T5: A collapsing gas cloud:
gravity meets hydodynamics

Before the tutorials:

As discussed in the Lecture, collapsing structures virialize. For a collapsing gas cloud, the potential energy thereby is converted into internal energy during the collapse. Here we will try to perform the so called Evrard collapse, which is a standard test case and very detailed described in this article in section 3.3, see also figure 6.
So think about:

• How is this different from the experiment done in T01?
• How can you create a larger, uniform density distribution out of the small patches used in T03?
• How can such a uniform distribution be changed to represent other, non uniform density fields?
• Which transformation has to be applied to get a density with a 1/r profile?

During the tutorials:

To run the experiment, we first need to

• Create a uniform distribution of particles with many particles (say 100x100x100)
• Transform this into a spherical distribution, following a given density profile
• Scale all to M_star=1.5815 and R_star=1.0 using G=1.0
• Compute the characteristic quantities eps*, rho*, v*, t*, P* etc.)
• Set the internal energy to 0.05 of the characteristic value.

Now we can perform the simulation and analyze it.

• When compiling the code, do not forget to switch off PERIODIC and NOGRAVITY and switch on EVALPOTENTIAL in the Config.sh file before compiling.
• When setting proper values in the file box.param, do not forget to also set PeriodicBoundariesOn 0 before running the simulation.
• Check the time evolution of the global properties (e.g. Epot, Ekin, Eint, Etot).
  Note that the first 4 columns in energy.txt contain t, Eint, Epot and Ekin for the full simulation (note that the energies still have to be divided by the total mass).
• Check the evolution of the density profiles.
• If you want to compare with an solution by an Eulerian code, you need to:
  • Copy over the PPM files provided: cp -r $HOME/Hydro/PPM .
  • Run the simulation by setting TimeBetSnapshot 0.1046949 to get the same output times.
  • Then use the files in the PPM folder. They contain radius, density and pressure as the first 3 columns.

Programming goals for T5:

Again, we are producing more complex initial conditions and run larger simulations, especially we will

• glue together particle distributions to create regions with more particles,
• cut out special geometries from such particle distributions,
• transform particle distributions to get representations of non uniform densities,
• learn to analyze some of the log files to check global properties.

Solutions

• Examples for a script to create a larger box of particles out of the small example patches from T03
  • enlarge_boxes.pro in IDL
  You should see an image like this:
  
• Examples for a script to create a 1/r density profile and to scale to our problem
  • setup_evcoll.pro in IDL
  You should see an image like this:
  
• Examples for a script to analyze results
  • show_collapse in IDL
  You should see images like this:
  

  

  

• Example using Fortran and gnuplot:
  • ifort -g -traceback -check all -fpe0 -o cloudsetup cloudsetup.f90
    (this uses glass_100x100x100.txt [warning: large file: 37 Mbytes], which is a text version of the large glass file created with enlarge_boxes.pro above, with coordinates in the range of 0 . . . 1)
  • ./cloudsetup
  • check that we actually have a 1/r profile:
    • ifort -g -traceback -check all -fpe0 -o histogram histogram.f90
    • ./histogram >histogram.txt
    • gnuplot histogram.plt
    • gv histogram.ps
  • run Gadget using cloud.ic as the initial conditions file and output as the snapshot file base in the parameter file
  • ifort -g -traceback -check all -fpe0 -o readsnap readsnap.f90
  • for file in output_???; do ./readsnap $file >$file.txt; done
  • gnuplot evolution.plt
  • gv evolution.ps