Two-fluid dust and gas mixtures in smoothed particle hydrodynamics II: an improved semi-implicit approach

We present an improved version of the Loren-Aguilar & Bate (2014) method to integrate the two-fluid dust/gas equations that correctly captures the limiting velocity of small grains in the presence of net differences (excluding the drag force) between the accelerations of the dust and the gas. A series of accelerated DUSTYBOX tests and a simulation of dust-settling in a protoplanetary disc are performed comparing the performance of the new and old methods. The modified method can accurately capture the correct limiting velocity while preserving all the conservation properties of the original method.