A fast and explicit algorithm for simulating the dynamics of small dust
  grains with smoothed particle hydrodynamics
  We describe a simple method for simulating the dynamics of small grains in a
dusty gas, relevant to micron-sized grains in the interstellar medium and
grains of centimetre size and smaller in protoplanetary discs. The method
involves solving one extra diffusion equation for the dust fraction in addition
to the usual equations of hydrodynamics. This "diffusion approximation for
dust" is valid when the dust stopping time is smaller than the computational
timestep. We present a numerical implementation using Smoothed Particle
Hydrodynamics (SPH) that is conservative, accurate and fast. It does not
require any implicit timestepping and can be straightforwardly ported into
existing 3D codes.
