOD[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(3): 219-228.

参考文献

[1] Patterson, J.and J.Imberger, unsteady natural convection in a rectangular cavity, J.Fluid Mech., 100(1980), 65-86.
[2] Patterson, J.C., On the existence of an oscillatory approach to steady natural convection in cavities, ASME Journal of Heat Transfer, 106(1984), 104-108.
[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] Wang, P.and R.Kahawita, The numerical solution of burgers equation using splines, Acta Aerodynamica Sinica, 2(1984), 11-18.
[7] Wang, P., Spline-Lax-Wendroff scheme.and spline-leap-frog scheme, Acta Aerodynamica Sinica, 3(1985), 90-96.(in Chinese).
[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] Wang, P., Spline simulations of unsteady natural convection flow in a square cavity at Ra=10~7 with method of fractional steps.(to appear in Acta Mechanica Sinica).
[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).

THE NUMERICAL SOLUTION OF THE UNSTEADY NATURAL CONVECTION FLOW IN A SQUARE CAVITY AT HIGH RAYLEIGH NUMBER USING SADI METHOD

THE NUMERICAL SOLUTION OF THE UNSTEADY NATURAL CONVECTION FLOW IN A SQUARE CAVITY AT HIGH RAYLEIGH NUMBER USING SADI METHOD

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 9

编辑推荐

Metrics

本文评价

[1]	田立新;许伯强;刘曾荣. WAVELET APPROXIMATE INERTIAL MANIFOLD AND NUMERICAL SOLUTION OF BURGERS' EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(10): 1140-1152.
[2]	田立新;储志俊;刘曾荣;蒋勇. NUMERICAL ANALYSIS OF LONGTIME DYNAMIC BEHAVIOR IN WEAKLY DAMPED FORCED KdV EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(10): 1123-1130.
[3]	侯延仁;李开泰. A SIMPLE POSTPROCESS PROCEDURE FOR GALERKIN METHOD[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(1): 79-86.
[4]	王宗信;范先令;朱正佑. CONVERGENT FAMILIES OF APPROXIMATE INERTIAL MANIFOLDS FOR NONAUTONOMOUS EVOLUTION EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(8): 765-775.
[5]	王宗信;范先令;朱正佑. INERTIAL MANIFOLDS FOR NONAUTONOMOUS INFINITE DIMENSIONAL DYNAMICAL SYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(7): 695-704.
[6]	林玉蕊;田立新;刘曾荣. THE WILD SOLUTIONS OF THE INDUCED FORM UNDER THE SPLINE WAVELET BASIS IN WEAKLY DAMPED FORCED KdV EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(12): 1161-1166.
[7]	卢殿臣;田立新;刘曾荣. WAVELET BASIS ANALYSIS IN PERTURBED PERIODIC KdV EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(11): 1053-1058.
[8]	徐振源;田立新. THE RESEARCH OF LONGTIME DYNAMIC BEHAVIOR IN WEAKLY DAMPED FORCED KdV EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(10): 1021-1028.
[9]	蔡日增;徐振源. APPROXIMATE INERTIAL MANIFOLDS FOR THE SYSTEM OF THE J-J EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 1996, 17(4): 341-349.