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An evolutionary algorithm for controlling numerical convergence of the radiative transfer equation with participating media using TVD interpolation schemes

Carlos Enrique Torres-Aguilar (Department of Mechanical Engineering, Tecnológico Nacional de Méxcio/CENIDET, Cuernavaca, Mexico)
Pedro Moreno-Bernal (Facultad de Contaduría, Administración e Informática, Universidad Autónoma del Estado de Morelos – UAEM, Cuernavaca, Mexico)
Jesús Xamán (Department of Mechanical Engineering, Tecnológico Nacional de Méxcio/CENIDET, Cuernavaca, Mexico)
Ivett Zavala Guillen (Centro de Investigación Científica y de Educación Superior de Ensenada – CICESE, Ensenada, México)
Irving Osiris Hernández-López (Universidad de Sonora – UNISON, Hermosillo, México)

Engineering Computations

ISSN: 0264-4401

Article publication date: 4 January 2021

Issue publication date: 9 July 2021

131

Abstract

Purpose

This paper aims to present an evolutionary algorithm (EA) to accelerate the convergence for the radiative transfer equation (RTE) numerical solution using high-order and high-resolution schemes by the relaxation coefficients optimization.

Design methodology/approach

The objective function minimizes the residual value difference between iterations in each control volume until its difference is lower than the convergence criterion. The EA approach is evaluated in two configurations, a two-dimensional cavity with scattering media and absorbing media.

Findings

Experimental results show the capacity to obtain the numerical solution for both cases on all interpolation schemes tested by the EA approach. The EA approach reduces CPU time for the RTE numerical solution using SUPERBEE, SWEBY and MUSCL schemes until 97% and 135% in scattering and absorbing media cases, respectively. The relaxation coefficients optimized every two numerical solution iterations achieve a significant reduction of the CPU time compared to the deferred correction procedure with fixed relaxation coefficients.

Originality/value

The proposed EA approach for the RTE numerical solution effectively reduces the CPU time compared to the DC procedure with fixed relaxation coefficients.

Keywords

Acknowledgements

This work acknowledges Shirley Ainsworth Gore and Juan Manuel Hurtado Ramirez of the Biotechnology Institute, Universidad Nacional Autónoma de México (UNAM) for bibliography support.

Citation

Torres-Aguilar, C.E., Moreno-Bernal, P., Xamán, J., Zavala Guillen, I. and Hernández-López, I.O. (2021), "An evolutionary algorithm for controlling numerical convergence of the radiative transfer equation with participating media using TVD interpolation schemes", Engineering Computations, Vol. 38 No. 6, pp. 2552-2574. https://doi.org/10.1108/EC-07-2020-0421

Publisher

:

Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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