Solution of Linear Radiative Transfer Equation in Hollow Sphere by Diamond Difference Discrete Ordinates and Decomposition Methods

Marcelo Schramm; Cibele Ladeia; Julio Cesar Fernandes

doi:10.5433/1679-0375.2024.v45.51961

Solution of Linear Radiative Transfer Equation in Hollow Sphere by Diamond Difference Discrete Ordinates and Decomposition Methods

Authors

Marcelo Schramm Universidade Federal de Pelotas https://orcid.org/0000-0002-0254-4277
Cibele Ladeia Universidade Federal do Rio Grande do Sul
Julio Cesar Fernandes Universidade Federal do Rio Grande do Sul

DOI:

https://doi.org/10.5433/1679-0375.2024.v45.51961

Keywords:

radiativetransfer, spherical geometry, decomposition method, diamond difference, discrete ordinates

Abstract

In this article, we present a methodology to solve radiative transfer problems in spherical geometry without other forms of heat exchange. We use a decomposition method based on the Adomian formulations, together with a diamond difference scheme and a trapezoidal rule to approximate the integral part of the solution. The algorithm is simple, highly reproducible, and can be easily adapted to further problems or geometries. Also, we demonstrate its consistency and showed that using an analytical solution with a trapezoidal rule improves the order of convergence compared to using the finite difference method. These considerations are necessary for future applications in more complex cases. The numerical results are compared with some classical and recent cases in the literature, along with a simplified version of a complete (fully coupled with heat exchange) case.

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Author Biographies

Marcelo Schramm, Universidade Federal de Pelotas

Dr. in Mechanical Engineering from the Universidade Federal do Rio Grande do Sul. Professor at the Universidade Federal de Pelotas

Cibele Ladeia, Universidade Federal do Rio Grande do Sul

Adjunct professor at Department of Pure and Applied Mathematics

Julio Cesar Fernandes, Universidade Federal do Rio Grande do Sul

Adjunct professor at Department of Pure and Applied Mathematics

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