Commun. Comput. Phys., 12 (2012), pp. 315-336.


A Unstructured Nodal Spectral-Element Method for the Navier-Stokes Equations

Lizhen Chen 1, Jie Shen 2, Chuanju Xu 1*

1 School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China.
2 School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China; and Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA.

Received 7 January 2011; Accepted (in revised version) 14 July 2011
Available online 30 January 2012
doi:10.4208/cicp.070111.140711a

Abstract

An unstructured nodal spectral-element method for the Navier-Stokes equations is developed in this paper. The method is based on a triangular and tetrahedral rational approximation and an easy-to-implement nodal basis which fully enjoys the tensorial product property. It allows arbitrary triangular and tetrahedral mesh, affording greater flexibility in handling complex domains while maintaining all essential features of the usual spectral-element method. The details of the implementation and some numerical examples are provided to validate the efficiency and flexibility of the proposed method.

AMS subject classifications: 65N35, 65N22, 65F05, 35J05

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Key words: Navier-Stokes equations, unstructured mesh, triangular spectral element method.

*Corresponding author.
Email: xunyicao2009@yeah.net (L. Chen), shen7@purdue.edu (J. Shen), cjxu@xmu.edu.cn (C. Xu)
 

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