  We present numerical simulations that include 1-D Eulerian multi-group
radiation-hydrodynamics, 1-D non-LTE radiative transfer, and 2-D polarised
radiative transfer for super-luminous interacting supernovae (SNe). Our
reference model is a ~10Msun inner shell with 10^51erg ramming into a ~3Msun
cold outer shell (the circumstellar-medium, or CSM) that extends from 10^15cm
to 2x10^16cm and moves at 100km/s. We discuss the light curve evolution, which
cannot be captured adequately with a grey approach. In these interactions, the
shock-crossing time through the optically-thick CSM is much longer than the
photon diffusion time. Radiation is thus continuously leaking from the shock
through the CSM, in disagreement with the shell-shocked model that is often
invoked. Our spectra redden with time, with a peak distribution in the near-UV
during the first month gradually shifting to the optical range over the
following year. Initially Balmer lines exhibit a narrow line core and the broad
line wings that are characteristic of electron scattering in the SNe IIn
atmospheres (CSM). At later times they also exhibit a broad blue shifted
component which arises from the cold dense shell. Our model results are broadly
consistent with the bolometric light curve and spectral evolution observed for
SN2010jl. Invoking a prolate pole-to-equator density ratio in the CSM, we can
also reproduce the ~2% continuum polarisation, and line depolarisation,
observed in SN2010jl. By varying the inner shell kinetic energy and the mass
and extent of the outer shell, a large range of peak luminosities and
durations, broadly compatible with super-luminous SNe IIn like 2010jl or
2006gy, can be produced.
