  We investigate the hydrodynamics of three-dimensional classical Bondi-Hoyle
accretion. A totally absorbing sphere of different sizes (1, 0.1 and 0.02
accretion radii) exerts gravity on and moves at different Mach numbers (0.6,
1.4, 3.0 and 10) relative to a homogeneous and slightly perturbed medium, which
is taken to be an ideal gas ($\gamma=4/3$). We examine the influence of Mach
number of the flow and size of the accretor upon the physical behaviour of the
flow and the accretion rates. The hydrodynamics is modeled by the ``Piecewise
Parabolic Method'' (PPM). The resolution in the vicinity of the accretor is
increased by multiply nesting several $32^3$-zone grids around the sphere, each
finer grid being a factor of two smaller in zone dimension than the next
coarser grid. This allows us to include a coarse model for the surface of the
accretor (vacuum sphere) on the finest grid while at the same time evolving the
gas on the coarser grids. For small Mach numbers (0.6 and~1.4) the flow
patterns tend towards a steady state, while in the case of supersonic flow
(Mach~3 and~10) and small enough accretors, (radius of~0.1 and~0.02 accretion
radii) an unstable Mach cone develops, destroying axisymmetry. Our 3D models do
not show the highly dynamic flip-flop flow so prominent in 2D calculations
performed by other authors. In the gamma=4/3 models, the shock front remains
closer to the accretor and the mass accretion rates are higher than in the
gamma=5/3 models, whereas the rms of the specific angular momentum accreted
does not change.
