Hello,
To answer to the only question concerning TELEMAC-2D, if you do not need that TELEMAC-2D knows the exact location of your domain (e.g. if you do not have to know latitude/longitude for features like varying Coriolis coefficient, astronomical tidal force, tidal boundary conditions) e.g. if you model a flume, you can work with local coordinates (what you call relative coordinates).
For the single tidal boundary conditions, it is possible to work with local coordinates if changing 2 integers in the geometry file, you can have a look at the TELEMAC-2D user manual:
"Since release 8.2, it is possible to use x and y origin coordinates stored in the geometry file to decrease the number of digits of coordinates when modelling tide, e.g. when using UTM or Lambert projections. The two numbers are stored in the I_ORIGIN and J_ORIGIN variables reachable with the help of GET_MESH_ORIG subroutine. Caution: these two numbers are integers, not floats as the preliminary structure available in the SERAFIN format expected this type for these 2 variables. The tidal computations automatically take into account this offset for UTM + Lambert projections when generating the HARMONIC CONSTANTS FILE for JMJ database or when interpolating harmonic constants to compute boundary or initial conditions for solutions coming from OSU (e.g. TPXO). In particular for the operations to locate the nodes correctly (a simple translation) but TELEMAC-2D still continues to compute other steps in a local coordinate system."
Otherwise, as suggested by the other users, you should use file format with SERAFIND (with a D as double precision) or MED.
Hope this helps,
Chi-Tuan