Comparison of transient radiative transfer models with the discrete ordinates method in absorbing and scattering three-dimensional media
Résumé
Four different models for transient radiative transfer in a three-dimensional absorption and scattering medium are compared in this work. Two of these models are frequently used and well-known in the radiative transfer communities: the radiative transfer equation, and the diffusion equation, based on the P1 approximation. The two others models are based on a multi-scale approach where the radiative intensity is decomposed into a macroscopic and a mesoscopic components. One of these multi-scale models is called the hybrid transport-diffusion (HTD) model, while the other is called the micro-macro model. The major difference between the two multi-scale models lies in the way the macroscopic component is defined. These multi-scale models aim to improve the efficiency of the numerical simulation of radiative transfer in transient problems. This kind of problems appear, for example, in optical tomography applications, where the propagation of a laser inside a biological tissue must be simulated efficiently in order to determine the optical properties of the tissue and to detect the presence of tumours or inhomogeneities. The impact of increasing the spatial and temporal schemes order, in the models where it applies, is also investigated.