Performance comparisons of the DOM, CCSM, and hybrid CCS-DOM for thermal radiation analysis in one-dimensional cylindrical coordinates

Recently, the Chebyshev collocation spectral method (CCSM) was developed to solve radiative transfer equation (RTE) directly in one-dimensional cylindrical medium (IJHMT, 189 (2017) 206-220). However, the direct solver is memory consuming and difficult to solve the problems with large grid number. In this paper, we develop a less memory consumed iterative solver based on the Schur decomposition. To simplify the solution procedure, a hybrid method of the CCSM and discrete ordinates method (DOM), named the CCS-DOM, is also investigated. In the CCS-DOM, the angular dependence is approximated by the DOM instead to avoid the coupling of radial and azimuthal directions as that in the pure CCSM. Performances of the CCSM and CCS-DOM are assessed by comparing to the DOM. In addition, the angular quadrature scheme and pole condition for the DOM are optimized in our study. The comparative results show that the CCS-DOM fails to obtain the radiative information accurately in cylindrical coordinates. Its performance is worse than that of the DOM. The CCSM presents a fifth order convergence, which is much higher than the second one of DOM, thus has great advantage on acquiring highly accurate results. It spends less CPU time and costs less memory than the DOM to achieve the same accuracy. Finally, results for the DOM and CCSM are compared and shown for various parameters. It is found that two methods have the same iterative convergence rate and present similar behaviors for the considered parameters. All these results support the CCSM to be a good alternative for thermal radiation calculation in the one-dimensional cylindrical medium with the newly developed iterative solver.