I'm simulating two phase immiscible drainage (air displacing water) in a rectangular domain of size .6mm x 2.4mm (2 dimensions) using Ansys FLUENT software.  I am using an implicit Volume of Fluid formulation with a PRESTO pressure solver and PISO pressure-velocity coupling, with 2nd order upwind schemes for momentum and volume fraction.  The problem is that even with a highly refined mesh, my scheme diverges very quickly (within the first few timesteps, using an algebraic multigrid solver).  When I try taking smaller timesteps (about $10^{-6}$ s), the solution takes a lot longer to diverge, but still diverges nonetheless.I'm not sure if the problem is with the choice of solver itself or if the boundary conditions were not set correctly.  I chose to use a constant inlet velocity of .0001m/s, and zero pressure conditions at the outlet.  I used no-slip boundary conditions at the other two walls, with wall adhesion and a constant air-to-water contact angle of 135 degrees.  Any help with this would be greatly appreciated! :)
What numerical methods are recommendable for simulating two phase immiscible fluid flow through a pipe with high capillary pressure?
linear solver;fluid dynamics;boundary conditions
It sounds like you are using Ansys Fluent. As I recall from some VOF articles most of them were using projection methods with explicit time stepping. If you are using Fluent you could try finding Non-iterative time advancement (NITE) option for time stepping.I would also suggest you trying to write your own solver! There are really good algorithms that you could try in that case. One of those is Moment of fluid (MOF) interface reconstruction developed by researchers from LANL. Here are some links that might be helpful:A paper from Int. J. Numer. Methods in Fluids, and a short note about the method from LANL web site