vof + hydrostatic pressure
 

Hello,
I hope this is not a Faq, I tried to search in the forum for a similar problem but I didn't find anything that helps me.

I'd like to model a free surface flow, basically a channel with a body inside (at this stage the body is kept fixed).

I set up a velocity inlet and a pressure outlet while the other BC are walls (or symmetry I don't think this is important now).
I used udf to proper set up the input and the output for Vof.

I set up the primary phase as air and the secondary phase as water. I left spatial discretization as default (Least square for gradients, PRESTO! for pressure First Order Upwind both for Momentum and VoF).

I'm interested in a steady simulation so I have chosen the steady solver.
If I don't consider gravity I am able to reach a converged solution (even if, pretty strange, it is better not to initialize the VOF but to start with the Vof set to the same value in the whole domain).
Since the density of water is constant I know that this solution would be still valid if gravity was present; the difference would be to consider p as p - rho_H20 g (H_0-y).

I tried afterward to switch on the gravity and set up air as reference density.
This should allow me to get rid of the hydrostatic contribution of the air. I changed the outlet pressure bc in order to account for the hydrostatic pressure by a proper udf that adds the water hydrostatic contribution.
In this way the computation blows up. I have a lot of reversed flow from outlet also. I tried to initialize properly via udf also the Vof and the pressure (I checked that the fields are correctly initialized) but nothing helps.
I guess the tricky point is to initialize properly the pressure but I'm not sure how to do this.

Am I misunderstood something? Does anybody have any suggestion? I searched for a tutorial that addresses a similar problem but was not able to find anything...

Thank you.