  We present initial results of our study of numerical methods for modeling
neutron star mergers (NSMs) with simulations that perform the full hydrodynamic
evolution required to capture tidal effects, particularly in the last several
orbits. Our simulations evolve the Euler equations using a modification of the
ZEUS-2D algorithm (Stone and Norman 1992). We describe some of the difficulties
of modeling NSMs and our approaches to these difficulties, and we discuss the
motivation for the choice of performing simulations in a co-rotating reference
frame. Our results establish what effects the choices of gravity coupling and
reference frame have on the numerical accuracy of the simulation.
