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Chebyshev-Legendre Spectral Domain Decomposition Method for Two-Dimensional Vorticity Equations

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  17 May 2016

Hua Wu ,
Jiajia Pan  and
Haichuan Zheng
Hua Wu*
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China
Jiajia Pan
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China
Haichuan Zheng
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China
*
*Corresponding author. Email address:hwu@staff.shu.edu.cn(H. Wu)
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Abstract

We extend the Chebyshev-Legendre spectral method to multi-domain case for solving the two-dimensional vorticity equations. The schemes are formulated in Legendre-Galerkin method while the nonlinear term is collocated at Chebyshev-Gauss collocation points. We introduce proper basis functions in order that the matrix of algebraic system is sparse. The algorithm can be implemented efficiently and in parallel way. The numerical analysis results in the case of one-dimensional multi-domain are generalized to two-dimensional case. The stability and convergence of the method are proved. Numerical results are given.

Keywords

Multi-domain spectral method(spectral element method)Chebyshev-Legendre spectral methodvorticity equations

MSC classification

Secondary: 65M12: Stability and convergence of numerical methods 65M70: Spectral, collocation and related methods
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016 , pp. 1221 - 1241
Copyright
Copyright © Global-Science Press 2016 

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