  Stars with masses of 80 - 130 Msun can encounter the pulsational
pair-instability at the end of their lives, which triggers consecutive episodes
of explosive burning that eject multiple massive shells. Collisions between
these shells produce bright transients known as pulsational pair-instability
supernovae (PPI SNe) that may explain some extreme supernovae. In this paper,
we present the first 2D and 3D radiation hydrodynamics simulations of PPI SNe
with the CASTRO code. Radiative cooling causes the collided shells to evolve
into thin, dense structures with hot spots that can enhance the peak luminosity
of the SN by factors of 2 - 3. The light curve peaks at $1.9 - 2.1 \times
10^{43}$ erg s$^{-1}$ for 50 days and then plateaus at $2 - 3 \times 10^{42}$
erg s$^{-1}$ for 200 days, depending on viewing angle. The presence of C and O
and absence of Si and Fe in its spectra can uniquely identify this transient as
a PPI SN in follow-up observations. Our models suggest that multidimensional
radiation hydrodynamics is required to model the evolution and light curves of
all shell-collision SNe such as Type IIne, not just PPI SNe.
