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

Carlos Enrique Torres-Aguilar, Pedro Moreno-Bernal, Jesús Xamán, Ivett Zavala Guillen, Irving Osiris Hernández-López

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)2552-2574
Number of pages23
JournalEngineering Computations (Swansea, Wales)
Volume38
Issue number6
DOIs
StatePublished - 1 Jan 2021

Bibliographical note

Funding Information:
This work acknowledges Shirley Ainsworth Gore and Juan Manuel Hurtado Ramirez of the Biotechnology Institute, Universidad Nacional Aut?noma de M?xico (UNAM) for bibliography support.

Publisher Copyright:
© 2020, Emerald Publishing Limited.

Keywords

  • Deferred correction
  • Evolutionary algorithm
  • High-resolution TVD schemes
  • Radiative transfer equation

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