A New Moment Model for Radiative-Transport Prediction - Morin, William (Université d'Ottawa / University of Ottawa, 2020)
Accurate modelling of radiative transfer is important in many engineering applications, such as, medical imaging, cancer treatment, nuclear-power generation, and heat transfer. Unfortunately, most existing models suﬀer from modelling artifacts that limits their applications. Methods based on the direct tracking of particles are accurate, however, they can be prohibitively expensive for many practical engineering applications. Spherical-harmonics and discrete-ordinates models are more aﬀordable to compute, however they often produce results that contain severe mathematical artifacts. The maximum-entropy closures feature many desirable mathematical properties. However, for all but the lowest-order members of the hierarchy, these models cannot be written in closed form. Thus, making their practical application exceedingly expensive. In order to address these issues, the goal of this project is to develop and con duct an investigation into a new hierarchy of models for radiative transport. This model produces ﬁeld equations for the prediction of general radiative transport. It is therefore expected that solutions will be far easier to compute, as compared to particle-based methods. The idea is based on a new special averaging procedure that is applied to a low order Discrete-Ordinance method. The resulting model is designed to preserve positivity of solutions, like the discrete ordinance model, while approaching rotational symmetry, like spherical-harmonics based models. In this thesis, the ﬁrst-order closure of the spherical-harmonics, the discrete-ordinates and the maximum-entropy hierarchy are compared with the ﬁrst member of the new hierarchy. The eigenstructure of the diﬀerent ﬁrst-order closures is studied and their general behaviours are compared using three standard radiation-transfer problems. Finally, the second order moment version of the closure is presented along with a discussion of the limitations of the proposed model.
Keywords: Radiative-Transport