  We introduce a GPU-accelerated hybrid hydro/N-body code (Enzo-N) designed to
address the challenges of concurrently simulating star clusters and their
parent galaxies. This task has been exceedingly challenging, primarily due to
the considerable computational time required, which stems from the substantial
scale difference between galaxies (~ 0.1 Mpc) and star clusters (~ pc). Yet,
this significant scale separation means that particles within star clusters
perceive those outside the star cluster in a semi-stationary state. By
leveraging this aspect, we integrate the direct N-body code (Nbody6++GPU) into
the cosmological (magneto-)hydrodynamic code (Enzo) through the utilization of
the semi-stationary background acceleration approximation. We solve the
dynamics of particles within star clusters using the direct N-body solver with
regularization for few-body interactions, while evolving particles outside --
dark matter, gas, and stars -- using the particle-mesh gravity solver and
hydrodynamic methods. We demonstrate that Enzo-N successfully simulates the
co-evolution of star clusters and their parent galaxies, capturing phenomena
such as core collapse of the star cluster and tidal stripping due to galactic
tides. This comprehensive framework opens up new possibilities for studying the
evolution of star clusters within galaxies, offering insights that were
previously inaccessible.
