Three-dimensional discrete ordinates method in transient radiative transfer

A complete transient three-dimensional discrete ordinates method is formulated for the first time to solve transient radiative transfer in a rectangular enclosure containing nonhomogeneous media that absorb, emit, and scatter. Twofold validation of the transient method is obtained: First, there is an excellent agreement between its results at long time stage with several steady-state solution methods. Second, the transient predictions of transmittance and reflectance compare very well with Monte Carlo simulations. The sensitivity and accuracy of the transient method against the sizes of time increment and grid cell and angular discrete order are examined. The false radiation propagation and numerical diffusion associated with the differencing schemes are discussed. Calculations show the behavior of the wave nature of propagation of transient radiation. The transient behavior of radiation is found to be influenced by many parameters, such as the boundary conditions, the optical thickness of the medium, the scattering albedo, and the incident radiation pulse width. Duhamel's superposition theorem is also applied to obtain the transient response to different temporal input pulses.