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Couette-Taylor流的谱Galerkin逼近 被引量:5

Spectral Galerkin Approximation of Couette-Taylor Flow
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摘要  利用谱方法对轴对称的旋转圆柱间的Couette_Taulor流进行数值模拟· 首先给出Navier_Stokes方程流函数形式,利用Couette流把边界条件齐次化· 其次给出Stokes算子的特征函数的解析表达式,证明其正交性,并对特征值进行估计· 最后利用Stokes算子的特征函数作为逼近子空间的基函数,给出谱Galerkin逼近方程的表达式· 证明了Navier_Stokes方程非奇异解的谱Galerkin逼近的存在性、唯一性和收敛性,给出了解谱Galerkin逼近的误差估计。 Axisymmetric Couette-Taylor flow between two concentric rotating cylinders was simulated numerically by the spectral method.First,stream function form of the Navier-Stokes equations which homogeneous boundary condition was given by introducing Couette flow.Second,the analytical expressions of the eigenfunction of the Stokes operator in the cylindrical gap region were given and its orthogonality was proved.The estimates of growth rate of the eigenvalue were presented.Finally,spectral Galerkin approximation of Couette-Taylor flow was discussed by introducing eigenfunctions of Stokes operator as basis of finite dimensional approximate subspaces.The existence,uniquence and convergence of spectral Galerkin approximation of nonsingular solution for the steady-state Navier-Stokes equations are proved.Moreover,the error estimates are given.Numerical result is presented.
出处 《应用数学和力学》 EI CSCD 北大核心 2004年第10期1083-1092,共10页 Applied Mathematics and Mechanics
基金 国家基础研究专项基金资助项目(G1999032801_07) 国家自然科学基金资助项目(10101020)
关键词 NAVIER-STOKES方程 Coutte—Taylor流 谱逼近 STOKES算子 Navier-Stokes equation Couette-Taylor flow spectral approximation Stokes operator
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  • 1[1]Anderreck C D, Liu S S, Swinney H L. Flow regimes in a circular Couette system with independent rotating cylinders[J]. J Fluid Mech, 1986,164( 1 ): 155-183.
  • 2[2]Yasusi Takada. Quasi-periodic state and transition to turbulence in a rotating Couette system[J]. J Fluid Mech, 1999,389(1) :81-99.
  • 3[3]Coughlin K T, Marcus P S, Tagg R P, et al. Distinct quasiperiodic modes with like symmetry in a rotating fluid[J]. Phys Rev Lett, 1991, 66(1) :1161-1164.
  • 4[4]Meincke O, Egbers C. Routes into chaos in small and wide gap Taylor-Coutte flow[ J ]. Phys Chem Earth B, 1999,24(5) :467-471.
  • 5[5]Takeda Y, Fischer W E, Sakakibara J. Messurement of energy spectral density of a flow in a rotating Couette system[J]. Phys Rev Lett, 1993,70( 1 ) :3569-3571.
  • 6[6]Wimmer M. Experiments on the stability of viscous flow between two concentric rotating spheres [J]. J Fluid Mech, 1980,103( 1 ): 117-131.
  • 7[7]Taylor G I. Stability of a viscous liquid contained between two rotating cylinders[J]. Phil Trans Roy Soc London A, 1923,223( 1 ): 289-343.
  • 8[9]刘式达,刘式适.特殊函数[M].北京:气象出版社,1988,202-203.
  • 9[3]萧树铁.代数与几何[M].北京:高等教育出版社,2000.
  • 10王立周,李开泰.Navier-Stokes方程的非奇异解分支的谱Galerkin逼近[J].计算数学,2002,24(1):39-52. 被引量:3

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  • 1张引娣,李开泰.两个非同心旋转圆柱间粘性流动的广义雷诺方程及其基本流[J].高校应用数学学报(A辑),2008,23(2):127-139. 被引量:1
  • 2Liguang Wang, R Dennis Vigil, Rodney O Fox. CFD simulation of shear-induced aggregation mad breakage in turbulent Taylor-Couette flow[J]. Journal of Colloid and Interface Science, 2005,285 .. 167-178.
  • 3Noah Fehrenbacher,Ralph C Aldredge,Joshua T Morgan. Turbulence structure in a Taylor-Couette apparatus[J]. Experimental Thermal and Fluid Science, 2007, 32 : 220-230.
  • 4N M Nouri, A Sarreshtehdari. An experimental study on the effect of air bubble injection on the flow induced rotational hub[J]. Experimental Thermal and Fluid Science, 2009,33 : 386-392.
  • 5Jun Cheng. Experimental study of turbulence under planar straining and destraining and elimination of peak-lociking error in PIV analysis using the correlation mapping method[D]. Baltimore: Johns Hopkins University, 2005.
  • 6Taylor G I. Stability of a viscous liquid contained between two rotating cylinders [J]. Philos. Trans. Roy. Soc. London, 1923, A. 223 .. 289-343.
  • 7Schwarz K W, Springett B E, Dormelly R J. Modes of instability in spiral flow between rotating cylinders[J]. Journal of Fluid Mechanics, 1964,20(2) .. 281-293.
  • 8Alp Akonur. Fluid physics of a rotating membrane separator[D]. Evanston: Northwestern University, 2001.
  • 9Gravas N, Martin B W. Instability of viscous axial flow in annuli having a rotating inner cylinde[J].Journal of Fluid Mechanics, 1978,86(2) : 385-394.
  • 10Lueptow R M,Docter A,Min K. Stability of axial flow in an annulus with rotating inner eylinder[J]. Phys. Fluids, 1992,A4(11) :2446-2455.

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