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The article presents the foundation of a novel methodology developed for the solution of the neutron transport equation, named the transport driven-diffusion approach, which can be considered as an evolution of the classic multiple collision method. The idea behind this method is based on the expansion of the full solution in terms of the contributions of the particles emitted by successive collisions plus a residual term, accounting for particles which have undergone more than a predefined number of collisions. In order to determine the contribution at each collision order, a transport equation with a source term is solved, while the estimation of the residue is based on a diffusion theory model. The physical rationale for the choice of the diffusion model for the residue is discussed and justified, as physics suggests that the diffusion assumptions become more applicable for the description of the particles having suffered a certain number of collisions rather than to the original transport problem. Some results are presented for a set of steady-state and time-dependent test cases. Their analysis shows the remarkable advantage of the method proposed in terms of accuracy and computational time, when compared to standard diffusion and multiple collision at the same order.

“On the Foundation of Transport-Driven Diffusion for Neutron Transport Problems”