Chebyshev collocation spectral method to solve radiative transfer equation in one-dimensional cylindrical medium
Chebyshev collocation spectral method to solve radiative transfer equation in one-dimensional cylindrical medium
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DOI：
10.1016/j.ijheatmasstransfer.2017.04.094
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发表时间：
2017-08
影响因子：
5.2
通讯作者：
Rui-Rui Zhou-Rui;Ben-Wen Li
中科院分区：
文献类型：
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作者：
Rui-Rui Zhou-Rui;Ben-Wen Li
发展了求解无限长、柱对称、均匀介质中辐射传输方程的Chebyshev配置谱方法。RTE的空间和角度计算域均由Chebyshev配置点离散。对于CCSM，采用离散坐标法（DOM）中常用的守恒形式的RTE将产生较差的精度，而采用非守恒形式可以产生良好的预测。为了测试不同配置点格式在径向上的适用性，开发了三个求解器。SOLVER 1和SOLVER 2分别使用半径上的Chebyshev-Gauss-Radau（CGR）点和Chebyshev-Gauss-Lobatto（CGL）点。SOLVER 3使用直径上的CGL点，并采用偶数个节点来排除原点。结果表明，SOLVER 1和SOLVER 2都存在“奇异性效应”。这种影响可以通过增加径向上的网格数来减小。而SOLVER 3可以避免“奇异性效应”。我们还表明，映射（Kosloff-Tal-Ezer变换）实际上不能提高精度。另外，用极角的余弦代替极角本身作为自变量，会降低数值精度。我们的结果表明，CCSM的性能比DOM好得多，并产生指数收敛在空间和角度域。对于圆柱对称均匀介质的热辐射问题，CCSM是一种上级方法。
A Chebyshev collocation spectral method (CCSM) is developed to solve the radiative transfer equation (RTE) in an infinitely long, cylindrically symmetric, homogeneous medium. Both the spatial and angular computational domains of the RTE are discretized by the Chebyshev collocation points. For the CCSM, taking the conservation form of RTE, which is commonly used in the discrete ordinates method (DOM), will produce poor accuracy, whereas taking the non-conservation form can yield good prediction. To test the applicability of different collocation point schemes in the radial direction, three solvers are developed. SOLVER1 and SOLVER2 use the Chebyshev-Gauss-Radau (CGR) points and the Chebyshev-Gauss-Lobatto (CGL) points on the radius, respectively. SOLVER 3 uses the CGL points on the diameter, and an even number of nodes is taken to exclude the origin. The results show that SOLVER1 and SOLVER2 suffer from the “singularity effect”. This effect can be reduced by increasing the grid number in radial direction. Whereas SOLVER3 can avoid the “singularity effect”. We also show that the mapping (the Kosloff–Tal-Ezer transformation) actually cannot improve the accuracy. Besides, the numerical accuracy is declined by using cosine of the polar angle instead of the polar angle itself as the independent variable. Our results demonstrate that the CCSM performs much better than the DOM and produces the exponential convergence in both the spatial and angular domains. The CCSM is a superior method to achieve high accuracy for thermal radiation problem of homogeneous medium with cylindrical symmetry.