This identical to the 1D sod shock tube tests, but in 2D:

 make clean (be SURE to do this if you do this after the 1D test)
 make

 ./2DSPMHD sshk.in

To see the plots against the exact solutions, use:
  nsplash sshk_0*.dat -y 18

Things to note/try
------------------
The main differences are that in 2D the particles have to "rearrange"
themselves behind the shock, leading to some noise in the velocity
profile due to the particle "re-meshing" motions. You will notice
that artificial conductivity also improves things.

- Try plotting the particle positions to see exactly how
  the particles remesh themselves behind the shock. I have
  setup some splash files to show this plot.
  
  nsplash -p parts sshk_0*.dat -y 2 -x 1


Note that I have started these calculations using a close packed
lattice -- the results are much worse with a cubic lattice:

- So try using a cubic lattice:

  Type "make edit" and change the call on lines 209 and 217 to
       call set_uniform_cartesian(1,psep...)
  instead of
       call set_uniform_cartesian(1,psep...)

  Then re-run the calculations.
  
 (The reason the cubic lattice is worse is that it is NOT a minimum
  energy state for the particles, so there is "double-remeshing" 
  going on, as the particles rearrange themselves both before and
  after the shock.)

- One final thing, it *is* possible to greatly reduce this "noise".
  To do so, we take the "correct" approach to achieving convergence
  in SPH, and use the quintic kernel that extends to a larger radius
  (as we have already noted, this is NOT the same thing as running
   the cubic spline with more neighbours):
   
  ./2DSPMHD sshkquintic.in

  (you will see now that the results are in fact very close to the
   one dimensional version)

Added by Daniel Price, July 2010
Revised Feb 2014
