  We test the sensitivity of hydrodynamic and magnetohydrodynamic turbulent
convection simulations with respect to Mach number, thermal and magnetic
boundary conditions, and the centrifugal force. We find that varying the
luminosity, which also controls the Mach number, has only a minor effect on the
large-scale dynamics. A similar conclusion can also be drawn from the
comparison of two formulations of the lower magnetic boundary condition with
either vanishing electric field or current density. The centrifugal force has
an effect on the solutions, but only if its magnitude with respect to
acceleration due to gravity is by two orders of magnitude greater than in the
Sun. Finally, we find that the parameterisation of the photospheric physics,
either by an explicit cooling term or enhanced radiative diffusion, is more
important than the thermal boundary condition. In particular, runs with cooling
tend to lead to more anisotropic convection and stronger deviations from the
Taylor-Proudman state. In summary, the fully compressible approach taken here
with the Pencil Code is found to be valid, while still allowing the disparate
timescales to be taken into account.
