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.

中文翻译：

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一种使用 TVD 插值方案控制辐射传递方程与参与介质的数值收敛的进化算法

目的

本文旨在提出一种进化算法 (EA)，通过松弛系数优化使用高阶和高分辨率方案来加速辐射传递方程 (RTE) 数值解的收敛。

设计方法/方法

目标函数最小化每个控制体中迭代之间的残差值差异，直到其差异低于收敛标准。EA 方法在两种配置中进行评估，即具有散射介质和吸收介质的二维腔。

发现

实验结果表明，在通过 EA 方法测试的所有插值方案上，都能获得两种情况的数值解。EA 方法使用 SUPERBEE、SWEBY 和 MUSCL 方案减少了 RTE 数值解的 CPU 时间，直到在散射和吸收媒体情况下分别达到 97% 和 135%。与具有固定松弛系数的延迟校正程序相比，每两次数值求解迭代优化的松弛系数显着减少了 CPU 时间。

原创性/价值

与具有固定松弛系数的 DC 程序相比，针对 RTE 数值解决方案提出的 EA 方法有效地减少了 CPU 时间。