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Modelling the formation of super-km-sized planetesimals by gravitationalcollapse of regions overdense in small particles requires numerical algorithmscapable of handling simultaneously hydrodynamics, particle dynamics andparticle collisions. While the initial phases of radial contraction aredictated by drag forces and gravity, particle collisions become gradually moresignificant as filaments contract beyond Roche density. Here we present a newnumerical algorithm for treating momentum and energy exchange in collisionsbetween numerical superparticles representing a high number of physicalparticles. We adopt a Monte Carlo approach where superparticle pairs in a gridcell collide statistically on the physical collision time-scale. Collisionsoccur by enlarging particles until they touch and solving for the collisionoutcome, accounting for energy dissipation in inelastic collisions. Wedemonstrate that superparticle collisions can be consistently implemented at amodest computational cost. In protoplanetary disc turbulence driven by thestreaming instability, we argue that the relative Keplerian shear velocityshould be subtracted during the collision calculation. If it is not subtracted,density inhomogeneities are too rapidly diffused away, as bloated particlesexaggerate collision speeds. Local particle densities reach several thousandtimes the mid-plane gas density. We find efficient formation of gravitationallybound clumps, with a range of masses corresponding to contracted radii from 100to 400 km when applied to the asteroid belt and 150 to 730 km when applied tothe Kuiper belt, extrapolated using a constant self-gravity parameter. Thesmaller planetesimals are not observed at low resolution, but the masses of thelargest planetesimals are relatively independent of resolution and treatment ofcollisions.

Adding particle collisions to the formation of asteroids and Kuiper belt objects via streaming instabilities