  Supernova (SN) feedback is one of the key processes shaping the interstellar
medium (ISM) of galaxies. SNe contribute to (and in some cases may dominate)
driving turbulence in the ISM and accelerating galactic winds. Modern
cosmological simulations have sufficient resolution to capture the main
structures in the ISM of galaxies, but are typically still not capable of
explicitly resolving all of the small-scale stellar feedback processes,
including the expansion of supernova remnants (SNRs). We perform a series of
controlled three-dimensional hydrodynamic (adaptive mesh refinement)
simulations of single SNRs expanding in an inhomogeneous density field with
statistics motivated by those of the turbulent ISM. We use these to quantify
the momentum and thermal energy injection from SNe as a function of spatial
scale and the density, metallicity, and structure of the ambient medium. We
develop a series of analytic formulae that we fit to the simulations. These
formulae can be used as a basis for a more predictive sub-resolution model for
SN feedback for galaxy formation simulations. We then use simulations of
multiple, stochastically driven SNe that resolve the key phases of SNRs to test
the sub-resolution model, and show that it accurately captures the turbulent
kinetic energy and thermal energy in the ISM. By contrast, proposed SN feedback
models in the literature based on `delayed cooling' significantly overpredict
the late-time thermal energy and momentum in SNRs.
