  Stellar convection is a non-local process responsible for the transport of
heat and chemical species. It can lead to enhanced mixing through convective
overshooting and excitation of internal gravity waves (IGWs) at convective
boundaries. The relationship between these processes is still not well
understood and requires global hydrodynamic simulations to capture the
important large-scale dynamics. The steep stratification in stellar interiors
suggests that the radial extent of such simulations can affect the convection
dynamics, the IGWs in the stably stratified radiative zone, and the depth of
the overshooting layer. We investigate these effects using two-dimensional
global simulations performed with the fully compressible stellar hydrodynamics
code MUSIC. We compare eight different radial truncations of the same
solar-like stellar model evolved over approximately 400 convective turnover
times. We find that the location of the inner boundary has an insignificant
effect on the convection dynamics, the convective overshooting and the
travelling IGWs. We relate this to the background conditions at the lower
convective boundary which are unaffected by the truncation, as long as a
significantly deep radiative layer is included in the simulation domain.
However, we find that extending the outer boundary by only a few percent of the
stellar radius significantly increases the velocity and temperature
perturbations in the convection zone, the overshooting depth, the power and the
spectral slope of the IGWs. The effect is related to the background conditions
at the outer boundary, which are determined in essence by the hydrostatic
stratification and the given luminosity.
