T10: The MHD shocktube problem:
try it out on your own

Before the tutorials:

As discussed in the Lecture, in the presence of magnetic fields, several different waves can be formed. In the lecture, we looked at some special cases. So, start with a classic paper,
Numerical Magnetohydrodynamics in Astrophysics: Algorithm and Tests for One-dimensional Flow,
where the authors provide the numerical solution for 5 different types simple MHD shock tubes and several variations on it. In this tutorial we will try to reproduce the setup of 5A, so see the corresponding figure and table for the detailed setup:

• Read off the initial left and right state from the description
• Have a look at the solution

During the tutorials:

You can start from a similar setup as used for the Riemann Problem in T04 and collect some different particle distributions.

You can now write a program to set up a long slab (along the x-axis) that represents your initial conditions.

• Stack the basic particle files along the x-direction. You might use 50 domains on each side.
• Note that the density setup allows to just use the same particle files but duplicated 2 times in each spatial direction on one side.
• Set the left and right state (note that you need in addition now a magnetic field vector).

Now you can run the simulation.

• When compiling the code, do not forget to switch on PERIODIC and NOGRAVITY again. Also, you have to indicate the non-cubic form of the simulation domain by setting LONG_X=100, LONG_Y=1 and LONG_Z=1. For the MHD, switch on MAGNETIC, MU0_UNITY and NO_SHEAR_VISCOSITY_LIMITER in the Config.sh file before compiling.
• Set up the parameter file for the simulation, especially adapt TimeMax 6, InitCondFile, TimeBetSnapshot 0.2.

Solutions

• Examples for script to set up simulations
  • setup_slab.pro in IDL
• Example for visualising the results
  • show_slab.pro in IDL
• You should see a movie like this
• Example using Fortran and gnuplot:
  • ifx -g -traceback -check all -fpe0 -o slabsetup slabsetup.f90
    (this uses glass.txt from T04)
  • ./slabsetup
  • gnuplot grid.plt (to check that the particle positions are set up correctly)
  • compile Gadget with PERIODIC and NOGRAVITY and with LONG_X=100, LONG_Y=1, and LONG_Z=1.
  • run Gadget using slab.ic as the initial conditions file and BoxSize = 1
    in the parameter file (and TimeMax = 6, TimeBetSnapshot = 0.1)
  • ifx -g -traceback -check all -fpe0 -o readsnap readsnap.f90
  • for file in snap_???; do ./readsnap $file >$file.txt; done
  • gnuplot slab.plt
    (this requires ffmpeg, which is installed on the mpusm06 machine)
  • xine -l slab.mp4

Extra

We know that the way the numerical equations are formulated we explicitly zeroed any transport of internal energy or magnetic fields, even by numerical error. This leads to non-damping of any oscillations in the solutions (like the pressure blip we remember from the normal shock tube experiment. So we can here explore how the solution is approached if we artificially induce some transport of energy and magnetic fields which might mimic unavoidable microscopic processes of real material.

• When compiling the code, we can include ARTIFICIAL_CONDUCTIVITY and MAGNETIC_DISSIPATION in the Config.sh file before compiling.
• We then need to set the according parameters ArtCondConstant 0.2 and ArtificialMagneticDissipationConstant 0.1.
• Can you spot the differences?