  We look in detail at the process of mapping an astrophysical initial model
from a stellar evolution code onto the computational grid of an explicit,
Godunov type code while maintaining hydrostatic equilibrium. This mapping
process is common in astrophysical simulations, when it is necessary to follow
short-timescale dynamics after a period of long timescale buildup. We look at
the effects of spatial resolution, boundary conditions, the treatment of the
gravitational source terms in the hydrodynamics solver, and the initialization
process itself. We conclude with a summary detailing the mapping process that
yields the lowest ambient velocities in the mapped model.
