MULTIGRAIN: a smoothed particle hydrodynamic algorithm for multiple small dust grains and gas

We present a new algorithm, multigrain, for modelling the dynamics of an entire population of small dust grains immersed in gas, typical of conditions that are found in molecular clouds and protoplanetary discs. The multigrain method is more accurate than single-phase simulations because the gas experiences a backreaction from each dust phase and communicates this change to the other phases, thereby indirectly coupling the dust phases together. The multigrain method is fast, explicit and low storage, requiring only an array of dust fractions and their derivatives defined for each resolution element.