  We use the relativistic hydrodynamics code Cosmos++ to model the evolution of
the radio nebula triggered by the Dec. 27, 2004 giant flare event of soft gamma
repeater 1806-20. We primarily focus on the rebrightening and centroid motion
occurring subsequent to day 20 following the flare event. We model this period
as a mildly relativistic (gamma ~ 1.07 - 1.67) jetted outflow expanding into
the interstellar medium (ISM). We demonstrate that a jet with total energy ~
10^46 ergs confined to a half opening angle ~ 20 degrees fits the key
observables of this event, e.g. the flux lightcurve, emission map centroid
position, and aspect ratio. In particular, we find excellent agreement with
observations if the rebrightening is due to the jet, moving at 0.5c and
inclined ~ 0 - 40 degrees toward the observer, colliding with a density
discontinuity in the ISM at a radius of several 10^16 cm. We also find that a
jet with a higher velocity, >~ 0.7c, and larger inclination, >~ 70 degrees,
moving into a uniform ISM can fit the observations in general, but tends to
miss the details of rebrightening. The latter, uniform ISM model predicts an
ISM density more than 100 times lower than that of the former model, and thus
suggests an independent test which might discriminate between the two. One of
the strongest constraints of both models is that the data seems to require a
non-uniform jet in order to be well fit.
