Volume 1, Issue 3
Spectral Direction Splitting Schemes for the Incompressible Navier-Stokes Equations

Lizhen Chen, Jie Shen & Chuanju Xu

East Asian J. Appl. Math., 1 (2011), pp. 215-234.

Published online: 2018-02

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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 pressurestabilization 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 equations projection method direction splitting spectral methods

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@Article{EAJAM-1-215, author = {Lizhen Chen, Jie Shen and Chuanju Xu}, title = {Spectral Direction Splitting Schemes for the Incompressible Navier-Stokes Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {1}, number = {3}, pages = {215--234}, 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 pressurestabilization schemes. We prove that these schemes are unconditionally stable, and present numerical results which demonstrate the stability, accuracy, and efficiency of the proposed methods.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.190411.240511a}, url = {http://global-sci.org/intro/article_detail/eajam/10905.html} }
TY - JOUR T1 - Spectral Direction Splitting Schemes for the Incompressible Navier-Stokes Equations AU - Lizhen Chen, Jie Shen & Chuanju Xu JO - East Asian Journal on Applied Mathematics VL - 3 SP - 215 EP - 234 PY - 2018 DA - 2018/02 SN - 1 DO - http://doi.org/10.4208/eajam.190411.240511a UR - https://global-sci.org/intro/article_detail/eajam/10905.html KW - Navier-Stokes equations KW - projection method KW - direction splitting KW - spectral methods AB -

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 pressurestabilization schemes. We prove that these schemes are unconditionally stable, and present numerical results which demonstrate the stability, accuracy, and efficiency of the proposed methods.

Lizhen Chen, Jie Shen & Chuanju Xu. (1970). Spectral Direction Splitting Schemes for the Incompressible Navier-Stokes Equations. East Asian Journal on Applied Mathematics. 1 (3). 215-234. doi:10.4208/eajam.190411.240511a
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