We investigate the hydrodynamics of three-dimensional classical Bondi-
Hoyle accretion. A totally absorbing sphere of different sizes (I, 0.1
and 0.02 accretion radii) exerts gravity on and moves at different Ma
ch numbers (0.6, 1.4, 3.0 and 10) relative to a homogeneous and slight
ly perturbed medium, which is taken to be an ideal gas (gamma = 4/3).
We examine the influence of Mach number of the how and size of the acc
retor upon the physical behaviour of the how and the accretion rates.
The hydrodynamics is modeled by the ''Piecewise Parabolic Method'' (PP
M). The resolution in the vicinity of the accretor is increased by mul
tiply nesting several 32(3)-zone grids around the sphere, each finer g
rid being a factor of two smaller in zone dimension than the next coar
ser 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 an
d 1.4) the how patterns tend towards a steady state, while in the case
of supersonic how (Mach 3 and 10) and small enough accretors, (radius
of 0.1 and 0.02 accretion radii) an unstable Mach cone develops, dest
roying axisymmetry. Our 3D models do not show the highly dynamic flip-
flop how so prominent in 2D calculations performed by other authors. I
n 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 ch
ange.