Problems in assigning inlet-outlet boundary condition for a two phase flow

Dear all,

I am trying to simulate a laminar two phase flow passing over a cylinder with a phase-field model where the cylinder is submerged into the water (heavier fluid), as a part of my project. I have tried a couple of candidates for the boundary condition at the inlet and the outlet. Initially, I gave a uniform velocity at the inlet for both phases plus a zero pressure at the outlet, then I assigned a mass flow rate for both phases and mass flow rate at the exit and a few other failed attempts. Also I have tried to give a step function at the inlet for the volume fraction at the level of my free surface and give a uniform velocity which I could not even implement.

Receiving a piece of advice, I have recently tried to give a zero pressure gradient at both sides and a body force or a small acceleration in the x-direction (as my driving force), but it seems that after sometime (4% of run-time in my case) the "reciprocal of the step size" increases and causes a failure.

I would be glad if there is a solution for the problem. I also attached the basic model here.

Amin,