Adaptive refinement for P N neutron transport equation based on conjoint variational formulation and discontinuous finite element method

Sadeghi, Khashayar; Abbasi, M.; Zolfaghari, A.

doi:10.1016/j.pnucene.2017.08.009

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…Examples applying adaptive refinement of the equation's spatial dimension include Adaptive Mesh Refinement (AMR) [11][12][13] for structured meshes and fully unstructured adaptive mesh approaches [14,15]. Other approaches have based adaptive resolution on resolving the angular dimension through hierarchical schemes such as wavelets [16,17] and spherical harmonics [18][19][20] and more recently through optimised reduced-order basis functions [21]. These techniques have been further developed to adapt the combined space and angle domains simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Optimised Adjoint Sensitivity Analysis Using Adjoint Guided Mesh Adaptivity Applied to Neutron Detector Response Calculations

et al. 2022

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This article presents a new approach for the efficient calculation of sensitivities in radiation dose estimates, subject to imprecisely known nuclear material cross-section data. The method is a combined application of adjoint-based models to perform, simultaneously, both the sensitivity calculation together with optimal adaptive mesh refinement. Adjoint-based sensitivity methods are known for their efficiency since they enable sensitivities of all parameters to be formed through only two solutions to the problem. However, the efficient solutions can also be obtained by their computation on optimal meshes, here guided by goal-based adjoint approaches. It is shown that both mesh adaptivity and sensitivity can be computed by the same adjoint solution, meaning both can be performed without additional costs. A simple demonstration is presented based on the Maynard fixed-source problem where uncertainties, with respect to material cross-sections, of doses received in local regions are examined. It is shown that the method is able to calculate sensitivities with reduced computational costs in terms of memory and potentially computational time through reduced mesh size when using adaptive resolution in comparison to uniform resolution. In particular, it is the local spatial contributions to the sensitivity that are resolved more effectively due to the adaptive meshes concentrating resolution in those areas contributing the most to its value.

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Section: Introductionmentioning

confidence: 99%

Optimised Adjoint Sensitivity Analysis Using Adjoint Guided Mesh Adaptivity Applied to Neutron Detector Response Calculations

et al. 2022

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“…Finally, in 2018, Sadeghi et al [23] applied an adaptive refinement for the PN NTE based on conjoint variational formulation, and DFEM and the new computer code, discontinuous finite element method for neutron transport (DISFENT), in two-dimensional geometry was developed. The main goal of this study is to present a comparative analysis of numerical neutron transport calculations using the variational formulation based on the continuous and discontinuous FEMs.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Analysis of Neutron Transport Calculations Based on Variational Formulation and Finite Element Approaches

et al. 2020

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The application of continuous and discontinuous approaches of the finite element method (FEM) to the neutron transport equation (NTE) has been investigated. A comparative algorithm for analyzing the capability of various types of numerical solutions to the NTE based on variational formulation and discontinuous finite element method (DFEM) has been developed. The developed module is coupled to the program discontinuous finite element method for neutron (DISFENT). Each variational principle (VP) is applied to an example with drastic changes in the distribution of neutron flux density, and the obtained results of the continuous and discontinuous finite element (DFE) have been compared. The comparison between the level of accuracy of each approach using new module of DISFENT program has been performed based on the fine mesh solutions of the multi-PN (MPN) approximation. The obtained results of conjoint principles (CPs) have been demonstrated to be very accurate in comparison to other VPs. The reduction in the number of required meshes for solving the problem is considered as the main advantage of this principle. Finally, the spatial additivity to the context of the spherical harmonics has been implemented to the CP, to avoid from computational error accumulation.

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Multiblock Adaptive Mesh Refinement for the S _N Transport Equation Based on Lattice Boltzmann Method

Wang

Xie

2019

Nuclear Science and Engineering

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Adaptive refinement for P N neutron transport equation based on conjoint variational formulation and discontinuous finite element method

Cited by 3 publications

References 15 publications

Optimised Adjoint Sensitivity Analysis Using Adjoint Guided Mesh Adaptivity Applied to Neutron Detector Response Calculations

Optimised Adjoint Sensitivity Analysis Using Adjoint Guided Mesh Adaptivity Applied to Neutron Detector Response Calculations

A Comparative Analysis of Neutron Transport Calculations Based on Variational Formulation and Finite Element Approaches

Multiblock Adaptive Mesh Refinement for the S _N Transport Equation Based on Lattice Boltzmann Method

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Adaptive refinement for P N neutron transport equation based on conjoint variational formulation and discontinuous finite element method

Cited by 3 publications

References 15 publications

Optimised Adjoint Sensitivity Analysis Using Adjoint Guided Mesh Adaptivity Applied to Neutron Detector Response Calculations

Optimised Adjoint Sensitivity Analysis Using Adjoint Guided Mesh Adaptivity Applied to Neutron Detector Response Calculations

A Comparative Analysis of Neutron Transport Calculations Based on Variational Formulation and Finite Element Approaches

Multiblock Adaptive Mesh Refinement for the S N Transport Equation Based on Lattice Boltzmann Method

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Multiblock Adaptive Mesh Refinement for the S _N Transport Equation Based on Lattice Boltzmann Method