We have performed two-dimensional relativistic hydrodynamical simulations o
f initially conical axisymmetric jets using a newly developed relativistic
magnetohydrodynamic simulation code. The simulation code employs a simplifi
ed total variation diminishing method. These jets emerge from the atmospher
es of active galaxies and then cross a pressure-matched interface into a ho
tter, but less-dense, intracluster-medium, whereupon they are accelerated a
nd collimated. We compared the nonrelativistic and relativistic jets to fin
d any relativistic effects in this kind of propagation processes. The simul
ation results show that there are clear relativistic effects as well as int
erface impacts in several aspects. Compared with a nonrelativistic jet prop
agating in a uniform medium, three results are notable: (1) when a jet prop
agates from a higher density medium region to lower density region, the var
iation in the amplitude of the Mach disk between concave and convex is grea
ter; nonrelativistic jets show this feature more obviously; (2) the interfa
ce causes the jet to undergo a quasi-periodical shrinkage and expansion, wh
ich may correspond to a chain of knots in an extragalactic jet; (3) the jet
head advance velocity formula, nu(h) = nu(o) root eta/(1 + root eta), shou
ld be replaced by nu(h) = nu(o)gamma(o)root l eta/(1 + gamma(o) root eta),
where nu(o) and gamma(o) are the velocity of the inflowing jet fluid and it
s Lorentz factor, respectively, and eta is the initial ratio of jet density
to medium density.