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

Authors:
Z. Belhachmi;C. Bernardi;S. Deparis;F. Hecht
Affiliations:
L.M.A.M. (U.M.R. 7122), Université de Metz, Metz Cedex 01, France 57045;Laboratoire Jacques-Louis Lions, C.N.R.S. & Universitéé Pierre et Marie Curie, Paris Cedex 05, France 75252;Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, USA 02139;Laboratoire Jacques-Louis Lions, C.N.R.S. & Universitéé Pierre et Marie Curie, Paris Cedex 05, France 75252
Venue:
Journal of Scientific Computing
Year:
2006

Citing 2
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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.