We present calculations of the radio emission from supernovae based on high
-resolution simulations of the hydrodynamics and radiation transfer, using
simple energy density relations that link the properties of the radiating e
lectrons and the magnetic field to the hydrodynamics. As a specific example
we model the emission from SN 1993J, which cannot be adequately fitted wit
h the often-used analytic minishell model, and present a good Dt to the rad
io evolution at a single frequency. Both free-free absorption and synchrotr
on self-absorption are needed to Dt the light curve at early times, and a c
ircumstellar density profile of rho similar to r(-1.7) provides the best Dt
to the later data. We show that the interaction of density structures in t
he ejecta with the reverse supernova shock may produce features in the radi
o light curves such as have been observed. We discuss the use of high-resol
ution radio images of supernovae to distinguish between different absorptio
n mechanisms and determine the origin of specific light curve features. Com
parisons of VLBI images of SN 1993J with synthetic model images suggest tha
t internal free-free absorption completely obscures emission at 8.4 GHz pas
sing through the center of the supernova for the first few tens of years af
ter explosion. We predict that at 8.4 GHz the internal free-free absorption
is currently declining, and that over the next similar to 40 yr the surfac
e brightness of the center of the source should increase relative to the br
ight ring of emission seen in VLBI images. Similar absorption in a nearby s
upernova would make the detection of a radio pulsar at 1 GHz impossible for
similar to 150 yr after explosion.