touch each other. By solving for momentum conservation and energy conservation, with the possibility for inelastic collisions to dissipate kinetic energy to heat and deformation, the two colliding particles acquire their new velocity vectors instantaneously.

All simulations include collisions with a coefficient of restitution of $\epsilon=0.3$ [e.g @BlumMuench1993], meaning that each collision leads to the dissipation of approximately 90% of the relative kinetic energy to deformation and heating of the colliding boulders. We include particle collisions here to obtain a more complete physical modelling. Detailed tests and analysis of the effect of particle collisions on clumping and gravitational collapse will appear in a future publication (Johansen, Youdin, & Lithwick, in preparation).

Computing resources and code optimisation {#s:code}
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For this project we were kindly granted access to 4096 cores on the “Jugene” Blue Gene/P system at the Jülich Supercomputing Centre (JSC) for a total of five months. Each core at the BlueGene/P has a clock speed of around 800 MHz. The use of the Pencil Code on several thousand cores required both trivial and more fundamental changes to the code. We describe these technical improvements in detail in this appendix.

In the following [nxgrid]{}, [nygrid]{}, [nzgrid]{} refer to the full 