A Particle Module for the PLUTO Code: III -- Dust

The implementation of a new particle module describing the physics of dust grains coupled to the gas via drag forces is the subject of this work. The proposed particle-gas hybrid scheme has been designed to work in Cartesian as well as in cylindrical and spherical geometries. The numerical method relies on a Godunov-type second-order scheme for the fluid and an exponential midpoint rule for dust particles which overcomes the stiffness introduced by the linear coupling term. Besides being time-reversible and globally second-order accurate in time, the exponential integrator provides energy errors which are always bounded and it remains stable in the limit of arbitrarily small particle stopping times yielding the correct asymptotic solution. Such properties make this method preferable to the more widely used semi-implicit or fully implicit schemes at a very modest increase in computational cost. Coupling between particles and grid quantities is achieved through particle deposition and field-weighting techniques borrowed from Particle-In-Cell simulation methods. In this respect, we derive new weight factors in curvilinear coordinates that are more accurate than traditional volume- or area-weighting. A comprehensive suite of numerical benchmarks is presented to assess the accuracy and robustness of the algorithm in Cartesian, cylindrical and spherical coordinates. Particular attention is devoted to the streaming instability which is analyzed in both local and global disk models. The module is part of the PLUTO code for astrophysical gas-dynamics and it is mainly intended for the numerical modeling of protoplanetary disks in which solid and gas interact via aerodynamic drag.