  Numerical simulations of magneto-convection have greatly expanded our
understanding of stellar interiors and stellar magnetism. Recently, fully
compressible hydrodynamical simulations of full-star models have demonstrated
the feasibility of studying the excitation and propagation of pressure and
internal gravity waves in stellar interiors, which would allow for a direct
comparison with asteroseismological measurements. However, the impact of
magnetic fields on such waves has not been taken into account yet in
three-dimensional simulations. We conduct a proof of concept for the
realization of three-dimensional, fully compressible, magneto-hydrodynamical
numerical simulations of stellar interiors with the RAMSES code. We adapted the
RAMSES code to deal with highly subsonic turbulence, typical of stellar
convection, by implementing a well-balanced scheme in the numerical solver. We
then ran and analyzed three-dimensional hydrodynamical and
magneto-hydrodynamical simulations with different resolutions of a
plane-parallel convective envelope on a Cartesian grid. Both hydrodynamical and
magneto-hydrodynamical simulations develop a quasi-steady, turbulent convection
layer from random density perturbations introduced over the initial profiles.
The convective flows are characterized by small-amplitude fluctuations around
the hydrodynamical equilibrium of the stellar interior, which is preserved over
the whole simulation time. Using our compressible well-balanced scheme, we were
able to model flows with Mach numbers as low as $\mathcal{M} \sim 10^{-3}$, but
even lower Mach number flows are possible in principle. In the
magneto-hydrodynamical runs, we observe an exponential growth of magnetic
energy consistent with the action of a small-scale dynamo. (Abridged)
