Hi,
I'm looking at axisymmetric solutions to the incompressible Navier-Stokes equations. The $r^{-2}$ terms and boundary conditions pose a problem at the axis.
From some papers I've found one solution is to extend the domain from $[0,r]$ to $[-r,r]$ and reduce the azimuthal extent of the domain from $[0,2\pi]$ to $[0,\pi]$. Provided there are no nodes on $r=0$ then everything works out fine. Unfortunately your domain is now twice as big as it was previously.
The domain can then be reduced by considering only the $r>0$ section and applying antisymmetric boundary conditions to the boundary by the axis. I.e. if a point on one side of the axis has a $u_r$ component of $a$ then its corresponding point on the other side of the axis has $u_r = -a $
How would one go doing about this in FEniCS? Is it possible? I can see how one would do it if you were applying symmetric boundary conditions (you would just set $\frac{du_r}{dr}= 0 $ on the symmetric boundary).
Thanks for any help
