Eliete Biasotto Hauser

A Laplace transform exponential method for monoenergetic three-dimensional fixed source discrete ordinates problems in Cartesian geometry

We describe a Laplace transform exponential method applied to x-y-z geometry heterogeneous neutron transport problems in the discrete ordinates (SN) formulation that we refer to as the LTSN – Exp method. This numerical method uses the space Laplace transform technique to solve the one-dimensional transverse-integrated SN exponential equations within one of the homogeneous regions of the domain of solution. Based on the physics of shielding problems where the neutron flux attenuates exponentially with increasing distance from the source, we approximate the transverse leakage terms by exponential functions. We show in two numerical experiments that the LTSN – Exp method generates very accurate results in highly absorbing media.

Modelo Logístico de Verhulst e Métodos Numéricos na Análise do Censo Populacional Mundial

O presente trabalho tem por objetivo estudar o crescimento populacional mundial. Esse crescimento inicialmente e da forma exponencial e supomos que a populacao podera crescer tendendo a um limite maximo (recursos limitados). Esse limite maximo e denominado capacidade suporte.

On the Convergence of the Multi-group Isotropic Neutron LTS N Nodal Solution in Cartesian Geometry

The discrete ordinate nodal approach (nodal SN approximation) is presented in the context of neutron transport. Here an analytical method, the LTSN nodal approach is presented for the transverse integrated multi-group neutron transport equation in a multidimensional Cartesian geometry domain. The resulting coupled system of one-dimensional SN equations for the average angular fluxes are solved by the Laplace Transform technique (LT SN method). We present convergence analysis of the nodal method.

The Error Bounds for Three-Dimensional Nodal LTSN Method

In this paper we present a proof about the convergence of the 3D Nodal-LTSN Method in order to solve the transport problem in a parallelepiped domain. For that, we define functions associated to the errors, one in the approximated flux, another in the quadrature formula and establish a relation between them. We present a Nodal-LTSN method to generate an analytical solution for discrete ordinates problems in three-dimensional cartesian geometry. We first transverse integrate the SN equations and then we apply the Laplace transform. The essence of this method is the diagonalization of the LTSN transport matrices and the spectral analysis garantees this. The transverse leakage terms that appear in the transverse integrated SN equations are represented by exponential functions with decay constants that depend on the characteristics of the material of the medium the particles leave behind. We present numerical results generated by the offered method applied to typical shielding model problems.Copyright