Volume 24, Issue 4
A Uniformly Convergent Scheme for Radiative Transfer Equation in the Diffusion Limit Up to the Boundary and Interface Layers

Hongfei Chen ,  Gaoyu Chen ,  Xiang Hong ,  Hao Gao and Min Tang

10.4208/cicp.2018.hh80.06

Commun. Comput. Phys., 24 (2018), pp. 1021-1048.

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  • Abstract

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.

  • History

Published online: 2018-06

  • AMS Subject Headings

65L12, 76N20, 35Q70

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