Numerical integration of the discrete-ordinate radiative transfer equation in strongly non-homogeneous media.

*(English)*Zbl 1067.65152Summary: We consider the radiation transfer problem in the discrete-ordinate, plane-parallel approach. We introduce two benchmark problems with exact known solutions and show that for strongly non-homogeneous media the homogeneous layers approximation can lead to errors of 10% in the estimation of the intensity. We propose and validate a general purpose numerical method that transforming the two-point boundary value problem into an initial boundary value problem, using an adaptative step integration and an interpolation of the local optical properties, can improve the accuracy of the solution up to two orders of magnitude. This is furthermore of interest for practical applications, such as atmospheric radiation transfer, where the scattering and absorbing properties of the media vary strongly with height and are only known, based on measurements or models, at certain discrete points.

##### MSC:

65R20 | Numerical methods for integral equations |

45J05 | Integro-ordinary differential equations |

85A25 | Radiative transfer in astronomy and astrophysics |

##### Keywords:

numerical examples; radiation transfer; discrete-ordinate, plane-parallel approach; two-point boundary value problem; initial boundary value problem; scattering
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\textit{M. P. Zorzano} et al., Appl. Math. Comput. 164, No. 1, 263--274 (2005; Zbl 1067.65152)

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##### References:

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