  Supernova (SN) explosions deposit prodigious energy and momentum in their
environments, with the former regulating multiphase thermal structure and the
latter regulating turbulence and star formation rates in the interstellar
medium (ISM). However, systematic studies quantifying the impact of SNe in
realistic inhomogeneous ISM conditions have been lacking. Using
three-dimensional hydrodynamic simulations, we investigate the dependence of
radial momentum injection on both physical conditions (considering a range of
mean density n=0.1-100) and numerical parameters. Our inhomogeneous simulations
adopt two-phase background states that result from thermal instability in
atomic gas. Although the SNR morphology becomes highly complex for
inhomogeneous backgrounds, the radial momentum injection is remarkably
insensitive to environmental details. For our two-phase simulations, the final
momentum produced by a single SN is given by 2.8*10^5 M_sun*km/s n^{-0.17}.
This is only 5% less than the momentum injection for a homogeneous environment
with the same mean density, and only 30% greater than the momentum at the time
of shell formation. The maximum mass in hot gas is quite insensitive to
environmental inhomogeneity. Strong magnetic fields alter the hot gas mass at
very late times, but the momentum injection remains the same. Initial
experiments with multiple spatially-correlated SNe show a momentum per event
nearly as large as single-SN cases. We also present a full numerical parameter
study to assess convergence requirements. For convergence in the momentum and
other quantities, we find that the numerical resolution dx and the initial size
of the SNR r_init must satisfy dx, r_init<r_sf/3, where the shell formation
radius is given by r_sf = 30 pc n^{-0.46} for two-phase models (or 30% smaller
for a homogeneous medium).
