  We present results from large-scale particle simulations of the viscous
overstability in Saturn's rings. The overstability generates a variety of
structure on scales covering a few hundred metres to several kilometres,
including axisymmetric wavetrains and larger-scale modulations. Such patterns
have been observed in Saturn's rings by the Cassini spacecraft. Our simulations
model the collisional evolution of particles in a co-rotating patch of the
disk. These are the largest N-body simulations of the viscous overstability yet
performed. The radial box size is five orders of magnitude larger than a
typical particle radius, and so describes a 20-50 km radial portion of the
rings. Its evolution is tracked for more than 10,000 orbits. In agreement with
hydrodynamics, our N-body simulations reveal that the viscous overstability
exhibits a rich set of dynamics characterised by nonlinear travelling waves
with wavelengths of a few hundred meters. In addition, wave defects, such as
sources and shocks, punctuate this bed of waves and break them up into
large-scale divisions of radial width ~5 km. We find that the wavelength of the
travelling waves is positively correlated with the mean optical depth. In order
to assess the role of the numerical boundary conditions and also background
ring structure, we include simulations of broad spreading rings and simulations
with a gradient in the background surface density. Overall, our numerical
results and approach provide a tool with which to interpret Cassini occultation
observations of microstructure in Saturn's rings. We present an example of such
a synthetic occultation observation and discuss what features to expect. We
also make the entire source code freely available.
