Hello Shenh, thank you for your answer.
Yes, my two boundaries represents the observed data and I have impose discharge, inflow and outflow, because I need to obtain information close to the outlet so I don't want the measurements to be influenced by the imposed level. I was wondering if a totally free boundary (444) would make any difference.
As for the Manning, I tried with values around 0.03/0.04 the first time but since the level was to low I increase it, since it is a more or less coarse river bed I figured this value was not so far up from the reality. But it did not changed that much the level.
I will try 1 for the viscosity and see how it change.