Two-fluid dust and gas mixtures in smoothed particle hydrodynamics: 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.