Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
521921 | Journal of Computational Physics | 2012 | 28 Pages |
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.