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Spectral Direction Splitting Schemes for the Incompressible Navier-Stokes Equations

Published online by Cambridge University Press:  28 May 2015

Lizhen Chen ,
Jie Shen  and
Chuanju Xu
Lizhen Chen
Affiliation:
School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China
Jie Shen
Affiliation:
School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA
Chuanju Xu*
Affiliation:
School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China
*
Corresponding author. Email: cjxu@xmu.edu.cn
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Abstract

We propose and analyze spectral direction splitting schemes for the incompressible Navier-Stokes equations. The schemes combine a Legendre-spectral method for the spatial discretization and a pressure-stabilization/direction splitting scheme for the temporal discretization, leading to a sequence of one-dimensional elliptic equations at each time step while preserving the same order of accuracy as the usual pressure-stabilization schemes. We prove that these schemes are unconditionally stable, and present numerical results which demonstrate the stability, accuracy, and efficiency of the proposed methods.

Keywords

Navier-Stokes equationsprojection methoddirection splittingspectral methods
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 1 , Issue 3 , August 2011 , pp. 215 - 234
Copyright
Copyright © Global-Science Press 2011

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