  The advent of massively parallel supercomputing has begun to permit explicit
3--D simulations of turbulent convection occurring within the cores of
early-type main sequence stars. Such studies should complement the stellar
structure and evolution efforts that have so far largely employed 1--D nonlocal
mixing length descriptions for the transport, mixing and overshooting achieved
by core convection. We have turned to A-type stars as representative of many of
the dynamical challenges raised by core convection within rotating stars. The
differential rotation and meridional circulations achieved deep within the star
by the convection, the likelihood of sustained magnetic dynamo action there,
and the bringing of fresh fuel into the core by overshooting motions, thereby
influencing main sequence lifetimes, all constitute interesting dynamical
questions that require detailed modelling of global-scale convection. Using our
anelastic spherical harmonic (ASH) code tested on the solar differential
rotation problem, we have conducted a series of 3--D spherical domain
simulations that deal with a simplified description of the central regions of
rotating A-type stars, i.e a convectively unstable core is surrounded by a
stable radiative envelope. A sequence of 3--D simulations are used to assess
the properties of the convection (its global patterns, differential rotation,
meridional circulations, extent and latitudinal variation of the overshooting)
as transitions are made between laminar and turbulent states by changing the
effective diffusivities, rotation rates, and subadiabaticity of the radiative
exterior. We report on the properties deduced from these models for both the
extent of penetration and the profile of rotation sustained by the convection.
