A Linear-Discontinuous Spatial Differencing Scheme forSnRadiative Transfer Calculations

Abstract

Various types of linear-discontinuous spatial differencing schemes have been developed for theSn(discrete-ordinates) equations approximating the linear Boltzmann transport equation. It has been shown through an asymptotic analysis that the 1D slab-geometry lumped linear-discontinuous scheme not only goes over to a convergent and robust differencing of the diffusion equation in the monoenergetic thick diffusion limit, but it also yields the correct interior solution, even when boundary layers are left unresolved by the spatial mesh. In the present work we generalize this scheme to obtain a 1D slab-geometry lumped linear-discontinuous scheme for the nonlinear radiative transfer equation and the associated material temperature equation. We present a full nonlinear energy-dependent asymptotic analysis of the behavior of this scheme in the thick equilibrium-diffusion limit. We find that this scheme goes over to a convergent and robust differencing of the equilibrium-diffusion equation on the interior of the mesh, but it does not yield the exact interior solution when boundary layers are left unresolved by the spatial mesh. Nevertheless, the interior solution obtained with spatially unresolved boundary layers is always well behaved and fairly accurate. Computational results are presented which test the predictions of our asymptotic analysis and demonstrate the efficiency of our solution technique.