Chebyshev-Legendre spectral method for solving the two-dimensional vorticity equations with homogeneous Dirichlet conditions

2009 ◽  
Vol 25 (3) ◽  
pp. 740-755 ◽  
Author(s):  
Hua Wu ◽  
Heping Ma ◽  
Huiyuan Li
Keyword(s):  
Spectral Method ◽  
Two Dimensional ◽  
Dirichlet Conditions ◽  
Vorticity Equations ◽  
Legendre Spectral Method

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

2016 ◽  
Vol 19 (5) ◽  
pp. 1221-1241 ◽  
Author(s):  
Hua Wu ◽  
Jiajia Pan ◽  
Haichuan Zheng
Keyword(s):  
Domain Decomposition Method ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
One Dimensional ◽  
Collocation Points ◽  
The Matrix ◽  
Vorticity Equations ◽  
Legendre Spectral Method ◽  
Legendre Galerkin Method ◽  
The Stability

AbstractWe 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.

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