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

Belhachmi, Z.Bernardi, C.Deparis, S.Hecht, F.2012-08-022012-08-022012-08-02200610.1007/s10915-005-9035-yhttps://infoscience.epfl.ch/handle/20.500.14299/84352Any 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.Navier–Stokes equationsFourier truncationfinite element methodAn Efficient Discretization of the Navier–Stokes Equations in an Axisymmetric Domain. Part 1: The Discrete Problem and its Numerical Analysistext::journal::journal article::research article