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.

最近，开发了 Chebyshev 积分方法来求解奇异点去除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。这种优越的特性使得 Chebyshev 积分方法具有吸引力，可以产生具有相当高准确度的结果作为基准解决方案。但是，切比雪夫积分方法是一种全局方法，只适用于参数平滑和温度分布平滑的问题。为了克服这个缺点，本文提出了复合切比雪夫积分方法。计算域被划分为若干子域，然后在每个子域中应用切比雪夫求积。解决了具有连续/逐步变化的散射反照率和发射的矩形介质中的几个基准问题。增加子域固定的网格数，可以观察到复合切比雪夫积分方法仍然具有较高的阶次收敛精度。此外，为方便起见，四舍五入到七位有效数字的解决方案以表格形式给出。它们还用作基准解决方案，以评估搭配光谱方法 (CSM) 及其辐射传递方程 (RTE) 的修改版本。结果表明，当散射反照率和温度分布出现不连续性时，CSM受到严重的射线效应。虽然修改后的 CSM 可以避免由于逐步变化的发射而产生的射线效应，与相同空间网格系统下的 RITE 复合切比雪夫积分方法相比，它需要更重的计算负载，但产生的结果精度较低。与求解 RTE 的 CSM 或改进的 CSM 相比，RITE 的复合 Chebyshev 积分方法可以在可接受的计算时间内获得更高的精度，因此也可以作为简单几何中热辐射计算的一个很好的替代方案。