  We investigate a massive ($\varSigma \sim 10000 g cm^{-2}$ at 1 AU)
protoplanetary disc model by means of 3D radiation magnetohydrodynamics
simulations. The vertical structure of the disc is determined self-consistently
by a balance between turbulent heating caused by the MRI and radiative cooling.
Concerning the vertical structure, two different regions can be distinguished:
A gas-pressure dominated, optically thick midplane region where most of the
dissipation takes place, and a magnetically dominated, optically thin corona
which is dominated by strong shocks. At the location of the photosphere, the
turbulence is supersonic ($M \sim 2$), which is consistent with previous
results obtained from the fitting of spectra of YSOs. It is known that the
turbulent saturation level in simulations of MRI-induced turbulence does depend
on numerical factors such as the numerical resolution and the box size.
However, by performing a suite of runs at different resolutions (using up to
64x128x512 grid cells) and with varying box sizes (with up to 16 pressure
scaleheights in the vertical direction), we find that both the saturation
levels and the heating rates show a clear trend to converge once a sufficient
resolution in the vertical direction has been achieved.
