Hello Leo
Actually these informations are nomore up-to-date. First, when it was implemented, this scheme was dependant to node numbering, but later, this problem was overcame and this scheme is one of the best ones of the FE kernel of Telemac-2D. It is positive, mass conservative, with low numerical diffusion, and recommanded for models having wetting and drying passages.
It's only drawback is the fact that it is explicit in time, thus a little bit more expensive in CPU time. Note that, although it is explicit, this remains completely transparent for user, Telemac makes internal sub-iterations to take into account the stability criterion.
In a nutshell, this scheme is the one to use for severe unsteady models and especially for tracer transport. As far as I know, there is no difference between serial and parallel results. The only differences could be observed only when looking at machine precision level and these differences are mainly due to round-off error.
I hope that this is helpful
With my best regards,
Riadh