Hello,
Unfortunately the whole theory is explained in my book "Hydrodynamics of free surface flows" which is for sale, with a pending Copyright, but you can browse most of it on a few websites, where only a few pages are removed. You also have the release notes, with a number of issues on Telemac-3D. Basically it solves the full non hydrostatic free surface Navier-Stokes equations.
With best regards,
Jean-Michel Hervouet