A generalized mean intensity approach for the numerical solution of the radiative transfer equation

Computing ◽  
1995 ◽  
Vol 54 (1) ◽  
pp. 27-38 ◽  
Author(s):  
S. Turek
Keyword(s):  
Radiative Transfer ◽  
Numerical Solution ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Mean Intensity ◽  
Generalized Mean

Acceleration of the numerical solution for the radiative transfer equation using a modified relaxation factor

2020 ◽  
Vol 37 (5) ◽  
pp. 1823-1847 ◽  
Author(s):  
Carlos Enrique Torres-Aguilar ◽  
Jesús Xamán ◽  
Pedro Moreno-Bernal ◽  
Iván Hernández-Pérez ◽  
Ivett Zavala-Guillén ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Numerical Solution ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Boundary Surface ◽  
Processing Unit ◽  
Content Type ◽  
Cpu Time ◽  
Relaxation Factor ◽  
Factor Method

Purpose The purpose of this study is to propose a novel relaxation modified factor to accelerate the numerical solution of the radiative transfer equation (RTE) with several high-resolution total variation diminishing schemes. The methodology proposed is denoted as the X-factor method. Design/methodology/approach The X-factor method was compared with the technique deferred-correction (DC) for the calculations of a two-dimensional cavity with absorting-emiting-scatteting gray media using the discrete ordinates method. Four parameters were considered to evaluate: the absorption coefficient, the emissivity of boundary surface, the scattering albedo and under-relaxation factor. Findings The results showed the central processing unit (CPU) time of X-factor method was lower than DC. The reductions of CPU time with the X-factor method were observed from 0.6 to 75.4%. Originality/value The superiority of the X-factor method over DC was showed with the reduction of CPU time of the numerical solution of RTE for evaluated cases.

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

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Carlos Enrique Torres-Aguilar ◽  
Pedro Moreno-Bernal ◽  
Jesús Xamán ◽  
Ivett Zavala Guillen ◽  
Irving Osiris Hernández-López
Keyword(s):  
Radiative Transfer ◽  
Numerical Solution ◽  
Evolutionary Algorithm ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Scattering Media ◽  
Content Type ◽  
Cpu Time ◽  
Absorbing Media ◽  
Relaxation Coefficients

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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