No abstract

In this paper, we propose a new deterministic numerical methodology to solve the one-dimensional linearized Boltzmann equation applied to neutron shielding problems (fixed-source), using the transport equation in the discrete ordinates formulation (SN) considering the multigroup theory. This is a hybrid methodology, entitled Modified Spectral Deterministic Method (SDM-M), that derives from the Spectral Deterministic Method (SDM) and Diamond Difference (DD) methods. This modification in the SDM method aims to calculate neutron scalar fluxes with lower computational cost. Two model-problems are solved using the SDM-M, and the results are compared to the coarse-mesh methods SDM, Spectral Green's Function (SGF) and Response Matrix (RM), and the fine-mesh method DD. The numerical results were obtained in the programming language JAVA version 1.8.0_91.

Neste trabalho, é mostrada a aplicação de um método da classe dos espectronodais (malha grossa) na solução de problemas de blindagem de nêutrons em geometria unidimensional nas formulações de ordenadas discretas e multigrupo de energia. Este método, denominado Modi ed Spectral Deterministic (MSD), representou uma modificação na estrutura de obtenção dos fluxos angulares de nêutrons emergentes no processo de varredura que foi utilizado no Método Espectral Deterministico (do inglês Spectral Deterministic Method, SDM). São apresentados os resultados numéricos para 3 problemas-modelo, com diferentes dimensões, número de grupos de energia, grau de anisotropia no fenômeno de espalhamento e tipos de condição de contorno, usando um aplicativo computacional desenvolvido na linguagem de programação C++.

In this work, a coarse-mesh method used in the solution of neutron shielding problems in slab geometry is parallelized, using the memory shared environment OpenMP. The neutron transport problem is modelled using the linearized Boltzmann equation considering the energy multigroup theory and the discrete ordinate formulation (𝑆 𝑁 ). The numerical method, named Modified Spectral Deterministic (MSD), uses the neutrons transport intranodal general solution alongside an iterative process to calculate the outgoing neutron angular fluxes on the nodal interfaces. Two model-problems are solved, comparing the iterative process execution time using different number of threads. The numerical results, which achieved around 30% and 50% better execution time, were generated using the programming language C++.

A new approach for the application of the coarse–mesh Modified Spectral Deterministic method to numerically solve the two–dimensional neutron transport equation in the discrete ordinates (Sn) formulation is presented in this work. The method is based on within node general solution of the conventional one–dimensional Sn transverse integrated equations considering constant approximations for the transverse leakage terms and obtaining the Sn spatial balance equations. The discretized equations are solved by using a modified Source Iteration scheme without additional approximations since the average angular fluxes are computed analytically in each iteration. The numerical algorithm of the method presented here is algebraically simpler than other spectral nodal methods in the literature for the type of problems we have considered. Numerical results to two typical model problems are presented to test the accuracy of the offered method.