Two fluid dust and gas mixtures in SPH: A semi-implicit approach
  A method to avoid the explicit time integration of small dust grains in the two fluid gas/dust smoothed particle hydrodynamics (SPH) approach is proposed. By assuming a very simple exponential decay model for the relative velocity between the gas and dust components, all the effective characteristics of the drag force can be reproduced. A series of tests has been performed to compare the accuracy of the method with analytical and explicit integration results. We find that the method performs well on a wide range of tests, and can provide large speed ups over explicit integration when the dust stopping time is small. We have also found that the method is much less dissipative than conventional explicit or implicit two-fluid SPH approaches when modelling dusty shocks. 
Pablo Loren-Aguilar and Matthew R. Bate
astro-ph.EP