  We discuss the general design of the ANTARES code which is intended for
simulations in stellar hydrodynamics with radiative transfer and realistic
microphysics in 1D, 2D and 3D. We then compare the quality of various numerical
methods. We have applied ANTARES in order to obtain high resolution simulations
of solar granulation which we describe and analyze. In order to obtain high
resolution, we apply grid refinement to a region predominantly occupied by an
exploding granule. Strong, rapidly rotating vortex tubes of small diameter
(~100 km) generated by the downdrafts and ascending into the photosphere near
the granule boundaries evolve, often entering the photosphere from below in an
arclike fashion. They essentially contribute to the turbulent velocity field
near the granule boundaries.
