A Discrete Ordinates Nodal Method for One-Dimensional Neutron Transport Calculation in Curvilinear Geometries

In this work, the Analytical Discrete Ordinates Method (ADO method) is used to provide a closed form solution for a class of one-dimensional neutron transport problems in Cartesian geometry, considering heterogeneous media with linearly anisotropic scattering effects. In this context, the mathematical model will describe a steady-state phenomenon, with neutron sources located inside and on the boundaries of the domain of interest. In the process, the integro-differential transport equation is transformed into an ODE system by the SN angular discretization, which homogeneous solution is obtained with a quadratic eigenvalues problem with reduced order. A particular solution in terms of constants is used. To validate the code, the method and provide benchmark results, test problems will be treated and results will be discussed.

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The modified spectral deterministic method applied to fixed–source discrete ordinates problems in X,Y–geometry

Brazilian Journal of Radiation Sciences ◽

10.15392/bjrs.v8i3a.1268 ◽

2021 ◽

Vol 8 (3A) ◽

Author(s):

Jesús Pérez Curbelo ◽

Rafael Barbosa Libotte ◽

Amaury Muñoz Oliva ◽

Ricardo Carvalho Barros ◽

Hermes Alves Filho

Keyword(s):

Neutron Transport ◽

Iteration Scheme ◽

Discrete Ordinates ◽

Coarse Mesh ◽

Neutron Transport Equation ◽

Balance Equations ◽

Deterministic Method ◽

New Approach ◽

One Dimensional ◽

Typical Model

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.

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The spectral nodal method applied to multigroup SN neutron transport problems in One-Dimensional geometry with Fixed–Source

Progress in Nuclear Energy ◽

10.1016/j.pnucene.2017.12.017 ◽

2018 ◽

Vol 105 ◽

pp. 106-113 ◽

Cited By ~ 1

Author(s):

Amaury Muñoz Oliva ◽

Hermes Alves Filho ◽

Davi José Martins e Silva ◽

Carlos Rafael García Hernández

Keyword(s):

Neutron Transport ◽

One Dimensional ◽

Nodal Method ◽

Transport Problems

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Spectral-Nodal Deterministic Methodology for Neutron Shielding Calculations using the X, Y - geometry Multigroup Transport Equation in the Discrete Ordinates Formulation

VETOR - Revista de Ciências Exatas e Engenharias ◽

10.14295/vetor.v31i1.13472 ◽

2021 ◽

Vol 31 (1) ◽

Author(s):

Amaury Munoz Oliva ◽

Hermes Alves Filho

Keyword(s):

Neutron Transport ◽

Numerical Results ◽

Isotropic Scattering ◽

Discrete Ordinates ◽

Reactor Physics ◽

Neutron Shielding ◽

Nodal Method ◽

Fine Mesh ◽

Mesh Method ◽

Neutron Transport Equations

In this work, we present the most recent numerical results in a nodal approach, which resulted in the development of a new numerical spectral nodal method, based on the spectral analysis of the multigroup, isotropic scattering neutron transport equations in the discrete ordinates ($S_N$) formulation for fixed-source calculations in non-multiplying media (shielding problems). The numerical results refer to simulations of typical problems from the reactor physics field, in rectangular two-dimensional Cartesian geometry, $X, Y$ geometry, and are compared with the traditional Diamond Difference ($DD$) fine-mesh method results, used as a reference, and the spectral coarse-mesh method Green's function ($SGF$) results.

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