Computational efficiency improvements of the radiative transfer problems with or without conduction--a comparison of the collapsed dimension method and the discrete transfer method

This paper deals with the performance evaluation of the collapsed dimension method (CDM) and the discrete transfer method (DTM) in terms of computational time and their abilities to provide accurate results in solving radiation and/or conduction mode problems in a 2-D rectangular enclosure containing an absorbing, emitting and scattering medium. For some pure radiation cases, studies were made for two representative benchmark problems dealing with radiative equilibrium and non-radiative equilibrium. For the combined mode, the transient conduction and radiation problem was solved. The alternating direction implicit scheme was used for the solution of the finite difference part of the energy equation. For the three types of problems considered, tests were performed for a wide range of aspect ratio, extinction coefficient, scattering albedo, conduction-radiation parameter and boundary emissivity. For pure radiation problems, results from the two methods were validated against the results from the Monte Carlo method. For the combined mode, some steady-state results were compared with results available in the literature. For the transient situations, results from the two methods were validated against each other. While both the methods were found to give the same results, the CDM was found to be much more economical than the DTM.