Daniel,
I had went through step-21 and it appears step-43 extends step-21 with the 
intentions of improving preconditioning et cetera. In essence both the 
tutorials solve the same set of equations, namely Darcy's Law, conservation 
of mass and saturation equation. But for this set of approximate model 
equations the issue of 'spurious currents' doesn't arise (as far as I 
know). The set of equations I am solving are essentially same in nature to 
the ones solved in the 'Two phase flow interaction' code gallery program. 
These are very strong equations to model the two phase phenomenon and 
require sophisticated numerical treatment.
The exact problem I am currently facing in my code is 'spurious currents in 
the velocity field'. The test case is as follows. The problem is 2D and I 
am using homogeneous Dirichlet BC throughout the boundary. There is a 
droplet/bubble at the center of domain. So ideally my velocity vector 
should be homogeneous throughout the domain for all the time steps. Please 
have a look at the images of first few time steps - here 
<https://goo.gl/photos/8ww6erVhk92x4ESF9>. You can see in the images that 
with increment in time steps a non-physical velocity appears and the 
solution numerically diverges. This non-physical phenomenon is discussed in 
the papers I mentioned in the earlier post (just the abstracts are 
sufficient to know the reasons for 'spurious currents'). 

You mentioned the 'Two phase flow interaction' code gallery program and it 
shall be a good starting point for me. I shall then have to learn MPI as it 
is heavily used in this code. Also the material on XFEM 
<http://journals.ub.uni-heidelberg.de/index.php/ans/article/view/22317>page 
shall be helpful. Thank you!

 

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