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Spectral Direction Splitting Schemes for the Incompressible Navier-Stokes Equations

Spectral Direction Splitting Schemes for the Incompressible Navier-Stokes Equations
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Year:    2011

East Asian Journal on Applied Mathematics, Vol. 1 (2011), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.190411.240511a

East Asian Journal on Applied Mathematics, Vol. 1 (2011), Iss. 3 : pp. 215–234

Published online:    2011-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Navier-Stokes equations projection method direction splitting spectral methods.

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