  Modelling the formation of super-km-sized planetesimals by gravitational
collapse of regions overdense in small particles requires numerical algorithms
capable of handling simultaneously hydrodynamics, particle dynamics and
particle collisions. While the initial phases of radial contraction are
dictated by drag forces and gravity, particle collisions become gradually more
significant as filaments contract beyond Roche density. Here we present a new
numerical algorithm for treating momentum and energy exchange in collisions
between numerical superparticles representing a high number of physical
particles. We adopt a Monte Carlo approach where superparticle pairs in a grid
cell collide statistically on the physical collision time-scale. Collisions
occur by enlarging particles until they touch and solving for the collision
outcome, accounting for energy dissipation in inelastic collisions. We
demonstrate that superparticle collisions can be consistently implemented at a
modest computational cost. In protoplanetary disc turbulence driven by the
streaming instability, we argue that the relative Keplerian shear velocity
should be subtracted during the collision calculation. If it is not subtracted,
density inhomogeneities are too rapidly diffused away, as bloated particles
exaggerate collision speeds. Local particle densities reach several thousand
times the mid-plane gas density. We find efficient formation of gravitationally
bound clumps, with a range of masses corresponding to contracted radii from 100
to 400 km when applied to the asteroid belt and 150 to 730 km when applied to
the Kuiper belt, extrapolated using a constant self-gravity parameter. The
smaller planetesimals are not observed at low resolution, but the masses of the
largest planetesimals are relatively independent of resolution and treatment of
collisions.
