A realizability-preserving discontinuous Galerkin method for the M1 model of radiative transfer

Edgar Olbrant, Cory D. Hauck, Martin Frank

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

The M1 model for radiative transfer coupled to a material energy equation in planar geometry is studied in this paper. For this model to be well-posed, its moment variables must fulfill certain realizability conditions. Our main focus is the design and implementation of an explicit Runge-Kutta discontinuous Galerkin method which, under a more restrictive CFL condition, guarantees the realizability of the moment variables and the positivity of the material temperature. An analytical proof for our realizability-preserving scheme, which also includes a slope-limiting technique, is provided and confirmed by various numerical examples. Among other things, we present accuracy tests showing convergence up to fourth-order, compare our results with an analytical solution in a Riemann problem, and consider a Marshak wave problem.

Original languageEnglish
Pages (from-to)5612-5639
Number of pages28
JournalJournal of Computational Physics
Volume231
Issue number17
DOIs
StatePublished - Jul 1 2012

Keywords

  • Discontinuous Galerkin method
  • Hyperbolic partial differential equations
  • Radiative transfer

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