T4: Propagating sound waves:
sound speed and interference

Before the tutorials:

Think about:

What are waves?
What is the difference between a longitudinal wave and a transversal wave?
What is the sound speed of a medium?
What is the Amplitude of a wave?
What is the wavelength?

During the tutorials:

To run the experiment, we first need to

Create a slab with uniform distribution of particles (say, 200×10×10)
Initialize a sound wave

Now we can perform the simulation and analyze it.

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=20, LONG_Y=1 and LONG_Z=1 in the Config.sh file before compiling.
When setting proper values in the file box.param, do not forget to also set PeriodicBoundariesOn 1 again, before running the simulation.
Think about what is a good value for TimeMax?
Verify that the perturbation propagates with the sound speed.
Verify that the propagation speed does not depend on the amplitude of the wave.
Check what happens if you increase the wavelength.

Also remember the tutorials where we used different Kernels. To resolve the sound wave properly, we need to go to very good recovery of the density, as the amplitude of the wave is really tiny. Therefore, you might see significant noise in your standard settings. So try to use a more elaborated kernel by setting WENDLAND_C6_KERNEL within your Config.sh. The code sets DesNumNgb by default, but from the experience of the previous tutorials, you can set your own vale in the box.param file.

Programming goals for T6:

Again, we are producing different initial conditions and run simulations on non-cubic domains, especially we will

glue together particle distributions to create a slab-like region
set up some initial perturbation
Explore the use of MPI or OpenMP for parallel features and see if there are speedups of the code.
- Try to use different values (like 2 or 4) for export OMP_NUM_THREADS=2 before unning the simulations
- Try different numbers (like 1,2,4 or 8) when running mpiexec -np 2 OpenGadget3/OpenGadget3 box.param

Solutions

If you notice some damping of the wave, this might be caused by the so called artificial viscosity which the underlying SPH code needs to work properly in presence of strong shocks. So to play around with this, you can reduce the amount of artificial viscosity used by reducing the value of ArtBulkViscConst within your box.param file significantly (e.g. try a value ten times smaller).

First use the example initial condition file to start a simulation:
wget https://www.usm.uni-muenchen.de/~dolag/Lille2026/T04/box.ic
Later, build your own initial condition file:
- wget https://www.usm.uni-muenchen.de/~dolag/Hydro/Hydro/glass_10x10x10
- wget https://www.usm.uni-muenchen.de/~dolag/Hydro/Hydro/Python/ic_header
  (if not already done before)
- wget https://www.usm.uni-muenchen.de/~dolag/Lille2026/T04/setup_slab.py
- python3 setup_slab.py
Examples for the initial velocity perturbation
Examples for a script to show the time evolution
Solutions in Python:
- wget https://www.usm.uni-muenchen.de/~dolag/Lille2026/T04/show_wave.py
- python3 show_wave.py
Examples for the propagation of a longitudinal wave
Examples for a transverse wave
Examples comparing waves with different wavelength or amplitudes

Useful commands