Multi-scale methods for the solution of the radiative transfer equation
Résumé
Various methods have been developed and tested over the years to solve the radiative transfer equation (RTE) with different results and trade-offs, such as the Monte Carlo, the finite volume, the discrete ordinates and the spherical harmonics methods. Although the RTE is extensively used, the approximate diffusion equation is sometimes preferred, particularly in optically thick media, due to the lower computational requirements. Recently, multi-scale models, namely the domain decomposition methods, the micro-macro model and the hybrid transport-diffusion model, have been proposed as an alternative to the RTE. The idea behind the domain decomposition methods is to decompose the domain into two subdomains, namely a mesoscopic subdomain where the RTE is solved and a macroscopic subdomain where the diffusion equation is solved. In the micro-macro and hybrid-transport diffusion models, the radiation intensity is decomposed into a macroscopic component and a mesoscopic one. In both cases, the aim is to reduce the computational requirements, while maintaining the accuracy, or improve the accuracy for similar computational requirements. In this paper, these methods are described, and a few recent results reported. It is shown that in problems where the diffusion approximation is accurate, but not over all the domain, the multi-scale methods may reduce the computational requirements or improve the solution accuracy in comparison with the solution of the RTE.