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

An evolutionary algorithm for controlling numerical convergence of the radiative transfer... 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/approachThe 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.FindingsExperimental 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/valueThe proposed EA approach for the RTE numerical solution effectively reduces the CPU time compared to the DC procedure with fixed relaxation coefficients. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations: International Journal for Computer-Aided Engineering and Software Emerald Publishing

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

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References (42)

Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
0264-4401
DOI
10.1108/ec-07-2020-0421
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Engineering Computations: International Journal for Computer-Aided Engineering and SoftwareEmerald Publishing

Published: Jul 9, 2021

Keywords: Evolutionary algorithm; Radiative transfer equation; High-resolution TVD schemes; Deferred correction

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