We present the results of self-consistent models of Compton-heated acc
retion disk coronae. The models are calculated using a new method for
computing monochromatic radiative transfer in two dimensions. The meth
od splits the radiation into direct and scattered components. The dire
ct radiation is computed by calculating the optical depth along rays,
while transfer of the scattered radiation is approximated by flux-limi
ted diffusion. The resulting code agrees with more accurate treatments
to within 50%, and is highly efficient, making it practical for use i
n large hydrodynamic simulations. The coronal models are used to confi
rm the results of earlier work, and to extend it to higher luminositie
s. In contrast to earlier work, which found the outer disks to be shad
owed by the inner corona at high luminosities, we find our results to
form an almost continuous extension of the models at lower luminositie
s. This is due to the presence of multiply scattered radiation, which
acts to partially offset the loss of direct radiation from the central
source. Although the analytic methods derived at lower luminosities c
annot be used to derive the coronal structure for L/L(Edd) greater tha
n or similar to 0.1, the results of the models are amenable to semiemp
irical fits. We also discuss possible observational consequences of th
e results for coronal veiling and line fluorescence from the disk.