  We have developed a one-dimensional code to solve ultra-relativistic
hydrodynamic problems, using the Glimm method for an accurate treatment of
shocks and contact discontinuities. The implementation of the Glimm method is
based on an exact Riemann solver and van der Corput sampling sequence. In order
to improve computational efficiency, the Glimm method is replaced by a finite
differencing scheme in those regions where the fluid flow is sufficiently
smooth. The accuracy and convergence of this hybrid method is investigated in
tests involving planar, cylindrically and spherically symmetric flows that
exhibit strong shocks and Lorentz factors of up to ~2000. This hybrid code has
proven to be successful in simulating the interaction between a thin,
ultra-relativistic, spherical shell and a low density stationary medium, a
situation likely to appear in Gamma-Ray Bursts, supernovae explosions, pulsar
winds and AGNs.
