A spectral nodal method for the adjoint <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si195.svg"><mml:mrow><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> neutral particle transport equations in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si196.svg"><mml:mrow><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>Y</mml:mi></mml:mrow></mml:math>-geometry: Application to direct and inverse multigroup sourc

Curbelo, Jesús P.; Barros, Ricardo C.

doi:10.1016/j.anucene.2020.107822

Cited by 4 publications

(6 citation statements)

References 35 publications

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Section: The Adjoint 𝑺 𝑵 In 𝑿 𝒀Geometrymentioning

confidence: 99%

“…Here 𝒥 𝑏,𝑔 † is the leakage through boundary 𝑏 in the energy group 𝑔; the quantities 𝜓 ̃𝑛 To numerically solve the adjoint transport problem in Equation ( 6), we use the adjoint spectral Green's function-constant nodal (SGF † -CN) method [6] with the adjoint partial one-node block inversion iterative scheme. The SGF † -CN method has been successfully applied to fixed-source multigroup adjoint 𝑆 𝑁 problems in 𝑋, 𝑌-geometry [6]. Only the terms referred to as the transverse leakage in the adjoint transverse-integrated 𝑆 𝑁 nodal equations are approximated by constants, as the scattering source terms are treated analytically in the spectral nodal class of numerical methods.…”

Section: The Adjoint 𝑺 𝑵 In 𝑿 𝒀Geometrymentioning

confidence: 99%

“…Only the terms referred to as the transverse leakage in the adjoint transverse-integrated 𝑆 𝑁 nodal equations are approximated by constants, as the scattering source terms are treated analytically in the spectral nodal class of numerical methods. The SGF † -CN method is less sensitive to the spatial discretization grid for coarse-mesh calculations and offers running time economy when compared with the conventional fine-mesh methods [6].…”

Section: The Adjoint 𝑺 𝑵 In 𝑿 𝒀Geometrymentioning

confidence: 99%

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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: The Adjoint 𝑺 𝑵 In 𝑿 𝒀Geometrymentioning

confidence: 99%

Section: The Adjoint 𝑺 𝑵 In 𝑿 𝒀Geometrymentioning

confidence: 99%

Section: The Adjoint 𝑺 𝑵 In 𝑿 𝒀Geometrymentioning

confidence: 99%

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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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“…Based on the literature [17,20,21], we write the homogeneous solution of Eq. (3.2a) within a node Γ k, as…”

Section: Homogeneous Solutions To the Multigroup Adjoint Transverse-i...mentioning

confidence: 99%

“…In this work we use the adjoint partial one-node block inversion (partial NBI † ) iterative scheme that uses the boundary conditions and the most recent estimates available for the adjoint node-edge average angular fluxes in the outgoing directions to evaluate the incoming fluxes that constitute the exiting fluxes for the adjacent nodes in the directions of the transport sweeps. The partial NBI † iterative scheme can be found in more details in the literature [21].…”

Section: The Rm † -Cn Discretized Equationsmentioning

confidence: 99%

On the calculation of neutron sources generating steady prescribed power distributions in subcritical systems using multigroup X,Y-geometry discrete ordinates models

Léonardo¹,

Moraes²,

Filho³

et al. 2021

Preprint

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In this paper a methodology is described to estimate multigroup neutron source distributions which must be added into a subcritical system to drive it to a steady state prescribed power distribution. This work has been motivated by the principle of operation of the ADS (Accelerator Driven System) reactors, which have subcritical cores stabilized by the action of external sources. We use the energy multigroup two-dimensional neutron transport equation in the discrete ordinates formulation (S N ) and the equation which is adjoint to it, whose solution is interpreted here as a distribution measuring the importance of the angular flux of neutrons to a linear functional. These equations are correlated through a reciprocity relation, leading to a relationship between the interior sources of neutrons and the power produced by unit length of height of the domain. A coarse-mesh numerical method of the spectral nodal class, referred to as adjoint response matrix constant-nodal method, is applied to numerically solve the adjoint S N equations. Numerical experiments are performed to analyze the accuracy of the present methodology so as to illustrate its potential practical applications.

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On the calculation of neutron sources generating steady prescribed power distributions in subcritical systems using multigroup X,Y-geometry discrete ordinates models

Moraes

Filho

Barros

2022

Annals of Nuclear Energy

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A spectral nodal method for the adjoint SN neutral particle transport equations in X,Y-geometry: Application to direct and inverse multigroup sourc

Cited by 4 publications

References 35 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 calculation of neutron sources generating steady prescribed power distributions in subcritical systems using multigroup X,Y-geometry discrete ordinates models

On the calculation of neutron sources generating steady prescribed power distributions in subcritical systems using multigroup X,Y-geometry discrete ordinates models

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