Journal of Scientific Computing

, Volume 27, Issue 1–3, pp 97–110

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

Article

## Abstract

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.

## Keywords

Navier–Stokes equations Fourier truncation finite element method

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## References

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## Authors and Affiliations

• Z. Belhachmi
• 1
• C. Bernardi
• 2
• S. Deparis
• 3
• F. Hecht
• 2
1. 1.L.M.A.M. (U.M.R. 7122)Université de MetzMetz Cedex 01France
2. 2.Laboratoire Jacques-Louis LionsC.N.R.S. & Université Pierre et Marie CurieParis Cedex 05France
3. 3.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA