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A Mixed Spectral/Wavelet Method for the Solution of the Stokes Problem

✍ Scribed by A. Garba

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
202 KB
Volume
145
Category
Article
ISSN
0021-9991

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✦ Synopsis

The paper presents a mixed wavelet/spectral Chebychev method for solving the unsteady 2D Stokes equations in the vorticity-stream function formulation with periodicity condition in one direction. After an appropriate time discretisation of the equations, one has to solve at each time step a stationary Stokes-like problem. A capacitance matrix method is used to eliminate the problem of boundary conditions. This leads to solving a series of Helmholtz problems. The spatial discretisation makes use of the wavelet method in the periodic direction and the spectral collocation Chebychev method in the non-periodic direction. The resolution of the discrete Helmholtz problem is done by means of the diagonalisation technique in the nonperiodic direction. The system then splits into a sequence of one dimensionnal periodic Helmholtz problems which are efficiently inverted using FFTs. Numerical tests show both the stability and the accuracy of the method.

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