Problema inverso de reconstrução analítica aproximada da solução da equação de transporte de partículas neutras monoenergéticas em geometria unidimensional cartesiana com espalhamento isotrópico

• Autor(a) principal: Oliveira, Francisco Bruno Souza
• Data de Publicação: 2007
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13645
• topic: Transport theory - Discrete ordinates method; Neutrons - Transport - Simulation methods; Particles (Nuclear physics) - Transport - Simulation methods; Inverse problems (Differential equations); Teoria cinética do transporte - Método das ordenadas discretas; Nêutrons - Transporte - Métodos de simulação; Partículas (Física nuclear) - Transporte - Métodos de simulação; Problemas inversos (Equações diferenciais); CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::FISICA DAS PARTICULAS ELEMENTARES E CAMPOS::TEORIA GERAL DE PARTICULAS E CAMPOS

We offer in this work an application of the SGF method, cf., spectral Green s function, to generate the angular fluxes at the region interfaces of multilayer slabs, using high-order angular quadrature sets in the one-speed discrete ordinates (SN) formulation of the neutral particle transport equation. Using the SGF coarse-mesh numerical solution, we first determine the arbitrary constants of the analytical general solution of the SN equations within each spatial node. Then, we use the angular quadrature formula to estimate the expression of the scalar flux distribution, that we substitute into the isotropic scattering source term of the transport equation. We solve analytically the slab-geometry transport equation, with the scattering source so approximated, in order to generate the angular flux profile within each spatial node. As the SGF method generates coarse-mesh numerical solution, which is completely free from spatial truncation errors, we expect that the offered approximate analytical reconstruction scheme be accurate enough for the localized angular flux distribution, considering the node interface continuity conditions within the domain. This technique is thought of as an inverse problem since from the SGF coarse-mesh nodal solution we are able to reconstruct the angular flux profile at any point inside the domain.