  We derive a hierarchy of closures based on perturbations of well-known
entropy-based closures; we therefore refer to them as perturbed entropy-based
models. Our derivation reveals final equations containing an additional
convective and diffusive term which are added to the flux term of the standard
closure. We present numerical simulations for the simplest member of the
hierarchy, the perturbed M1 or PM1 model, in one spatial dimension. Simulations
are performed using a Runge-Kutta discontinuous Galerkin method with special
limiters that guarantee the realizability of the moment variables and the
positivity of the material temperature. Improvements to the standard M1 model
are observed in cases where unphysical shocks develop in the M1 model.
