Collapse of a Uniform Sphere

t_{ff}=\sqrt{\frac{3 \pi}{32 G \rho}}$

The free fall time should be 1.5323

A single sink particle appears at approximately that time but then drifts from the center of the grid. This may be due to poor resolution (only based on the Jeans length)

movie​

Artificial fragmentation will occur whenever the density violates the TrueLove criterion. However, the Federrath criteria for forming sink particles requires more then just a single cell above the truelove criterion. The cell must be in the minimum of a local potential well, have converging flow from each direction, and the surrounding sphere with a radius of 4*dx where dx is the finest level resolution must also be a bound system. If the sphere of 4*dx is much larger then the collapsing condensation, then it can lead to problems since particles will likely not form although the jeans criterion will lead to artificial fragmentation. The only solution is to add more resolution…

Resolution study

The same problem was run with a maxlevel of 0 through 5. Note that when the MaxLevel is 0, 4 particles are created instantly (although this is puzzling since they are not all local potential minima) Also note that for MaxLevel = 5, the particle wanders.

movie​

Choice of PhiDot

To investigate the wandering we modified the program to allow for calculating \frac{\partial \phi}{\partial t} for a coarse step and then prolongating this to the finer level to use for updating the potential in ghost zones. This required advancing the coarse step before the finer steps and disables level threading. However as the movie​ shows it seems to have fixed the wandering problem.