  The Feedback In Realistic Environments (FIRE) project explores feedback in
cosmological galaxy formation simulations. Previous FIRE simulations used an
identical source code (FIRE-1) for consistency. Motivated by the development of
more accurate numerics - including hydrodynamic solvers, gravitational
softening, and supernova coupling algorithms - and exploration of new physics
(e.g. magnetic fields), we introduce FIRE-2, an updated numerical
implementation of FIRE physics for the GIZMO code. We run a suite of
simulations and compare against FIRE-1: overall, FIRE-2 improvements do not
qualitatively change galaxy-scale properties. We pursue an extensive study of
numerics versus physics. Details of the star-formation algorithm, cooling
physics, and chemistry have weak effects, provided that we include metal-line
cooling and star formation occurs at higher-than-mean densities. We present new
resolution criteria for high-resolution galaxy simulations. Most galaxy-scale
properties are robust to numerics we test, provided: (1) Toomre masses are
resolved; (2) feedback coupling ensures conservation, and (3) individual
supernovae are time-resolved. Stellar masses and profiles are most robust to
resolution, followed by metal abundances and morphologies, followed by
properties of winds and circum-galactic media (CGM). Central (~kpc) mass
concentrations in massive (L*) galaxies are sensitive to numerics (via
trapping/recycling of winds in hot halos). Multiple feedback mechanisms play
key roles: supernovae regulate stellar masses/winds; stellar mass-loss fuels
late star formation; radiative feedback suppresses accretion onto dwarfs and
instantaneous star formation in disks. We provide all initial conditions and
numerical algorithms used.
