  The brief transient emitted as a shock wave erupts through the surface of a
presupernova star carries information about the stellar radius and explosion
energy. Here the CASTRO code, which treats radiation transport using multigroup
flux-limited diffusion, is used to simulate the light curves and spectra of
shock breakout in very low-energy supernovae (VLE SNe), explosions in giant
stars with final kinetic energy much less than 10$^{51}$ erg. VLE SNe light
curves, computed here with the KEPLER code, are distinctively faint, red, and
long-lived, making them challenging to find with transient surveys. The
accompanying shock breakouts are brighter, though briefer, and potentially
easier to detect. Previous analytic work provides general guidance, but
numerical simulations are challenging due to the range of conditions and lack
of equilibration between color and effective temperatures. We consider previous
analytic work and extend discussions of color temperature and opacity to the
lower energy range explored by these events. Since this is the first
application of the CASTRO code to shock breakout, test simulations of normal
energy shock breakout of SN1987A are carried out and compared with the
literature. A set of breakout light curves and spectra are then calculated for
VLE SNe with final kinetic energies in the range $10^{47} - 10^{50}$ ergs for
red supergiants with main sequence masses 15 Msun and 25 Msun. The importance
of uncertainties in stellar atmosphere model, opacity, and ambient medium is
discussed, as are observational prospects with current and forthcoming
missions.
