Spectral Galerkin Approximation of Couette-Taylor Flow

WANG He-yuan; LI Kai-tai

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WANG He-yuan, LI Kai-tai. Spectral Galerkin Approximation of Couette-Taylor Flow[J]. Applied Mathematics and Mechanics, 2004, 25(10): 1083-1092.

Citation:

WANG He-yuan, LI Kai-tai. Spectral Galerkin Approximation of Couette-Taylor Flow[J]. Applied Mathematics and Mechanics, 2004, 25(10): 1083-1092.

Citation:

WANG He-yuan, LI Kai-tai. Spectral Galerkin Approximation of Couette-Taylor Flow[J]. Applied Mathematics and Mechanics, 2004, 25(10): 1083-1092.

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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;

Received Date: 2003-01-10
Rev Recd Date: 2004-06-08
Publish Date: 2004-10-15

Abstract

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 NavierStokes equations are proved.Moreover,the error estimates are given.Numerical result is presented.
- Navier-Stokes equation,
- Couette-Taylor flow,
- spectral approximation,
- Stokes operator

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References(13)

References

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