The merger of compact binaries, especially black holes and neutron stars, i
s frequently invoked to explain gamma-ray bursts (GRBs). In this paper, we
present three-dimensional hydrodynamical simulations of the relatively negl
ected mergers of white dwarfs and black holes. During the merger, the white
dwarf is tidally disrupted and sheared into an accretion disk. Nuclear rea
ctions are followed, and the energy release is negligible. Peak accretion r
ates are similar to 0.05 M. s(-1) (less for lower mass white dwarfs) and la
st for approximately a minute. Many of the disk parameters can be explained
by a simple analytic model that we derive and compare to our simulations.
This model can be used to predict accretion rates for white dwarf and black
hole (or neutron star) masses that are not simulated here. Although the me
rgers studied here create disks with larger radii and longer accretion time
s than those from the merger of double neutron stars, a larger fraction of
the white dwarfs mass becomes part of the disk. Thus the merger of a white
dwarf and a black hole could produce a long-duration GRB. The event rate of
these mergers may be as high as 10(-6) yr(-1) per galaxy.