We present the first results of axisymmetric jet simulations for both
nonrelativistic and relativistic (gamma = 5 and 10) flow speeds, emplo
ying a relativistic hydrodynamic code which we have found to be both r
obust and efficient. We find the same gross morphology in all cases, b
ut the relativistic runs exhibit little instability and less well-defi
ned structure internal to the jet: this might explain the difference b
etween (relatively slow) BL Lac objects and (faster) QSOs. We find tha
t the choice of adiabatic index makes a small but discernible differen
ce to the structure of the shocked jet and ambient media. Our code emp
loys a solver of the Godunov type, with approximate solution of the lo
cal Riemann problems, applied to laboratory frame variables. Lorentz t
ransformations provide the rest frame quantities needed for the estima
tion of wave speeds, etc. This is applied within the framework of an a
daptive mesh refinement algorithm, allowing us to perform high-resolut
ion, two-dimensional simulations with modest computing resources.