<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml203" display="inline" overflow="scroll" altimg="si3.gif"><mml:mi>X</mml:mi></mml:math>- factor: A modified relaxation factor to accelerate the convergence rate of the radiative transfer equation with high-order resolution schemes using the Normalized Weighting-Factor method

Xamán, J.; Hernández-López, I.; Uriarte-Flores, J.; Hernández-Pérez, I.; Zavala-Guillén, I.; Moreno-Bernal, Pedro; Hinojosa, J.

doi:10.1016/j.cpc.2018.05.001

Cited by 4 publications

(9 citation statements)

References 51 publications

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“…The initial guessed intensity field is zero, it is used for all configurations and the STEP scheme is used in the first iteration. Equation ( 17) (Xam an et al, 2018a(Xam an et al, , 2018b expresses the relative improvements on CPU time for the numerical solution between the DC procedure and DC Evolutive that apply (1 þ 1)-ES-RTE optimization.…”

Section: Study Cases Experimental Results and Discussionmentioning

confidence: 99%

“…Results showed that the parallel method converged 35 times more than a sequential methodology. Xam an et al (2018aXam an et al ( , 2018b implemented the NWF EC 38,6 method to reduce the CPU time in the numerical solution of the radiative transfer equation (RTE) using HO and HR schemes. Results showed that modified relaxation factors using NWF and DC procedures reduce the computational cost by 219% and 75.4%, respectively.…”

mentioning

confidence: 99%

“…Results showed that modified relaxation factors using NWF and DC procedures reduce the computational cost by 219% and 75.4%, respectively. (Xam an et al, 2018a(Xam an et al, , 2018bTorres-Aguilar et al, 2020). Dragojlovic et al (2001) and Juntaek Ryoo et al (2005) proposed two approaches based on fuzzy logic to determine the suitable relaxation coefficients to solve some examples of computational fluid dynamics (CFD).…”

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confidence: 99%

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

Torres-Aguilar

Moreno-Bernal

Xamán

et al. 2021

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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.

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Section: Study Cases Experimental Results and Discussionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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

Torres-Aguilar

Moreno-Bernal

Xamán

et al. 2021

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“…This approach reduces the computational time up to 85% with a maximum error of less than 2%. In references [8,9], the convergence rate to solve a radiative transfer equation with several high-order and high-resolution schemes, applying the normalized weighting-factor method (WFM), is evaluated. In reference [8], the WFM convergence time is compared with that obtained by a deferred correction (DC) technique.…”

Section: Introductionmentioning

confidence: 99%

“…In reference [9], the X-factor method is compared, in terms of computer time needed to obtain a converged solution, with the widely used deferred-correction (DC) method for calculating a two-dimensional cavity with emitting-absorbing-scattering gray media using the discrete ordinates method. A time reduction rate of up to 211%, 181% and 219% is obtained.…”

Section: Introductionmentioning

confidence: 99%

Metaheuristic to Optimize Computational Convergence in Convection-Diffusion and Driven-Cavity Problems

Enríquez-Urbano¹,

Cruz-Chávez²,

Rivera-López

et al. 2021

Mathematics

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This work presents an optimization proposal to better the computational convergence time in convection-diffusion and driven-cavity problems by applying a simulated annealing (SA) metaheuristic, obtaining optimal values in relaxation factors (RF) that optimize the problem convergence during its numerical execution. These relaxation factors are tested in numerical models to accelerate their computational convergence in a shorter time. The experimental results show that the relaxation factors obtained by the SA algorithm improve the computational time of the problem convergence regardless of user experience in the initial low-quality RF proposal.

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Radiation heat transfer in a gas slab with properties characteristics of a jet engine combustor

Maurente

Alves

2019

International Journal of Heat and Mass Transfer

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X- factor: A modified relaxation factor to accelerate the convergence rate of the radiative transfer equation with high-order resolution schemes using the Normalized Weighting-Factor method

Cited by 4 publications

References 51 publications

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 equation with participating media using TVD interpolation schemes

Metaheuristic to Optimize Computational Convergence in Convection-Diffusion and Driven-Cavity Problems

Radiation heat transfer in a gas slab with properties characteristics of a jet engine combustor

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