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

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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.

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References

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Authors and Affiliations

  1. L.M.A.M. (U.M.R. 7122), Université de Metz, I.S.G.M.P., bât. A, Ile de Saulcy, 57045, Metz Cedex 01, France

    Z. Belhachmi

  2. Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252, Paris Cedex 05, France

    C. Bernardi & F. Hecht

  3. Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    S. Deparis

Authors
  1. Z. Belhachmi
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  2. C. Bernardi
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  3. S. Deparis
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  4. F. Hecht
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Correspondence to Z. Belhachmi.

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Belhachmi, Z., Bernardi, C., Deparis, S. et al. An Efficient Discretization of the Navier–Stokes Equations in an Axisymmetric Domain. Part 1: The Discrete Problem and its Numerical Analysis. J Sci Comput 27, 97–110 (2006). https://doi.org/10.1007/s10915-005-9035-y

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  • DOI: https://doi.org/10.1007/s10915-005-9035-y

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