  The ultra-relativistic Euler equations for an ideal gas are described in
terms of the pressure, the spatial part of the dimensionless four-velocity and
the particle density. Radially symmetric solutions of these equations are
studied in two and three space dimensions. Of particular interest in the
solutions are the formation of shock waves and a pressure blow up. For the
investigation of these phenomena we develop a one-dimensional scheme using
radial symmetry and integral conservation laws. We compare the numerical
results with solutions of multi-dimensional high-order numerical schemes for
general initial data in two space dimensions. The presented test cases and
results may serve as interesting benchmark tests for multi-dimensional solvers.
