Chebyshev Finite Spectral Method With Extended Moving Grids

ZHAN Jie-min; LI Yok-sheung; DONG Zhi

doi:10.3879/j.issn.1000-0887.2011.03.012

Volume 32 Issue 3

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ZHAN Jie-min, LI Yok-sheung, DONG Zhi. Chebyshev Finite Spectral Method With Extended Moving Grids[J]. Applied Mathematics and Mechanics, 2011, 32(3): 365-374. doi: 10.3879/j.issn.1000-0887.2011.03.012

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Chebyshev Finite Spectral Method With Extended Moving Grids

doi: 10.3879/j.issn.1000-0887.2011.03.012

1.
Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China;

Received Date: 2010-01-25
Rev Recd Date: 1900-12-30
Publish Date: 2011-03-15

Abstract

Abstract

A Chebyshev finite spectral method on non-uniform mesh was proposed.An equidistribution scheme for two types of extended moving grids was proposed for grid generation.One type of grid was designed to provide better resolution for wave surface.The other type was for highly variable gradients.The method was of high-order accuracy because of the use of Chebyshev polynomial as the basis function.The polynomial was used to interpolate values between the two non-uniform meshes from the previous time step to the current time step.To attain high accuracy in time discretization,the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme was used.To avoid numerical oscillations caused by the dispersion term in the KdV equation,a numerical technique on non-uniform mesh was introduced to improve the numerical stability.The proposed numerical scheme was validated by applications to the Burgers equation (nonlinear convection-diffusion problem) and KdV equation (single solitary and 2-solitary wave problems),where analytical solutions were available for comparison.Numerical results agree very well with the corresponding analytical solutions in all cases.
- Chebyshev polynomial,
- finite spectral method,
- nonlinear wave,
- non-uniform mesh,
- moving grids

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References

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