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EFFECT OF ANGULAR QUADRATURE SCHEMES ON THE COMPUTATIONAL EFFICIENCY OF THE DISCRETE TRANSFER METHOD FOR SOLVING RADIATIVE TRANSPORT PROBLEMS WITH PARTICIPATING MEDIUM

This article deals with the effects of angular quadrature schemes on the computational efficiency of the discrete transfer method (DTM) used for solving radiative transport problems with a participating medium. Four different quadrature schemes are considered. The first scheme uses the ray directions and the associated weights as per the original formulation of the DTM. In the second and third schemes, the ray arrangements are different but the quadrature schemes are the same as that used in the collapsed dimension method. The fourth scheme uses the ray directions and the corresponding weights according to the imporved quadrature scheme employed in the discrete ordinates method (DOM). The effects of the four quadrature schemes on the computational efficiency are tested for four benchmark radiative transport problems. Results are compared with the exact methods and with those available in the literature. It has been found that if the ray directions and the weights are chosen as per the DOM, the computational efficiency of the DTM is the best.