  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 which link the properties of the radiating
electrons and the magnetic field to the hydrodynamics. As a specific example we
model the emission from SN1993J, which cannot be adequately fitted with the
often-used analytic mini-shell model, and present a good fit to the radio
evolution at a single frequency. Both free-free absorption and syncrotron self-
absorption are needed to fit the light curve at early times and a circumstellar
density profile of rho~r^-1.7 provides the best fit to the later data. We show
that the interaction of density structures in the ejecta with the reverse
supernova shock may produce features in the radio light curves such as have
been observed. We discuss the use of high-resolution radio images of supernovae
to distinguish between different absorption mechanisms and determine the origin
of specific light curve features. Comparisons of VLBI images of SN1993J with
synthetic model images suggest that internal free-free absorption completely
obscures emission at 8.4 GHz passing through the center of the supernova for
the first few tens of years after explosion. We predict that at 8.4 GHz the
internal free-free absorption is currently declining, and that over the next 40
years the surface brightness of the center of the source should increase
relative to the bright ring of emission seen in VLBI images. Similar absorption
in a nearby supernova would make the detection of a radio pulsar at 1 GHz
impossible for ~150 years after explosion.
