Analytical adjoint discrete ordinates formulation for monoenergetic slab-geometry source-detector calculations

Pazinatto, Cássio Baissvenger; Barros, Ricardo C.; Barichello, Liliane Basso

doi:10.1504/ijnest.2016.077478

Cited by 10 publications

(3 citation statements)

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“…(3.1) is linear, we write its general solution as a superposition of the homogeneous and particular solutions of Eq. (3.1a) [19,21,24,25,29,30].…”

Section: An Analytical Discrete Ordinates Solutionmentioning

confidence: 99%

On the Application of the Analytical Discrete Ordinates Method to the Solution of Nonclassical Transport Problems in Slab Geometry

Moraes,

Barichello,

Barros

et al. 2021

Preprint

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In this work we investigate the use of the Analytical Discrete Ordinates (ADO) method when solving the spectral approximation of the nonclassical transport equation. The spectral approximation is a recently developed method based on the representation of the nonclassical angular flux as a series of Laguerre polynomials. This representation generates, as outcome, a system of equations that have the form of classical transport equations and can therefore be solved by current deterministic algorithms. Thus, the investigation of efficient approaches to solve the nonclassical transport equation is of interest and shall be pursued. This is the case of the ADO method which has been successfully used to solve a wide class of problems in the general area of particle transport. Numerical results are presented for two nonclassical test problems in slab geometry. These nonclassical transport problems are chosen in such way that their solution exactly reproduces the solution of the classical diffusion problem. Very accurate results are obtained for both test problems. However, the use of high precision arithmetic is sometimes required as illustrated in the second test problem. Limitations of the spectral approximation are also analyzed and discussed.

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“…(3.1) is linear, we write its general solution as a superposition of the homogeneous and particular solutions of Eq. (3.1a) [19,21,24,25,29,30].…”

Section: An Analytical Discrete Ordinates Solutionmentioning

confidence: 99%

On the Application of the Analytical Discrete Ordinates Method to the Solution of Nonclassical Transport Problems in Slab Geometry

Moraes,

Barichello,

Barros

et al. 2021

Preprint

Self Cite

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“…We follow our previous paper on the monoenergetic adjoint transport equation (Pazinatto et al 2016) and the work of Siewert (2000) for the ADO solution of the multigroup transport equation, to derive an ADO solution for the adjoint to the multigroup transport equation. Thus, we start by writing the homogeneous version of Equation (7a) (r d ¼ 0) in the form…”

Section: Homogeneous Solutionmentioning

confidence: 99%

“…In this context, given that the Analytical Discrete Ordinates (ADO) method (Barichello and Siewert 1999a) has shown to be fast, accurate, and easily implementable for solving many problems related to transport calculations (Barichello and Siewert 1999b;Siewert 2000;Scherer, Prolo Filho, and Barichello 2009), such a formulation was used to solve monoenergetic adjoint transport problems (Pazinatto, Barros, and Barichello 2016), with a successful application in source estimation (Pazinatto and Barichello 2017).…”

Section: Introductionmentioning

confidence: 99%

Energy Dependent Source Reconstructions via Explicit Formulations of the Adjoint Particles Flux

Pazinatto

Barichello

2018

Journal of Computational and Theoretical Transport

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An analytical solution to the discrete ordinates approximation of the adjoint to the multigroup transport equation in onedimensional slab geometry is developed in this work, in order to be used in source estimation problems. The solution is firstly tested in a source-detector problem, where explicit expressions are derived to approximate the absorption rate of particles of internal detectors. Noisy data generated from readings of internal detectors were then used, along with the adjoint formulation, in an iterative process to solve an energydependent inverse problem of source reconstruction in the cases of polynomials and piecewise constant sources. The approach is shown to be fast and accurate.

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An analytical discrete ordinates nodal solution to the two-dimensional adjoint transport problem

Barichello

Pazinatto

Rui

2020

Annals of Nuclear Energy

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Analytical adjoint discrete ordinates formulation for monoenergetic slab-geometry source-detector calculations

Cited by 10 publications

References 0 publications

On the Application of the Analytical Discrete Ordinates Method to the Solution of Nonclassical Transport Problems in Slab Geometry

On the Application of the Analytical Discrete Ordinates Method to the Solution of Nonclassical Transport Problems in Slab Geometry

Energy Dependent Source Reconstructions via Explicit Formulations of the Adjoint Particles Flux

An analytical discrete ordinates nodal solution to the two-dimensional adjoint transport problem

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