Método de solução da equação de transporte de nêutrons integradas transversalmente em cálculos bidimensionais usando a formulação SN com aproximação de expansão polinomial quadrática para os termos de fuga transversal em problemas de fonte-fixa

Abstract

In solving problems involving the phenomenon of neutron transport in two-dimensional Cartesian geometry using spectral nodal methods, a transverse integration must be performed in the neutron transport equation, giving originating a term known as transverse neutron leakage. In order to make this system of equations possible and determined, it is necessary to approximate the transverse neutron leakage term. Therefore, in this thesis, we present a quadratic polynomial approximation for this term. This approach was applied to the solution of fixed-source problems, making use of the multigroup energy neutron transport equation in the discrete ordinates formulation. This type of approximation can also be truncated to obtain, in addition to the quadratic approximation, a linear or constant approximation, which is widely used in spectral nodal methods. Four model problems were solved using the spectral nodal methods Spectral Deterministic Method and Response Matrix. The numerical results obtained were compared in terms of accuracy and execution times between the quadratic, linear, and constant approximations with a reference fine-mesh method, using various meshes and different quadrature orders. The numerical results obtained showed low relative percentage deviations, as well as time savings when using linear and quadratic approximations with relatively coarse meshes, compared to solutions that use constant approximation.