  We present MULTIGRAIN, an algorithm for simulating multiple phases of small
dust grains embedded in a gas, building on our earlier work in simulating
two-phase mixtures of gas and dust in SPH (Laibe & Price 2012a,b; Price & Laibe
2015). The MULTIGRAIN method (Hutchison, Price & Laibe 2018) 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. We demonstrate the MULTIGRAIN
algorithm on test problems related to the settling of dust in the discs of gas
around young stars, where solar systems are born. Finally I will discuss
possible extensions of the method to incorporate both large and small grains,
together with recent improvements in our numerical techniques for gas and dust
mixtures. In particular, I will show how the 'overdamping' problem identified
by Laibe & Price (2012a) can be solved.

Instrumentation and Methods for Astrophysics