model collisions between superparticles based on a Monte Carlo algorithm. We obtain the correct collision frequency by letting nearby superparticle pairs collide on the average once per collisional time-scale of the swarms of physical particles represented by each superparticle.

We have implemented the superparticle collision algorithm in the Pencil Code and will present detailed numerical tests that show its validity in a paper in preparation (Johansen, Youdin, & Lithwick, in preparation). The algorithm gives each particle a chance to interact with all other particles in the same grid cell. The characteristic time-scale $\tau_{\rm coll}^{(ij)}=1/(n_j
\sigma_{ij} \delta v_{ij})$ for a representative particle in the swarm of superparticle $i$ to collide with any particle from the swarm represented by superparticle $j$ is calculated by considering the number density $n_j$ represented by each superparticle, the collisional cross section $\sigma_{ij}$ of two swarm particles, and the relative speed $\delta v_{ij}$ of the two superparticles. For each possible collision a random number $P$ is chosen. If $P$ is smaller than $\delta t/\tau_{\rm coll}$, where $\delta t$ is the time-step set by magnetohydrodynamics, then the two particles collide. The collision outcome is determined as if the two superparticles were actual particles with radii large enough to 