A Kelvin-Helmholtz test and a new version of the 'blob test' for testing the evolution of multiphase flow in smoothed particle hydrodynamics.
Blob test: A spherical cloud of gas with uniform density, in pressure equilibrium with an ambient medium, is placed in a wind-tunnel with periodic boundary conditions. The imposed wind has a mach number M=2.7, and the density and temperature ratios are 10.
Kelvin-Helmholtz test: Two fluids in pressure equilibrium with a density contrast of 2 with opposing velocities. The interface between the fluids is perturbed leading to a phase in which the layers roll-up into a vortex (see image on the top of this page) and subsequent evolution mixes the fluids.
Non-selfgravitating hydrodynamical test. Solve only the Euler equations.
Blob test: To test processes of astrophysical interest such as ram-pressure stripping, multiphase interactions, mixing, Kelvin-Helmholtz (KH) and Rayleigh-Taylor (RT) instabilites.
Kelvin-Helmholtz test: To asses the ability of a code to treat multiphase flows and the interaction between the phases.
Blob test: No full analytical solution exists. However, KH and RT instabilites grows freely and a typical time-scale for cloud destruction can be assigned to time when largest possible mode (size of the cloud) has fully grown, see Agertz et al. (2007) for details.
Kelvin-Helmholtz test: The growth-time for the initial phase in which the two layers form a vortex is well described by linear perturbation analysis (Chandrasekhar 1961). The analysis for this specific initial condition can be found in Read, Hayfield & Agertz 2009.
Blob test: Similar experiments, including shock wave interactions with clouds, have been studied by
KH test: Most standard textbooks on fluid dynamics discuss this problem. A few examples of recent numerical work is:
Same as the Wengen 3 blob test.
The initial conditions are similar to the Wengen 3 blob test. The only changes are the smaller simulation domain, particle configuration and blob perturbation:
The simulation domain is a periodic rectangular box with dimensions
where the cloud is centered on .
The initial conditions were generated by placing equal-mass in a lattice configuration satisfying the above description. To seed an initial instability we use spherical harmonics to apply large scale perturbations to the surface layer of the cloud. A full description of this can be found in Read, Hayfield & Agertz 2009.
The Kelvin-Helmholtz test uses gas variables that represent the surface of the cloud. The simulation domain is a periodic slab of size
centered on where the equal mass particles sit in a lattice configuration in order to satisfy the following domains:
In the units specified above,
To trigger instabilities, velocity perturbations are imposed on the two boundaries of the form
where the perturbation velocity and is the wavelength of the mode.
The first and third files are the main initial conditions used in Read, Hayfield & Agertz 2009. The stacked KH test is useful when many smoothing neighbours are used. The last file is a low resolution version of the real blob test and we caution the user that the turbulent outcome of this test can be very different from the higher resolution one!
To first order, central density slices are useful in determining how and if the cloud disrupts. Expect to see large scale intabilitiy-modes modes to have grown around, in the units of the IC:s, t_KH=2 Gyr (see references). In the section of performed runs so far we present slices at t=1,2 and 3 t_KH
Mass-loss diagrams are useful to track how well the instabilities can disrupt the cloud. Agertz et al. (2007) defined any element with density rho > 0.64 rho_cl to be associated with the cloud.
More detailed suggestions are welcome (Sub-clump survival, numerical diffusion due to resolution, entropy conservation etc.)!
The table below lists the codes that have run these tests so far. Please feel free to add yours!
The images are density contours.
These are movies of the GADGET-2 patch version of OSPH:
blobosph.mov Movie of the blob test using OSPH (density)
sph12_den.mov Movie of the KH test using SPH (density)
sph12_parts.mov Movie of the KH test using SPH (particles)
osph12442_den.mov Movie of the KH test using OSPH-HOCT4-442 (density)
osph12442_parts.mov Movie of the KH test using OSPH-HOCT4-442 (particles)