A Uniformly Convergent Scheme for Radiative Transfer Equation in the Diffusion Limit Up to the Boundary and Interface Layers (Communications in Computational Physics, 2020)
In this paper, we present a numerical scheme for the steady-state radiativetransfer equation (RTE) with Henyey-Greenstein scattering kernel. The scattering kernelis anisotropic but not highly forward peaked. On the one hand, for the velocity discretization,we approximate the anisotropic scattering kernel by a discrete matrix thatcan preserve the diffusion limit. On the other hand, for the space discretization, a uniformlyconvergent scheme up to the boundary or interface layer is proposed. The ideais that we first approximate the scattering coefficients as well as source by piecewiseconstant functions, then, in each cell, the true solution is approximated by the summationof a particular solution and a linear combinations of general solutions to thehomogeneous RTE. Second-order accuracy can be observed, uniformly with respect tothe mean free path up to the boundary and interface layers. The scheme works wellfor heterogenous medium, anisotropic sources as well as for the strong source regime.