@Article{CiCP-24-4,
author = {},
title = {A Uniformly Convergent Scheme for Radiative Transfer Equation in the Diffusion Limit Up to the Boundary and Interface Layers},
journal = {Communications in Computational Physics},
year = {2018},
volume = {24},
number = {4},
pages = {1021--1048},
abstract = {<p style="text-align: justify;">In this paper, we present a numerical scheme for the steady-state radiative
transfer equation (RTE) with Henyey-Greenstein scattering kernel. The scattering kernel
is anisotropic but not highly forward peaked. On the one hand, for the velocity discretization,
we approximate the anisotropic scattering kernel by a discrete matrix that
can preserve the diffusion limit. On the other hand, for the space discretization, a uniformly
convergent scheme up to the boundary or interface layer is proposed. The idea
is that we first approximate the scattering coefficients as well as source by piecewise
constant functions, then, in each cell, the true solution is approximated by the summation
of a particular solution and a linear combinations of general solutions to the
homogeneous RTE. Second-order accuracy can be observed, uniformly with respect to
the mean free path up to the boundary and interface layers. The scheme works well
for heterogenous medium, anisotropic sources as well as for the strong source regime.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2018.hh80.06},
url = {https://global-sci.com/article/79979/a-uniformly-convergent-scheme-for-radiative-transfer-equation-in-the-diffusion-limit-up-to-the-boundary-and-interface-layers}
}