i solve axisymmetric Navier-Stokes equation with periodic boundary condition in 2D domain.

- my first question : how can i do to represent the solution in the rest of the domain in 2D . Example suppose i solve the equation in [0,2 ]
*[0,3 ] and i the have (u1, u2) in [0,2 ]*[0,3 ] we have the symmetric with axe y=0 . how can i do to have the solution (u1, u2) in the other sider [-2,0]*[0,3] , then export with paraview

If I understand the question correctly, you are solving the axisymmetric Navier-Stokes in (r,z) \in [0,2 ] x [0,3 ] domain, and then want to visualize the 3D result.

The only way I see of doing this is by writing the VTK files yourself. You can define 3D cells obtained by rotating the 2D mesh. If the solution is axisymmetric, then you know the values everywhere in the cylinder. If you are using Fourier/Finite Elements, then still you can compute the value of the solution by hand.

There is also a Fourier/Finite Elements code SFEMANS (written in Fortran), which does that SFEMaNS, but I think it would be much easier for you to write the vtk files yourself. It can be done.