A Fourier-Legendre spectral element method in polar coordinates

Authors:
Zhouhua Qiu;Zhong Zeng;Huan Mei;Liang Li;Liping Yao;Liangqi Zhang
Affiliations:
Department of Engineering Mechanics, College of Resources and Environmental Science, Chongqing University, Chongqing 400044, PR China;Department of Engineering Mechanics, College of Resources and Environmental Science, Chongqing University, Chongqing 400044, PR China and State Key Laboratory of Coal Mine Disaster Dynamics and Co ...;Department of Engineering Mechanics, College of Resources and Environmental Science, Chongqing University, Chongqing 400044, PR China;Department of Engineering Mechanics, College of Resources and Environmental Science, Chongqing University, Chongqing 400044, PR China;Department of Engineering Mechanics, College of Resources and Environmental Science, Chongqing University, Chongqing 400044, PR China;Department of Engineering Mechanics, College of Resources and Environmental Science, Chongqing University, Chongqing 400044, PR China
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

In this paper, a new Fourier-Legendre spectral element method based on the Galerkin formulation is proposed to solve the Poisson-type equations in polar coordinates. The 1/r singularity at r=0 is avoided by using Gauss-Radau type quadrature points. In order to break the time-step restriction in the time-dependent problems, the clustering of collocation points near the pole is prevented through the technique of domain decomposition in the radial direction. A number of Poisson-type equations subject to the Dirichlet or Neumann boundary condition are computed and compared with the results in literature, which reveals a desirable result.