Hi Riadh,
I've finished simulating with the changes you mentionned and although there is still quite a bit of variation in the flow at the downstream boundary, the level variation near the upstream boundary has decreased about tenfold, which is quite good. But, after 2 hours, it still hasn't totally stabilized. I will try to run it for much longer over the weekend to see what happens.
Martin,
I've tried what you suggested and the time step for the same Courant number has increased by about 12 %, which is nice. The simulation has finished yet, so I can't comment on the other impacts.
Thanks again to both of you for the provided help !
Martin