An Efficient Discretization of the Navier–Stokes Equations in an Axisymmetric Domain. Part 1: The Discrete Problem and its Numerical Analysis

Any solution of the Navier–Stokes equations in a three-dimensional axisymmetric domain admits a Fourier expansion with respect to the angular variable, and it can be noted that each Fourier coefficient satisfies a variational problem on the meridian domain, all problems being coupled due to the nonl...

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Bibliographic Details
Published in:Journal of scientific computing 2006-06, Vol.27 (1-3), p.97-110
Main Authors: Belhachmi, Z., Bernardi, C., Deparis, S., Hecht, F.
Format: Article
Language:English
Subjects:
Discretization
Finite element method
Fluid flow
Mathematical analysis
Navier-Stokes equations
Numerical analysis
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Summary:Any solution of the Navier–Stokes equations in a three-dimensional axisymmetric domain admits a Fourier expansion with respect to the angular variable, and it can be noted that each Fourier coefficient satisfies a variational problem on the meridian domain, all problems being coupled due to the nonlinear convection term. We propose a discretization of these equations which combines Fourier truncation and finite element methods applied to each two-dimensional system. We perform the a priori and a posteriori analysis of this discretization.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-005-9035-y