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East Asian Journal on Applied Mathematics, 1 (2011), pp. 215-234. |
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Spectral Direction Splitting Schemes for the Incompressible 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 19 April 2011; Accepted (in revised version) 24 May 2011 Available online 27 July 2011 doi:10.4208/eajam.190411.240511a 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. Key words: Navier-Stokes equations, projection method, direction splitting, spectral methods. *Corresponding author. Email: cjxu@xmu.edu.cn (C. Xu) |