  The characteristic formalism of numerical relativity is based on a system of
coordinates aligned with outgoing null cones. While these coordinates were
designed for studying gravitational waves, they can also be easily adapted to
model cosmological past null cones (PNCs). Similar to observational coordinates
in the observational approach to cosmology, this then provides a model that
only makes use of information causally connected to an observer. However, the
diameter distance, which is used as a radial coordinate, limits the model's
cosmological application to the region prior to the PNC refocussing. This is
because after refocussing, the diameter distance ceases to be a unique measure
of distance. This paper addresses the problem by introducing a metric based on
the Bondi-Sachs metric where the radial coordinate is replaced by an affine
parameter. A model is derived from this metric and it is then shown how an
existing numerical scheme can be adapted for simulation of cosmological PNC
behaviour. Numerical calculations on this model are found to have the same
stability and convergence properties as the standard characteristic formalism.
