Volume 19, Issue 5
Chebyshev-Legendre Spectral Domain Decomposition Method for Two-Dimensional Vorticity Equations

Hua Wu, Jiajia Pan & Haichuan Zheng

Commun. Comput. Phys., 19 (2016), pp. 1221-1241.

Published online: 2018-04

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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.

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@Article{CiCP-19-1221, author = {Hua Wu, Jiajia Pan and Haichuan Zheng}, title = {Chebyshev-Legendre Spectral Domain Decomposition Method for Two-Dimensional Vorticity Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {5}, pages = {1221--1241}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.scpde14.18s}, url = {http://global-sci.org/intro/article_detail/cicp/11126.html} }
TY - JOUR T1 - Chebyshev-Legendre Spectral Domain Decomposition Method for Two-Dimensional Vorticity Equations AU - Hua Wu, Jiajia Pan & Haichuan Zheng JO - Communications in Computational Physics VL - 5 SP - 1221 EP - 1241 PY - 2018 DA - 2018/04 SN - 19 DO - http://dor.org/10.4208/cicp.scpde14.18s UR - https://global-sci.org/intro/cicp/11126.html KW - AB -

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.

Hua Wu, Jiajia Pan & Haichuan Zheng. (1970). Chebyshev-Legendre Spectral Domain Decomposition Method for Two-Dimensional Vorticity Equations. Communications in Computational Physics. 19 (5). 1221-1241. doi:10.4208/cicp.scpde14.18s
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