Radiative transfer equation (RTE) is the governing equation of radiation propagation in a media, which plays a central role in the analysis of radiative transfer in gases, semitransparent liquids and solids, porous materials, and particulate media, and is important in many scientific and engineering disciplines.
The RTE states that when radiation (a light-ray) propagates through matter (gas, dust, liquid), the incident radiation could be absorbed or scattered by matter, or radiation emitted from matter could append to the incident radiation. As a result, the intensity of radiation would change temporally, spatially, and directionally. The study of the propagating way of radiation in matter is the radiative transfer. In more detail, the radiation traversing a medium may be attenuated due to the density, mass scattering and absorption of material. In contrast, the radiation’s intensity can be strengthened by emissions from the material plus multiple scattering from all directions. All the above interactions are described mathematically by the general radiative transfer equation.
There are different forms of RTEs that are suitable for different applications, including the RTE under different coordinate systems, the transformed RTE having good numerical properties, the RTE for refractive media, etc.. Furthermore, several fundamental numerical methods for solving RTEs are proposed up to now focusing on the deterministic methods, such as the spherical harmonics method, discrete-ordinate method, finite volume method, and finite element method.