Multilevel methods to solve the neutron diffusion equation

Abstract

In this paper, we develop multilevel strategies to solve the time dependent neutron diffusion equation. These methodologies are based on the discretization of the spatial part of the neutron diffusion equation using a nodal collocation method which makes use of an expansion of the neutron flux in terms of Legendre polynomials. The different levels or grids of the multilevel strategies have been defined in terms of the different number of polynomials used for the nodal collocation method expansions instead of using different nodalization sizes. Results for two transients associated with the bidimensional TWIGL reactor are reported.