  We present the first results of a two-dimensional MHD simulation of the solar
magnetogranulation. The medium was assumed to be compressible, gravitationally
stratified, radiatively coupled, partially ionized, and turbulent. The
simulated magnetogranulation evolved over the course of two hours of
hydrodynamic (solar) time. A surface (magnetic plume-like) mechanism which
forms thin magnetic elements was found to operate during the process of granule
fragmentation. The activity of such a mechanism suggests that the
magnetogranulation can concentrate and intensify the global magnetic flux at
the boundaries of convective cells and can also form nearly vertical compact
magnetic flux tubes by involving the weak horizontal photospheric field, which
may be, in general, of local (turbulent) nature.
