Solução da equação de difusão de nêutrons multigrupo multirregião estacionária em geometria cartesiana pelo método da potência via fronteiras fictícias

Abstract

In this work it is presented a solution of the stationary multi-layer multi-group neutron diffusion equation in cartesian geometry by fictitious borders power method. The equation is solved applying the iterative power method that consists in solving the neutron diffusion equation for each iteration in which the source term is always updated by neutron flux on the previous iteration. This process is held until a determined stop criterion for the convergence of the solution. However, for each new iteration, new terms are added, which becomes very laborious. To overcome this problem it is proposed the reconstruction of the neutron flux by interpolation. The solution remains in a standard form for all iterations. Nevertheless, when the problem has large dimensions and various regions, polynomials of high order to describe the neutron flux accurately are needed. In this interpolation process the matrices involved have large dimensions, both due to the order of the polynomial as the number of domain points. With the aim of reducing the order of the polynomial and the dimensions of the matrices involved, making the process faster in computational point of view, the domain is divided into R fictitious regions that interpolates and solves the diffusion equation neutron locally in each region. The arbitrary constants arising from solution of the homogeneous problem are found by apply boundary conditions, flux and current density continuity at interfaces. To analyze the sensitivity of the nuclear parameters in the convergence and behavior of the solution it is inserted a perturbation for each parameter of same magnitude order using a random fluctuation multiplied by a constant. The results obtained are compared with results present in the literature.