Updated information regarding code results can be found at the Wengen 4 Web site.
Highly gravitationally unstable disk comparison project
Self-gravitating hydrodynamics and an isothermal equation of state. The code must also be able to integrate the motion of the central star.
The objective of this test is to evaluate a code's ability to resolve disk fragmentation and, more generally, to follow the evolution of a strongly self-gravitating gaseous disk.
- Durisen et al. (2007, PPV Chapter). Note: discusses preliminary test results. See image below.
- Gawryszczak et al., in prep.
The system of units are tailored to protoplanetary disks scales: G=1, mass unit = 0.1 Msun, and length unit = 6.25 AU. This system yields a code time unit = 7.864 yr. In the initial conditions, the thermal energy structure is also given. Although the effective first adiabatic index gamma = 1 for an isothermal EOS, we do set gamma = 1.4 to calculate the temperature structure everywhere based on the initial thermal energy structure of the grid. We convert the specific thermal energy to a temperature and sound speed as follows: U = ( kB * T ) / (mean_mol_weight * (gamma - 1)) and cs = sqrt((gamma) * kB * T / mean_mol_weight). The resulting temperature should be about 20K everywhere. We reiterate that the subsequent evolution is isothermal, where the effective gamma = 1, and setting gamma=1.4 is only used to recover the temperature structure, which remains fixed for the simulation.
Data files are linked below.
Molecular weight = 2, gamma = 7/5 (see note above), disk mass = 0.5509956, disk temperature (constant in space and time) = 20 K, cass of central star = 10, and the gravitational softening of the point mass = 0.25 times the gravitational softening of the SPH particles. SPH results will depend on the choice of gravitational softening (e.g Bate & Burkert, 1997). For SPH codes with non-adaptive softening, we use soft = 0.01 in a test run that fragments. With soft = 0.02, fragmentation was suppressed. Please run the simulation until time = 20 code units with outputs every 0.5 steps. For grid codes, the computational volume in Cartesian coordinates should be at least 8x8x0.8 (XxYxZ)length units. The grid data files have a thermal energy array created following the example given below, as done for the other tests. Therefore, the disk is embedded in a very low density cold T = 3 K medium just to fill the Cartesian grid. We stress that this problem is extremely sensitive to the initial conditions. Please see the Wengen 4 Web site for additional information.
The following data are Tipsy binary and ascii files. SPHers, please note: The initial conditions were generated in Gasoline. Take care when loading the data and choosing your neighbors, smoothing kernel, etc.
Gridded initial conditions are stored in the HDF5 format, where each file contains the complete Euler fields, i.e. density, x,y and z velocities and thermal energy. The gridded ICs were generated from the SPH particles using the tools available in the Tools section. The syntax for an case with a 64x64x256 output mesh is:
# smooth -s 32g -px 2000 -py 2000 -pz 8000 hsmooth -o test3 < test3.bin # hsmtoeps test3.bin test3.hsm > test3.eps # tipgrid -v -n 64 64 256 -l 2000 -xpd 1 -ypd 2 -p -dmin 0 -tmin 0 -msol 2.3262e5 -m 4 -o test3 < test3.eps # h5import test3.grid.d -c test3.cfg.d test3.grid.t -c test3.cfg.t test3.grid.vx -c test3.cfg.vx test3.grid.vy -c test3.cfg.vy test3.grid.vz -c test3.cfg.vz -o test3.h5
IMPORTANT! Note that this problem is highly sensitive to the noise imposed from the particle distribution. It is also suggested to transform the data to the frame of the star. A version of the gridded ICs that have this transformation are available on the Wengen 4 Web site.
See the Wengen 4 Web site.