  We present a systematic procedure for the construction of relativistic
lattice Boltzmann models (R-SLB) appropriate for the simulation of flows of
massless particles. Quadrature rules are used for the discretization of the
momentum space in spherical coordinates. The models are optimized for
one-dimensional flows. The applications considered in this paper are the Sod
shock tube and the one-dimensional boost invariant expansion (Bjorken flow).
Our models are tested against exact solutions in the inviscid and ballistic
limits. At intermediate relaxation times (finite viscosity), we compare with
the results obtained using the Boltzmann approach of multiparton scattering
model for the Sod shock tube problem, as well as with a semi-analytic solution
for the non-ideal Bjorken flow. In all cases our models give remarkably good
results. We define a convergence test in order to find the quadrature order
necessary to obtain convergence at a predefined accuracy. We show that, while
in the hydrodynamic regime the number of velocities is comparable to that
required for the more popular collision-streaming type models, as we go towards
the ballistic regime, the size of the velocity set must be substantially
increased in order to accurately reproduce the analytic profiles.
