کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5428222 | 1508668 | 2014 | 16 صفحه PDF | دانلود رایگان |
- SKN methods are extended to linear anisotropic scattering media.
- Diagonalized simplified PN and simplified DPN equations are also derived.
- PN and DPN quadratures are used with the SKN and SKNâ methods.
- SKN methods are equivalent to SP2Nâ1 and SDPNâ1 approximations.
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 (SKNâ) 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 (P2Nâ1 or SP2Nâ1) and simplified double spherical harmonics (DPNâ1 or SDPNâ1) equations for linearly anisotropically scattering homogeneous medium are also derived. Resulting full P2Nâ1 and DPNâ1 (or SP2Nâ1 and SDPNâ1) 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, SKNâ equations become identical to P2Nâ1 or DPNâ1 (or SP2Nâ1 or SDPNâ1) 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 SKNâ approximation, but it is analytically more involved. It is shown that the SKNâ with proposed BCs converges with increasing order of approximation, and the BCs are applicable to SPN or SDPN methods.
Journal: Journal of Quantitative Spectroscopy and Radiative Transfer - Volume 147, November 2014, Pages 8-23