A Simple Numerical Scheme to Obtain Reflectivity and Transmissivity of an Isotropically Scattering Slab

C. A. Ladeia (), H. R. Zanetti (), D. L. Gisch (), M. Schramm () and J. C. L. Fernandes ()
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C. A. Ladeia: Federal University of Rio Grande do Sul
H. R. Zanetti: Federal University of Rio Grande do Sul
D. L. Gisch: Federal University of Rio Grande do Sul
M. Schramm: Federal University of Pelotas
J. C. L. Fernandes: Federal University of Rio Grande do Sul

Chapter Chapter 12 in Integral Methods in Science and Engineering, 2022, pp 169-178 from Springer

Abstract: Abstract In this chapter, we consider the linear radiative transfer model for a passive medium with no intrinsic thermal contributions. The domain is a one-dimensional slab for which reflectivity and transmissivity are determined from the total in- and outgoing radiative fluxes across the boundaries. Further, we assume isotropic scattering in the medium and no emissivity and reflectivity on the boundaries but thermal radiation from the latter and an isotropic incoming radiation from an external source. Our developments are based on the discrete ordinate method in the angular variable and a modified version of the finite volume method in the spatial variable. The solution is obtained by an iterative method, and we present a necessary condition for its convergence based on norm operations.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-07171-3_12

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DOI: 10.1007/978-3-031-07171-3_12

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