  A quadrature-based finite-difference lattice Boltzmann model is developed
that is suitable for simulating relativistic flows of massless particles. We
briefly review the relativistc Boltzmann equation and present our model. The
quadrature is constructed such that the stress-energy tensor is obtained as a
second order moment of the distribution function. The results obtained with our
model are presented for a particular instance of the Riemann problem (the Sod
shock tube). We show that the model is able to accurately capture the behavior
across the whole domain of relaxation times, from the hydrodynamic to the
ballistic regime. The property of the model of being extendable to arbitrarily
high orders is shown to be paramount for the recovery of the analytical result
in the ballistic regime.
