The outcome of a black hole-neutron star binary merger can depend
on the the unknown details of the neutron star equation of state
as well as the premerger masses and spins. Some of the nuclear
matter can form a hot, neutrino-dominated accretion flow onto the
black hole--an intrinsically interesting extreme of accretion physics
and also a promising engine for a short-duration gamma ray burst.
Meanwhile, the tidal tail and disk winds can produce outflows with
their own interesting evolution and possibility for detection as a
kilonova or radio afterglow. In this talk, I will present numerical
simulations of black hole-neutron star binaries carried out with the
Spectral Einstein Code (SpEC); simulations include general relativity,
a nuclear theory-based equation of state, and approximate effects of
neutrino radiation. We cover a range of binary types, but give most
attention to moderate black hole mass, high black hole spin systems.
We find that a wide variety of post-merger outcomes is possible,
depending on the masses and spins: disk-dominated, ejecta-dominated,
or mixed. The early accretion disk also can have a variety of behaviors
and levels of neutrino luminosity. I will also remark on applications of
our findings to the interpretation of future multi-messenger detections of these events.