The performances of the discrete ordinates-collocation spectral method for the three-dimensional radiative transfer equation

Abstract

ABSTRACTThe discrete ordinates-collocation spectral method (DO-CSM) is successfully applied to solve the three-dimensional radiative transfer equation (RTE). The RTE is angular discretized by the DOM first and then solved by the CSM. Two examples are adopted to identify the performances of the DO-CSM for 3D RTE. The results that are obtained from the DO-CSM and the discrete ordinates method with a diamond scheme (DOM-DS), respectively, are compared with those of the exact solutions or benchmarks. These comparisons indicate that the DO-CSM can give more accurate intensity distribution in both space and direction than the DOM-DS. The false scattering of the DO-CSM is much less than that of the DOM-DS. The errors of the DO-CSM are primarily due to the “ray-effect” and the errors caused by the false scattering can even be ignored when the resolutions are fine enough. The errors due to the ray-effect are significant especially for an optical thin medium and the ray-effects are largely suppressed by the finer angular discretization. The results of the DO-CSM improved more quickly than those of the DOM-DS with the increase in the number of directions because the errors caused by the false scattering of the DO-CSM are much less than those of the DOM-DS.