  We present a method for simulating the dynamics of a mixture of gas and
multiple species of large Stokes number dust grains, typical of evolved
protoplanetary discs and debris discs. The method improves upon earlier
methods, in which only a single grain size could be represented, by capturing
the differential backreaction of multiple dust species on the gas. This effect
is greater for large dust-to-gas ratios that may be expected in the later
stages of the protoplanetary disc life. We benchmark the method against
analytic solutions for linear waves, drag and shocks in dust-gas mixtures, and
radial drift in a protoplanetary disc showing that the method is robust and
accurate.
