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

DOI10.1016/J.AMC.2004.06.024zbMATH Open1067.65152arXivphysics/0507057OpenAlexW2056508925MaRDI QIDQ1774857

Publication date: 4 May 2005

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Abstract: 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-boundary problem into an initial boundary 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.

Full work available at URL: https://arxiv.org/abs/physics/0507057

zbMATH Keywords

numerical examples scattering two-point boundary value problem initial boundary value problem radiation transfer discrete-ordinate, plane-parallel approach

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Radiative transfer in astronomy and astrophysics (85A25)

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