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A Global Spectral Element Model for Poisson Equations and Advective Flow over a Sphere
Mei, Huan1; Wang, Faming1; Zeng, Zhong2; Qiu, Zhouhua2; Yin, Linmao2; Li, Liang3
2016-03-01
Source PublicationADVANCES IN ATMOSPHERIC SCIENCES
Volume33Issue:3Pages:377-390
SubtypeArticle
AbstractA global spherical Fourier-Legendre spectral element method is proposed to solve Poisson equations and advective flow over a sphere. In the meridional direction, Legendre polynomials are used and the region is divided into several elements. In order to avoid coordinate singularities at the north and south poles in the meridional direction, Legendre-Gauss-Radau points are chosen at the elements involving the two poles. Fourier polynomials are applied in the zonal direction for its periodicity, with only one element. Then, the partial differential equations are solved on the longitude-latitude meshes without coordinate transformation between spherical and Cartesian coordinates. For verification of the proposed method, a few Poisson equations and advective flows are tested. Firstly, the method is found to be valid for test cases with smooth solution. The results of the Poisson equations demonstrate that the present method exhibits high accuracy and exponential convergence. Highprecision solutions are also obtained with near negligible numerical diffusion during the time evolution for advective flow with smooth shape. Secondly, the results of advective flow with non-smooth shape and deformational flow are also shown to be reasonable and effective. As a result, the present method is proved to be capable of solving flow through different types of elements, and thereby a desirable method with reliability and high accuracy for solving partial differential equations over a sphere.
KeywordSpectral Element Method Spherical Coordinates Poisson Equations Advective Equation Legendre-gauss-radau
DOI10.1007/s00376-015-5001-2
Indexed BySCI
Language英语
WOS IDWOS:000370030300010
Citation statistics
Document Type期刊论文
Identifierhttp://ir.qdio.ac.cn/handle/337002/112459
Collection海洋环流与波动重点实验室
Affiliation1.Chinese Acad Sci, Inst Oceanol, Qingdao 266071, Peoples R China
2.Chongqing Univ, Coll Aerosp Engn, Dept Engn Mech, Chongqing 400044, Peoples R China
3.Chalmers, Dept Chem & Biol Engn, SE-41296 Gothenburg, Sweden
First Author AffilicationInstitute of Oceanology, Chinese Academy of Sciences
Recommended Citation
GB/T 7714
Mei, Huan,Wang, Faming,Zeng, Zhong,et al. A Global Spectral Element Model for Poisson Equations and Advective Flow over a Sphere[J]. ADVANCES IN ATMOSPHERIC SCIENCES,2016,33(3):377-390.
APA Mei, Huan,Wang, Faming,Zeng, Zhong,Qiu, Zhouhua,Yin, Linmao,&Li, Liang.(2016).A Global Spectral Element Model for Poisson Equations and Advective Flow over a Sphere.ADVANCES IN ATMOSPHERIC SCIENCES,33(3),377-390.
MLA Mei, Huan,et al."A Global Spectral Element Model for Poisson Equations and Advective Flow over a Sphere".ADVANCES IN ATMOSPHERIC SCIENCES 33.3(2016):377-390.
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