SPECTRAL GALERKIN APPROXIMATION OF COUETTE-TAYLOR FLOW

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (10): 1184-1193.

SPECTRAL GALERKIN APPROXIMATION OF COUETTE-TAYLOR FLOW

王贺元^1,2, 李开泰²

1. Department of Mathematics and Physics, Liaoning Institute of Technology, Jinzhou, Liaoning 121001, P.R.China;
2. School of Sciences, Xi’an Jiaotong University, Xi’an 710049, P.R.China

收稿日期:2003-01-10 修回日期:2004-06-08 出版日期:2004-10-18 发布日期:2004-10-18
通讯作者: ZHOU Xian-chu,Original Member of Editorial Committee,AMM
基金资助:
the National Key Basic Research Special Foundation of China(G19903280107),the National Natural Science Foundation of China(10101020)

SPECTRAL GALERKIN APPROXIMATION OF COUETTE-TAYLOR FLOW

WANG He-yuan^1,2, LI Kai-tai²

1. Department of Mathematics and Physics, Liaoning Institute of Technology, Jinzhou, Liaoning 121001, P.R.China;
2. School of Sciences, Xi’an Jiaotong University, Xi’an 710049, P.R.China

Received:2003-01-10 Revised:2004-06-08 Online:2004-10-18 Published:2004-10-18
Supported by:
the National Key Basic Research Special Foundation of China(G19903280107),the National Natural Science Foundation of China(10101020)

摘要/Abstract

摘要： 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.

关键词: Navier-Stokes equation, Couette-Taylor flow, spectral approximation, Stokes operator

Abstract: 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.

Key words: Navier-Stokes equation, Couette-Taylor flow, spectral approximation, Stokes operator

中图分类号:

王贺元;李开泰. SPECTRAL GALERKIN APPROXIMATION OF COUETTE-TAYLOR FLOW[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(10): 1184-1193.

WANG He-yuan;LI Kai-tai. SPECTRAL GALERKIN APPROXIMATION OF COUETTE-TAYLOR FLOW[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(10): 1184-1193.

参考文献

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SPECTRAL GALERKIN APPROXIMATION OF COUETTE-TAYLOR FLOW

SPECTRAL GALERKIN APPROXIMATION OF COUETTE-TAYLOR FLOW

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