The composite Chebyshev integration method for radiative integral transfer equations in rectangular enclosures
The composite Chebyshev integration method for radiative integral transfer equations in rectangular enclosures
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DOI：
10.1016/j.ijthermalsci.2021.107141
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发表时间：
2021-12
影响因子：
4.5
通讯作者：
Rui-Rui Zhou-Rui;Yasong Sun;Ben-Wen Li;Jing Ma
中科院分区：
文献类型：
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作者：
Rui-Rui Zhou-Rui;Yasong Sun;Ben-Wen Li;Jing Ma
最近，切比雪夫积分方法被用来求解去除奇点后的辐射积分传递方程(RITES)(IJTS，149(2020)106,158)，并显示出四阶收敛精度。这种优越的性质使得切比雪夫积分方法很有吸引力，可以产生具有相当高精度的结果作为基准解。然而，切比雪夫积分法是一种全局方法，只适用于参数光滑、温度分布均匀的问题。为了克服这一缺陷，本文提出了复合切比雪夫积分法。将计算区域划分为多个子域，然后在每个子域上应用切比雪夫求积。解决了矩形介质中具有连续/阶跃变化散射、反照率和辐射的几个基准问题。增加固定子域的网格数目，可以观察到组合切比雪夫积分方法仍然具有较高的阶数收敛精度。此外，为方便起见，四舍五入至七位有效数字的解以表格形式列出。它们也被用作辐射传递方程(RTE)的配置谱方法(CSM)及其修正版本的基准解。结果表明，当散射反照率和温度分布出现不连续时，CSM受到严重的射线效应的影响。虽然改进的CSM方法可以避免逐步变化发射的射线效应，但在相同的空间网格系统下，与组合切比雪夫积分方法相比，其计算量较大，但计算结果的精度较低。与求解RTE的CSM或修正CSM方法相比，组合切比雪夫积分方法在计算时间可接受的情况下，可以获得更高的精度，因此也可以作为简单几何形状下热辐射计算的一种很好的选择。
Recently, the Chebyshev integration method was developed to solve the radiative integral transfer equations (RITEs) after singularity removing (IJTS, 149 (2020) 106,158), and shown fourth order convergence accuracy. This superior property makes the Chebyshev integration method attractive to produce results with quite high accuracy to be benchmark solutions. However, the Chebyshev integration method, which is a global method, is only suitable for problems with smooth parameters and temperature distribution. To overcome this drawback, in this paper, the composite Chebyshev integration method is proposed. The computational domain is divided into several subdomains, and then the Chebyshev quadrature is applied in each subdomain. Several benchmark problems in the rectangular medium with continuous/stepwise-change scattering albedo and emissions are solved. Increasing the grid number with fixed subdomains, one can observe that the composite Chebyshev integration method still has the high order convergence accuracy. Besides, the solutions rounded to seven significant digits are given in tabular form for convenience. They are also used as benchmark solutions to assess the collocation spectral method (CSM) and its modified version for radiative transfer equation (RTE). The results indicate that the CSM suffers from severe ray effect when the discontinuities appear in the scattering albedo and temperature distribution. Though the modified CSM can avoid the ray effect due to stepwise-change emissions, it requires heavier computational load but produces less accurate results than the composite Chebyshev integration method for RITEs under the same spatial grid system. Compared with the CSM or modified CSM to solve the RTE, the composite Chebyshev integration method for RITEs can achieve much higher accuracy with acceptable computational time, thus could also be a good alternative for thermal radiation calculations in simple geometry.