Smoothed Particle Hydrodynamics with particle splitting, applied to self-gravitating collapse

We describe and demonstrate a method for increasing the resolution locally in a Smoothed Particle Hydrodynamic (SPH) simulation, by splitting particles. We show that in simulations of self-gravitating collapse (of the sort which are presumed to occur in star formation) the method is stable, and affords great savings in computer time and memory. When applied to the standard Boss & Bodenheimer test -- which has been shown to depend critically on fulfilment of the Jeans Condition -- the results are comparable both with those obtained using Adaptive Mesh Refinement, and with those obtained using a standard high-resolution SPH simulation, but they are achieved with considerably less computational resource. Further development and testing is required before the method can safely be applied to more general flows.