Solution of multi-dimensional radiative heat transfer in graded index media using the discrete transfer method

The discrete transfer method is extended to solve the radiative transfer equation in two- and three-dimensional semi-transparent media with variable refractive index. The radiative transfer equation and other related equations are organized based on the refracted quantities. A cell-based ray tracing approach is used to track the curve paths of radiative rays in the medium. The complex geometries in multi-dimensional media are simulated by a simple blocked-off strategy. The present method is verified by comparing its results with benchmark solutions, and the performance of the method is examined by some numerical experiments.