Spectral Element Discretization for the Vorticity, the Velocity and the Pressure Formulation of the Axisymmetric Navier-Stokes Problem

摘要

We deal with the Navier-Stokes equations set in a three-dimensional axisymmetric bounded domain with non standard boundary conditions which involve the normal component of the velocity and tangential component of the vorticity. The axisymmetric property of the domain allows to reduce the three-dimensional problem into a two-dimensional one. We write a variational formulation with three independent unknowns: the vorticity, the velocity and the pressure. For the discretization, we use the spectral element methods, which are well-adapted here. We show the well-posedness of the obtained formulations and we establish error estimates for the three unknowns which proves the convergence of the method.