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In the discrete-ordinates approach to solving the radiative transfer equation (RTE), the phase function or the phase matrix (for the vector, i.e. polarized light case) are expanded in terms of generalized spherical functions (for example, Hovenier JW et al 2004, Gelfand IM et al 1963). The radiance (or the Stokes vector) are expanded in terms of the harmonics of the azimuth angle. This enables the analytical integration with respect to the azimuth. The remaining integrals are approximated by sums using the Gaussian quadrature (for example, http://mathworld.wolfram.com/GaussianQuadrature.html). The resulting system of differential equations is solved analytically. The arbitrary constants of the solution are found by numerically solving a system of algebraic equations using, e.g., LAPACK standard routines (Anderson E et al 1999). For vertically inhomogeneous media, a layer of the medium is divided into a large number of homogeneous sub-layers and the requirement for the continuity of the solution is used to find values of additional arbitrary constants. [AAK]
See RTE solution, methods, numerical, discrete ordinates and RTE solution for additional references.
| CITATION: Kokhanovsky A. A. (ed.) 2008. Radiative transfer equation (RTE): Numerical solution methods - Discrete ordinates (www.tpdsci.com/Tpc/RTESolNumDo.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 2008 Modified: 11-Jun-2008 Peer-reviewed: PENDING |
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