Equation-Solving DRESOR Method for Radiative Transfer in an Absorbing–Emitting and Isotropically Scattering Slab With Diffuse Boundaries

The distribution of ratios of energy scattered by the medium or reflected by the boundary surface (DRESOR) method can provide radiative intensity with high directional resolution, but also suffers the common drawbacks of the Monte Carlo method (MCM), i.e., it is time-consuming and produces unavoidable statistical errors. In order to overcome the drawbacks of the MCM, the so-called equation-solving DRESOR (ES-DRESOR) method, an equation-solving method to calculate the DRESOR values differently from the MCM used before, was proposed previously. In this method, a unit blackbody emission is supposed within a small zone around a specified point, while there is no emission elsewhere in a plane-parallel, emitting, absorbing, and isotropically scattering medium with transparent boundaries. The set of equations for the DRESOR values based on two expressions for the incident radiation was set up and solved successfully. In this paper, the ES-DRESOR method is extended to a one-dimensional system with diffusely reflecting boundaries. The principle and formulas are given. Several examples with different parameters are taken to examine the performance of the proposed method. The results showed that all the DRESOR values obtained using the ES-DRESOR method agree well with those got using MCM. The average relative error for the intensity obtained by the ES-DRESOR method is 9.446 × 10⁻⁶, lower by over 1 order of magnitude than the 2.638 × 10⁻⁴ obtained by the MCM under the same conditions. More importantly, the CPU time for computing the DRESOR values, which ranges from several hundred seconds to several thousand seconds using the MCM, is reduced to 0.167 s using the ES-DRESOR method. The computation time is shortened by about 3 orders of magnitude. The overall performance of the ES-DRESOR method is excellent.