T9a: Viscosity:
flow between two plates

Before the tutorials:

Think about:

• The effect of viscosity can be important for astronomical objects, like galaxy clusters. See, for example, this paper.
  Note that here viscosity is dependent on the plasma parameters (like temperature).
• What does viscosity mean?
  You might find this video from the 1960s useful, even more information can be found here.

During the tutorials:

Today’s experiment (viscous flow between two plates)

To run this experiment, we first need to

• Use a basic 100×100×10 setup similar to T08 to check the role of viscosity between two moving plates, as shown in Figure 1 of the above mentioned paper.
  • Bring the grid to a dimension of 1×1×0.1 and set density and pressure to 1.
  • Mark two (thin) boundary layers (left and right) as boundary particles (i.e., set their ID to zero).
  • Give them opposite velocities in the y direction.
  • Just to avoid unwanted effects, set the pressure in the walls 5% larger than in the rest.
• To run the simulation:
  • Set PERIODIC and NOGRAVITY in the Config.sh.
  • Set LONG_X=1, LONG_Y=1, LONG_Z=0.1 and SPH_BND_PARTICLES and SPH_BND_PARTICLES_ALLOW_DRIFT in the Config.sh for the box geometry.
  • Set NAVIERSTOKES and NAVIERSTOKES_CONSTANT in the Config.sh to switch on viscosity.
  • Add ShearViscosityTemperature 5.0e7 and FractionSpitzerViscosity 1.0 to the parameter file.
  • Also set UnitLength_in_cm 3.085678e21, UnitMass_in_g 1.989e43 and UnitVelocity_in_cm_per_s 1e5 in the parameter file to get the right unit system.
• Look at the evolution of the y velocity and explain what happens.
• Do you see the similarity to the glacier shown in the above movie?

Programming goals for T9:

Improve your ability to set up special geometries in the initial conditions.

Solution

• Again, extending the setup script from T07 for the first test problem.
  • setup_slab.pro in IDL
  you should get something like:
• To look at the evolution of the velocity in y direction.
  • show_slab.pro in IDL
  you should get something like shown below
• Example using Fortran and gnuplot:
  • ifx -g -traceback -check all -fpe0 -o shearsetup shearsetup.f90
    (this uses glass.txt from T04)
  • ./shearsetup
  • gnuplot grid.plt (to check that the particle positions are set up correctly)
  • compile Gadget with PERIODIC, NOGRAVITY and SPH_BND_PARTICLES and SPH_BND_PARTICLES_ALLOW_DRIFT and with LONG_X=10, LONG_Y=10, and LONG_Z=1.
  • run Gadget using shear.ic as the initial conditions file and BoxSize = 1
    in the parameter file (and TimeMax = 200, TimeBetSnapshot = 1.0)
  • ifx -g -traceback -check all -fpe0 -o readsnap readsnap.f90
  • for file in snap_???; do ./readsnap $file | sort -g -k8,8 >$file.txt; done
  • gnuplot shear.plt
    (this requires ffmpeg, which is installed on the mpusm06 machine)
  • xine -l shear.mp4