  Direct multi-dimensional numerical simulation is the most reliable approach
for calculating the fluid dynamics and observational signatures of relativistic
jets in gamma-ray bursts (GRBs). We present a two-dimensional relativistic
hydrodynamic simulation of a GRB outflow during the afterglow phase, which uses
the fifth-order weighted essentially non-oscillatory scheme and adaptive mesh
refinement. Initially, the jet has a Lorentz factor of 20. We have followed its
evolution up to 150 years. Using the hydrodynamic data, we calculate
synchrotron radiation based upon standard afterglow models and compare our
results with previous analytic work. We find that the sideways expansion of a
relativistic GRB jet is a very slow process and previous analytic works have
overestimated its rate. In our computed lightcurves, a very sharp jet break is
seen and the post-break lightcurves are steeper than analytic predictions. We
find that the jet break in GRB afterglow lightcurves is mainly caused by the
missing flux when the edge of the jet is observed. The outflow becomes
nonrelativistic at the end of the Blandford-McKee phase. But it is still highly
nonspherical, and it takes a rather long time for it to become a spherical
Sedov-von Neumann-Taylor blast wave. We find that the late-time afterglows
become increasingly flatter over time. But we disagree with the common notion
that there is a sudden flattening in lightcurves due to the transition into the
Sedov-von Neumann-Taylor solution. We have also found that there is a bump in
lightcurves at very late times ($\sim 1000$ days) due to radiation from the
counter jet. We speculate that such a counter jet bump might have already been
observed in GRB 980703.
