We present Phantom, a fast, parallel, modular and low-memory smoothed particle hydrodynamics and magnetohydrodynamics code developed over the last decade for astrophysical applications in three dimensions. The code has been developed with a focus on stellar, galactic, planetary and high energy astrophysics and has already been used widely for studies of accretion discs and turbulence, from the birth of planets to how black holes accrete. Here we describe and test the core algorithms as well as modules for magnetohydrodynamics, self-gravity, sink particles, dust-gas mixtures, H2 chemistry, physical viscosity, external forces including numerous galactic potentials, Lense-Thirring precession, Poynting-Robertson drag and stochastic turbulent driving. Phantom is hereby made publicly available.

We study the dynamics of a viscous protoplanetary disc hosting a population of dust grains with a range of sizes. We compute steady-state solutions, and show that the radial motion of both the gas and the dust can deviate substantially from those for a single-size dust population. Although the aerodynamic drag from the dust on the gas is weaker than in the case where all grains are optimally coupled to the gas, the cumulative "back-reaction" of the dust particles can still alter the gas dynamics significantly. In typical protoplanetary discs, the net effect of the dust back-reaction decreases the gas accretion flow compared to the dust-free (viscous) case, even for dust-to-gas ratios of order 1%. In the outer disc, where dust grains are typically less strongly coupled to the gas and settle towards the midplane, the dust back-reaction can even drive outward gas flow. Moreover, the radial inward drift of large grains is reduced below the gas motion in the inner disc regions, while small dust grains follow the gas dynamics over all the disc extent. The resulting dust and gas dynamics can give rise to observable structures, such as gas and dust cavities. Our results show that the dust back-reaction can play a major role in both the dynamics and observational appearance of protoplanetary discs, and cannot be ignored in models of protoplanetary disc evolution.