  The ANTARES radiation hydrodynamics code is capable of simulating the solar
granulation in detail unequaled by direct observation. We introduce a
state-of-the-art numerical tool to the solar physics community and demonstrate
its applicability to model the solar granulation. The code is based on the
weighted essentially non-oscillatory finite volume method and by its
implementation of local mesh refinement is also capable of simulating turbulent
fluids. While the ANTARES code already provides promising insights into
small-scale dynamical processes occurring in the quiet-Sun photosphere, it will
soon be capable of modeling the latter in the scope of radiation
magnetohydrodynamics. In this first preliminary study we focus on the vertical
photospheric stratification by examining a 3-D model photosphere with an
evolution time much larger than the dynamical timescales of the solar
granulation and of particular large horizontal extent corresponding to $25\!"
\!\! \times \, 25\!"$ on the solar surface to smooth out horizontal spatial
inhomogeneities separately for up- and downflows. The highly resolved Cartesian
grid thereby covers $\sim 4~\mathrm{Mm}$ of the upper convection zone and the
adjacent photosphere. Correlation analysis, both local and two-point, provides
a suitable means to probe the photospheric structure and thereby to identify
several layers of characteristic dynamics: The thermal convection zone is found
to reach some ten kilometers above the solar surface, while convectively
overshooting gas penetrates even higher into the low photosphere. An $\approx
145\,\mathrm{km}$ wide transition layer separates the convective from the
oscillatory layers in the higher photosphere.
