Calculation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si54.svg"><mml:mrow><mml:mi>λ</mml:mi></mml:mrow></mml:math> modes of the multi-group neutron transport equation using the discrete ordinates and Finite Difference Method

Morató, S.; Bernal, Álvaro; Miró, R.; Román, José E.; Verdú, G.

doi:10.1016/j.anucene.2019.107077

Cited by 15 publications

(2 citation statements)

References 14 publications

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“…Here, we apply the SGF † -CN method to the adjoint problem (6) on a coarse spatial grid composed of 100 × 100 nodes and the level symmetric 𝑆 8 angular quadrature set to obtain the importance values to be substituted into the corresponding terms of Equation (7).…”

Section: Model-problem N Omentioning

confidence: 99%

The adjoint transport problem applied to estimate neutral particle leakage in the discrete ordinates formulations

Curbelo

Barros²

2022

Braz. J. Rad. Sci.

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In source–detector problems, neutron leakage is a quantity of interest that could lead to improve shielding structures, thus reducing the dose received by humans. In this work, we apply an adjoint technique with spectral nodal methods to compute neutron leakage in multigroup one– and two–dimensional problems in the discrete ordinates (SN) formulation. The use of the adjoint technique to calculate the leakages due to various source distributions is very convenient as it is possible to run adjoint problems and store the neutron importance maps. Here we solve the homogeneous adjoint SN transport equation by considering unit outgoing adjoint flux at the boundary. In order to numerically solve slab– and X, Y–geometry problems, we use spectral nodal methods that have been widely applied and discussed in the literature. Numerical results are given to illustrate the present adjoint technique to estimate the neutron leakage for each energy group in source–detector problems. For all the test problems, the results obtained by the adjoint technique as described in this paper do agree with the results obtained by solving the analogous forward problem.

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Section: Model-problem N Omentioning

confidence: 99%

The adjoint transport problem applied to estimate neutral particle leakage in the discrete ordinates formulations

Curbelo

Barros²

2022

Braz. J. Rad. Sci.

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“…The time-independent multigroup BTE with −'th order of anisotropy on both the scattering and fission terms within a region of a multiplying slab [9,10] is considered with appropriate boundary conditions…”

Section: Spectral Analysis Of the Transport Equationsmentioning

confidence: 99%

On the spectrum of discrete-ordinates neutron transport problems

Curbelo

2021

Braz. J. Rad. Sci.

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Over the last six decades, the discrete spectrum of the neutron transport operator has been widely studied. Important theoretical results can be found in the literature regarding the one-speed linear transport equation with anisotropic scattering. In this work, the discrete-ordinates (SN) transport problem with anisotropic scattering has been considered and the discrete spectrum results in multiplying media have been corroborated. The numerical results obtained for the dominant SN eigenvalues agreed with the ones for the analytic problem reported in the literature up to a triplet scattering order. A compact methodology to perform the spectral analysis to multigroup SN problems with high anisotropy order in the scattering and fission reactions is also presented in this paper.

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Development and verification of the higher-order mode neutron flux calculation code HARMONY2.0

Zhang,

Ni,

Deng

et al. 2024

NUCL SCI TECH

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Calculation of λ modes of the multi-group neutron transport equation using the discrete ordinates and Finite Difference Method

Cited by 15 publications

References 14 publications

The adjoint transport problem applied to estimate neutral particle leakage in the discrete ordinates formulations

The adjoint transport problem applied to estimate neutral particle leakage in the discrete ordinates formulations

On the spectrum of discrete-ordinates neutron transport problems

Development and verification of the higher-order mode neutron flux calculation code HARMONY2.0

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