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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 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.

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@Article{EAJAM-1-215, author = {}, 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 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.

}, 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 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, projection method, direction splitting, 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 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.

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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