Semi-analytical equation-solving RDFIEM method for radiative transfer in a plane-parallel anisotropic scattering medium

Abstract

Once the geometry and physical properties of the radiation system are determined, the integral equation method based on radiation distribution factor (RDFIEM) can be effectively used to calculate the directional radiation intensity with high resolution. However, there exists an inherent shortcoming of low efficiency for statistical ray sampling since the radiation distribution factors (RDFs) are obtained by reverse Monte Carlo (RMC) method. For overcoming this deficiency, an efficient semi-analytical equation-solving RDFIEM (ES-RDFIEM) method is proposed to solve the RDFs directly. In this paper, the principles and formulas of ES-RDFIEM in 1D radiation system with anisotropic scattering medium are developed in detail. Benefit from that the RDF is only related to the geometry and radiation properties of the medium, it can be assumed that only a certain element n has unit blackbody radiation intensity, while the remaining elements do not emit energy. In this way, a semi-analytical set of linear equations can be constructed to solve the RDF matrix directly. Compared with RMC, multiple cases with different radiative parameters are adopted to examine the performance of ES-RDFIEM. Numerical results show that ES-RDFIEM is in good agreement with RMC in most conditions, especially in isotropic scattering or weak scattering of anisotropic scattering. In addition, ES-RDFIEM can effectively avoid the random errors produced by RMC, making the result of ES-RDFIEM smoother than RMC. More importantly, it only takes a few CPU times for computing all the RDF values by ES-RDFIEM, which is one or two orders of magnitude less than that of RMC, and its computational efficiency is almost independent of the radiation properties, showing an excellent efficiency.