Formation of small-scale magnetic elements: surface mechanism
  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. 
A. S. Gadun, V. A. Sheminova, and S. K. Solanki
astro-ph.SR