A Coupled Legendre-Laguerre Spectral-Element Method for the Navier-Stokes Equations in Unbounded Domains

Authors:
Qingqu Zhuang;Jie Shen;Chuanju Xu
Affiliations:
School of Mathematical Sciences, Xiamen University, Xiamen, China 361005;Department of Mathematics, Purdue University, West Lafayette, USA 47907;School of Mathematical Sciences, Xiamen University, Xiamen, China 361005
Venue:
Journal of Scientific Computing
Year:
2010

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Abstract

A coupled Legendre-Laguerre spectral element method is proposed for the Stokes and Navier-Stokes equations in unbounded domains. The method combines advantages of the high accuracy of the Laguerre-spectral method for unbounded domains and the geometric flexibility of the spectral-element method. Rigorous stability and error analysis for the Stokes problem is carried out. Numerical results indicate that the proposed method is very effective for some realistic flow problems in unbounded domains, such as flows passing a circular cylinder.