An efficient equation-solving method for calculating radiative transfer in isotropic scattering medium

An efficient equation-solving integral equation method (ES-RDFIEM) is proposed to calculate the radiation distribution factor (RDF), which was required to be solved by the time-consuming ray tracing with reverse Monte Carlo method (RMC) in the past. Since the RDF is only related to the radiative properties and geometry of the medium, it can be assumed that the blackbody radiation intensity of a certain element n is 1, while there is no emission from the remaining elements of the radiation system. In this way, the RD(j, n) (j = 1, 2,…, N) can be obtained by solving N × N equations based on the equivalent relationship of incident radiation. As a result, the stochastic statistical process of the RMC can be effectively avoided. The numerical results show that the RDF and radiation intensity calculated by ES-RDFIEM and RMC are highly consistent for one-dimension and two-dimension emitting, absorbing, isotropic scattering medium with transparent boundary. The CPU time for ES-RDFIEM to calculate the RDFs of the whole radiation system is much shorter than RMC under the same condition, which, in addition, does not increase with the increase of scattering albedo or optical thickness. With the same calculation accuracy as RMC, ES-RDFIEM has the significant advantage of high efficiency, which shows great potential in solving inverse radiation problems.