A comparative study of limiting strategies in discontinuous Galerkin schemes for the M1 model of radiation transport

Abstract

The M 1 minimum entropy moment system is a system of hyperbolic balance laws that approximates the radiation transport equation, and has many desirable properties. Among them are symmetric hyperbolicity, entropy decay, moment realizability, 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 the realizability of the numerical solution and controlling spurious oscillations. In this paper, we extend a previously constructed one-dimensional realizability limiting strategy to 2D. In addition, we perform a numerical study of various combinations of the realizability limiter and the TVBM local slope limiter on a third order Discontinuous Galerkin (DG) scheme on both triangular and rectangular meshes. In several test cases, we demonstrate that in general, a combination of the realizability limiter and a TVBM limiter is necessary to obtain a robust and accurate numerical scheme. Our code is published so that all results can be reproduced by the reader.Keywords: discontinuous Galerkin, moment models, minimum entropy, realizability limiter 2010 MSC: 35L40, 65M08, 65M60, 65M70The quantities ψ (0) , ψ (1) , ψ (2) are, respectively, the zeroth (particle density), first (mean velocity) and second moment (pressure) over the unit sphere S 2 of the angular flux ψ,and are, respectively, a scalar, a vector, and a matrix. The system is supplemented by the closure condition

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