A Realizability-Preserving Discontinuous Galerkin Method for the $$M_1$$ Model of Radiative Transfer

Journal Article · Sun Jan 01 04:00:00 EST 2012 · Journal of Computational Physics

OSTI ID:1048144

Frank, Martin ^[1]; Olbrant, Edgar ^[1]; Hauck, Cory D ^[2]

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1. RWTH Aachen University
2. ORNL

The M{sub 1} 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.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: SC USDOE - Office of Science (SC)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1048144
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 17 Vol. 231; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
ANALYTICAL SOLUTION
CONVERGENCE
DESIGN
GEOMETRY
IMPLEMENTATION
PARTIAL DIFFERENTIAL EQUATIONS
RADIANT HEAT TRANSFER