Abstract
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 finalequations containing an additional convective and diffusive term which are added to theflux term of the standard closure. We present numerical simulations for the simplest member of the hierarchy, theperturbed $M_1$ or $PM_1$ model, in one spatial dimension. Simulations are performed using a Runge-Kuttadiscontinuous Galerkin method with special limiters thatguarantee the realizability of the moment variables and the positivity of the materialtemperature. Improvements to thestandard $M_1$ model are observed in cases where unphysical shocks develop in the $M_1$ model.
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