  We describe a method for simulating the dynamics of an $S_3$ cosmic string
network. We use a lattice Monte Carlo to generate initial conditions for the
network, which subsequently is allowed to relax continuously according to a
simplified model of string dynamics. The dynamics incorporates some novel
features which, to our knowledge, have not been studied in previous numerical
simulations: The existence of two types of string which may have different
tensions, and the possibility that two non-commuting strings may intersect.
Simulation of the non-commuting fluxes presents a computational challenge as it
requires a rather complex gauge-fixing procedure. The flux definitions change
as strings change their positions and orientations relative to each other and
must be carefully updated as the network evolves. The method is described here
in some detail, with results to be presented elsewhere.
