  We present new numerical algorithms for the coupled Einstein-perfect fluid
system in axisymmetry. Our framework uses a foliation based on a family of
light cones, emanating from a regular center, and terminating at future null
infinity. This coordinate system is well adapted to the study of the dynamical
spacetimes associated with isolated relativistic compact objects such as
neutron stars. In particular, the approach allows the unambiguous extraction of
gravitational waves at future null infinity and avoids spurious outer boundary
reflections. The code can accurately maintain long-term stability of polytropic
equilibrium models of relativistic stars. We demonstrate global energy
conservation in a strongly perturbed neutron star spacetime, for which the
total energy radiated away by gravitational waves corresponds to a significant
fraction of the Bondi mass. As a first application we present results in the
study of pulsations of axisymmetric relativistic stars, extracting the
frequencies of the different fluid modes in fully relativistic evolutions of
the Einstein-perfect fluid system and making a first comparison between the
gravitational news function and the predicted wave using the approximations of
the quadrupole formula.
