Development of a 3D Modal Neutron Code with the Finite Volume Method for the Diffusion and Discrete Ordinates Transport Equations. Application to Nuclear Safety Analyses

Abstract

The main objective of this thesis is the development of a Modal Method to solve two equations: the Neutron Diffusion Equation and the Discrete Ordinates Neutron Transport Equation. Moreover, this method uses the Finite Volume Method to discretize the spatial variables. The solution of these equations gives the neutron flux, which is related to the power produced in nuclear reactors; thus, the neutron flux is a paramount variable in Nuclear Safety Analyses. On the one hand, the use of Modal Methods is justified because one uses them to perform instability analyses in nuclear reactors. On the other hand, it is worth using the Finite Volume Method because one uses it to solve thermalhydraulic equations, which are strongly coupled with the energy generation in the nuclear fuel. First, I would like to thank the support and academic training of three persons. On the one hand, my supervisors, Rafael Miró and Gumersindo Verdú, who gave me an excellent training in Reactor Physics and numerical methods. On the other hand, José Román, because he trained me in parallel computing and solving eigenvalue problems. Without the knowledge in these areas, I would not have performed this thesis.