A representative particle approach to coagulation and fragmentation of dust aggregates and fluid droplets

Context. There is increasing need for good algorithms for modeling the aggregation and fragmentation of solid particles (dust grains, dust aggregates, boulders) in various astrophysical settings, including protoplanetary disks, planetary- and sub-stellar atmospheres and dense molecular cloud cores. Here we describe a new algorithm that combines advantages of various standard methods into one. Aims. The aim is to develop a method that 1) can solve for aggregation and fragmentation; 2) can easily include the effect and evolution of grain properties such as compactness, composition, etc.; and 3) can be built as a coagulation/fragmentation module into a hydrodynamics simulation where it 3a) allows for non-thermalized non-local motions of particles (e. g. movement of particles in turbulent flows with stopping time larger than eddy turn-over time) and 3b) focuses computational effort there where most of the mass is. Methods. We develop a Monte-Carlo method in which we follow the life of a limited number of representative particles. Each of these particles is associated with a certain fraction of the total dust mass and thereby represents a large number of true particles which all are assumed to have the same properties as their representative particle. Under the assumption that the total number of true particles vastly exceeds the number of representative particles, the chance of a representative particle colliding with another representative particle is negligibly small, and we therefore ignore this possibility. This now makes it possible to employ a statistical approach to the evolution of the representative particles, which is the core of our Monte Carlo method. Results. The method reproduces the known analytic solutions of simplified coagulation kernels, and compares well to numerical results for Brownian motion using other methods. For reasonably well-behaved kernels it produces good results even for moderate number of swarms.