Solução das equações de cinética espacial da teoria multigrupo de difusão de nêutrons em geometria cartesiana por um método iterativo de fonte

Abstract

Solution for the Multigroup Neutron Space Kinetics Equations in Cartesian Geometry by Source Iterative Method Abstract: This work presents a solution for the multigroup space kinetics equations of the neutron diffusion theory in Cartesian geometry. These equations represent the temporal dynamics of the neutron population and establish the distribution of the neutron population in a nuclear reactor. To solve this problem, an iterative source method was used based on the modification in the known Power Method. The method consists in assuming an initial distribution for the source term of the fast neutron flux equation, that becomes this system decoupled. For the solution of the fast, thermal neutron flux equations and the delayed neutron precursors, the Laplace Transform technique was used in time variable resulting in a second order ordinary differential equation system, which are solved by classical methods in the literature. After each iteration, the scalar neutron flux and the delayed neutron precursors are reconstructed by a third-order polynomial interpolation. We obtain the fluxes and precursors throught Numerical Inverse Laplace Transform. This process continues until the stop criterion is satisfied. In order to validate the proposed methodology, some numerical problems were simulated. The analysis of the sensitivity of the nuclear parameters is done by introducing a randomic perturbation in each parameter and, thus, the numerical convergence and the behavior of the solution are analyzed. The results obtained are compared with the results found in the literature and through a finite volume algorithm.