Chebyshev-Legendre Spectral Domain Decomposition Method for Two-Dimensional Vorticity Equations. (17th May 2016)

• Record Type: Journal Article
• Authors: Wu, Hua; Pan, Jiajia; Zheng, Haichuan
• Is Part Of: Communications in computational physics. Volume 19:Number 5(2016:May)
• Page Start: 1221
• Page End: 1241
• Publication Date: 2016-05-17
• Subjects: 65M12, -- 65M70; Multi-domain spectral method(spectral element method), -- Chebyshev-Legendre spectral method, -- vorticity equations; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.scpde14.18s
• Languages: English
• ISSNs: 1815-2406

Abstract

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.