  Radiative hydrodynamic simulations of solar and stellar surface convection
have become an important tool for exploring the structure and gas dynamics in
the envelopes and atmospheres of late-type stars and for improving our
understanding of the formation of stellar spectra. We quantitatively compare
results from three-dimensional, radiative hydrodynamic simulations of
convection near the solar surface generated with three numerical codes CO5BOLD,
MURaM, and STAGGER and different simulation setups in order to investigate the
level of similarity and to cross-validate the simulations. For all three
simulations, we considered the average stratifications of various quantities
(temperature, pressure, flow velocity, etc.) on surfaces of constant
geometrical or optical depth, as well as their temporal and spatial
fluctuations. We also compared observables, such as the spatially resolved
patterns of the emerging intensity and of the vertical velocity at the solar
optical surface as well as the center-to-limb variation of the continuum
intensity at various wavelengths. The depth profiles of the thermodynamical
quantities and of the convective velocities as well as their spatial
fluctuations agree quite well. Slight deviations can be understood in terms of
differences in box size, spatial resolution and in the treatment of non-gray
radiative transfer between the simulations. The results give confidence in the
reliability of the results from comprehensive radiative hydrodynamic
simulations.
