Solução das equações da cinética pontual de nêutrons com e sem retroalimentação de temperatura pelo método da aproximação polinomial

Abstract

In this dissertation, we report a solution to solve the Neutron Point Kinetics Equations applying the Polynomial Approach Method. For the solution, we consider one and six groups of delayed neutron precursors with and without temperature feedback effects, and for the following types of reactivity: constant, ramp, quadratic, sinusoidal, zig-zag and pulsed source. The objective of this work is to present accurate results with low computational cost using a simple method of hybrid structure. The main idea is to expand the neutron density, delayed neutron precursor concentrations and temperature as a power series considering the reactivity as an arbitrary function of time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions of the problem and the analytical continuation is used to determine the solutions of the next intervals. With the application of the Polynomial Approximation Method it is possible to overcome the stiffness problem of the equations. We compare the method with different types of approaches (linear, quadratic and cubic). The results obtained by numerical simulations with linear approximation are compared with results in the literature. We develop the control of the local error by Lagrange Estimator using the Rest Theorem and we perform the calculation of the global error based on the Stability Estimate and Lipschitz criterion. Furthermore, we perform convergence analysis and a perturbation is included in both reactivity as in the initial condition, in order to study the system behavior.