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The $M_1$ minimum entropy moment system is a system of hyperbolic balancelaws that approximates the radiation transport equation, and has many desirableproperties. Among them are symmetric hyperbolicity, entropy decay, momentrealizability, and correct behavior in the diffusion and free-streaming limits.However, numerical difficulties arise when approximating the solution of the$M_1$ model by high order numerical schemes; namely maintaining therealizability of the numerical solution and controlling spurious oscillations.In this paper, we extend a previously constructed one-dimensional realizabilitylimiting strategy to 2D. In addition, we perform a numerical study of variouscombinations of the realizability limiter and the TVBM local slope limiter on athird order Discontinuous Galerkin (DG) scheme on both triangular andrectangular meshes. In several test cases, we demonstrate that in general, acombination of the realizability limiter and a TVBM limiter is necessary toobtain a robust and accurate numerical scheme. Our code is published so thatall results can be reproduced by the reader.

A Comparative Study of Limiting Strategies in Discontinuous Galerkin Schemes for the $M_1$ Model of Radiation Transport