We present a ‘ two-fluid ’ implementation of dust in smoothed particle hydrodynamics ( SPH ) in the test particle limit .
The scheme is able to handle both short and long stopping times and reproduces the short friction time limit , which is not properly handled in other implementations .
We apply novel tests to verify its accuracy and limitations , including multi-dimensional tests that have not been previously applied to the drag-coupled dust problem and which are particularly relevant to self-gravitating protoplanetary discs .
Our tests demonstrate several key requirements for accurate simulations of gas-dust mixtures .
Firstly , in standard SPH particle jitter can degrade the dust solution , even when the gas density is well reproduced .
The use of integral gradients , a Wendland kernel and a large number of neighbours can control this , albeit at a greater computational cost .
Secondly , when it is necessary to limit the artificial viscosity we recommend using the switch , since the alternative , using \alpha \sim 0.1 , can generate a large velocity noise up to \sigma _ { v } \lesssim 0.3 c _ { s } in the dust particles .
Thirdly , we find that an accurate dust density estimate requires > 400 neighbours , since , unlike the gas , the dust particles do not feel regularization forces .
This density noise applies to all particle-based two-fluid implementations of dust , irrespective of the hydro solver and could lead to numerically induced fragmentation .
Although our tests show accurate dusty gas simulations are possible , care must be taken to minimize the contribution from numerical noise .