A hybrid SPH/N-body method for star cluster simulations
  We present a new hybrid Smoothed Particle Hydrodynamics (SPH)/N-body method
for modelling the collisional stellar dynamics of young clusters in a live gas
background. By deriving the equations of motion from Lagrangian mechanics we
obtain a formally conservative combined SPH/N-body scheme. The SPH gas
particles are integrated with a 2nd order Leapfrog, and the stars with a 4th
order Hermite scheme. Our new approach is intended to bridge the divide between
the detailed, but expensive, full hydrodynamical simulations of star formation,
and pure N-body simulations of gas-free star clusters. We have implemented this
hybrid approach in the SPH code SEREN (Hubber et al. 2011) and perform a series
of simple tests to demonstrate the fidelity of the algorithm and its
conservation properties. We investigate and present resolution criteria to
adequately resolve the density field and to prevent strong numerical scattering
effects. Future developments will include a more sophisticated treatment of
binaries.
