Hello Toby,
Thanks for your feedback.
Indeed, for the diffusion of sediment, due to the settling velocity, the matrix to invert may be non-symmetric and the conjugate gradient is not efficient anymore.
If you have a look at the TELEMAC-3D dictionary, you can see that default value for SOLVER FOR DIFFUSION OF THE SEDIMENT is 3 contrary to solvers for diffusion of other variables (velocities, tracers, k-epsilon) for which 1 = conjugate gradient is usually efficient.
Anyway, you are right, when the matrix is non symmetric, I would recommend to use GMRES. Be careful in that case if you use LIPS advection scheme for sediment, there may be oscillations close to tidal flats, Alexander Breugem noticed that in a specific case.
Hope this helps,
Chi-Tuan