Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media

- We survey recent advances in the discrete ordinates and finite volume methods.
- Developments in spatial and angular discretization schemes are described.
- Progress in solution algorithms and parallelization methods is reviewed.
- Advances in the transient solution of the radiative transfer equation are appraised.
- Non-gray media and variable refractive index media are briefly addressed.

Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed.