On radiative transfer using synthetic kernel and simplified spherical harmonics methods in linearly anisotropically scattering media

ALTAÇ Z.

JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, vol.147, pp.8-23, 2014 (SCI-Expanded, Scopus)

Abstract

The Synthetic Kernel (SKN) method is employed to a 3D absorbing, emitting and linearly anisotropically scattering inhomogeneous medium. Standard SKN approximation is applied only to the diffusive components of the radiative transfer equations. An alternative SKN (SKN*) method is also derived in full 3-D generality by extending the approximation to the direct wall contributions. Complete sets of boundary conditions for both SKN approaches are rigorously obtained. The simplified spherical harmonics (P2N-1 or SP2N-1) and simplified double spherical harmonics (DPN-1 or SDPN-1) equations for linearly anisotropically scattering homogeneous medium are also derived. Resulting full P(2N-1)and DPN-1 (or SP2N-1 and SDPN-1) equations are cast as diagonalized second order coupled diffusion-like equations. By this analysis, it is shown that the SKN method is a high-order approximation, and simply by the selection of full or half range Gauss-Legendre quadratures, SKN* equations become identical to P2N-1 or DPN-1 (or SP2N-1 or SDPN-1) equations. Numerical verification of all methods presented is carried out using a 1D participating isotropic slab medium. The SKN method proves to be more accurate than SKN* approximation, but it is analytically more involved. It is shown that the SKN* with proposed BCs converges with increasing order of approximation, and the BCs are applicable to SPN or SDPN methods. (C) 2014 Elsevier Ltd. All rights reserved.