Dear Frederik
The code for the Neuman boundary conditions were implemented in the cookiecutterbranch in TELEMAC, which can be downloaded from gitlab at:
gitlab.pam-retd.fr/otm/telemac-mascaret/...ee/cookiecuttershark
Note though that the code is based on v7p2 of TELEMAC, and have not been update to the latest TELEMAC releases. As far as I know, there are at the moment no plans to integrate this in a newer version.
The Neuman boundary conditions were implemented for the use in coastal models, were it is rather difficult to prescribe lateral boundary conditions (especially when you have wave driven currents). Internally, in converts the prescribed water level gradient to a velocity that is prescribed at the boundary. This works very well if the boundary is an inflow, but somewhat worse in case the boundary is an outflow. Therefore, I am not completely sure that it will be the best solution for your problem. My suggestion would that you change your model bathymetry, in order to have an extra (artificial zone) close to your boundary, where you have a downward slope, where the water can flow down to a river/lake, for which you prescribe the water level at the boundary, which you a few meters below the elevations of the bathymetry in your city. In this way, the water will flow down from the slope into this river, and it will not influence what happens in the city (which if I understood your question well is what you are after).
I hope this helps
Kind regards,
Alexander