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

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, 361005, Xiamen, China

    Qingqu Zhuang & Chuanju Xu

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Jie Shen

Authors
  1. Qingqu Zhuang
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  2. Jie Shen
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  3. Chuanju Xu
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Corresponding author

Correspondence to Chuanju Xu.

Additional information

The work of J. Shen was partially supported by NFS grant DMS-0610646 and AFOSR grant FA9550-08-1-0416.

The research of C. Xu was partially supported by National NSF of China under Grant 10531080, the Excellent Young Teachers Program by the Ministry of Education of China, and 973 High Performance Scientific Computation Research Program 2005CB321703.

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Zhuang, Q., Shen, J. & Xu, C. A Coupled Legendre-Laguerre Spectral-Element Method for the Navier-Stokes Equations in Unbounded Domains. J Sci Comput 42, 1 (2010). https://doi.org/10.1007/s10915-009-9313-1

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  • DOI: https://doi.org/10.1007/s10915-009-9313-1

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