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

• Articles • Previous Articles     Next Articles

SPECTRAL GALERKIN APPROXIMATION OF COUETTE-TAYLOR FLOW

WANG He-yuan1,2, LI Kai-tai2   

  1. 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)

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

2010 MSC Number: 

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