>> 
> The simulation does start with both phases and the geometry is supposed to 
> become more complex as the simulation progresses.
> But so far the run is stopped before there are significant changes in the 
> shape of the droplet. 

Humm,  not sure why you are seeing degradation then.  I imagine the initial 
geometry is not grid aligned so I'm not sure why you are seeing degradation in 
convergence rate.

> I can give a shot to AMG: which options would you suggest to use.

-pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1

> Also, how can I project out the constant from the rhs? Thanks a lot!

http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetNullSpace.html#KSPSetNullSpace

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