The spectral element method for static neutron transport in AN approximation. Part I

Barbarino, Andrea; Dulla, Sandra; Mund, E. H.; Ravetto, Piero

doi:10.1016/j.anucene.2012.10.013

Cited by 9 publications

(4 citation statements)

References 8 publications

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“…Furthermore, comparisons with Monte Carlo calculations have shown the excellent level of accuracy that can be attained by A N . The SEM is also being deeply investigated [BaEtAl13] and may prove to be a powerful tool to obtain accurate results and to be suitable for simulations in which a high fidelity is required.…”

Section: Comparison Of Numerical Resultsmentioning

confidence: 99%

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Integral Methods in Science and Engineering

2013

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Section: Comparison Of Numerical Resultsmentioning

confidence: 99%

“…The general multidimensional configuration can be treated by starting from the 1D situation and taking a tensorial product of the coefficient matrices. Finally, all equations are recast into the single matrix form [BaEtAl13] …”

Section: The Spectral Element Approachmentioning

confidence: 99%

Integral Methods in Science and Engineering

2013

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“…In fact most of the unstructured mesh neutron transport literature is devoted to the development of FE based discretisation schemes. However, more recently high-order accurate spectral element (SE) [29,30,31,32] and isogeometric analyis (IGA) methods have been developed for modelling neutron transport [33,34,35,36,37,38]. The IGA method is a spatial discretisation methodology first introduced in 2005 by T. J. R Hughes [39].…”

Section: Introductionmentioning

confidence: 99%

A geometry conforming isogeometric method for the self-adjoint angular flux (SAAF) form of the neutron transport equation with a discrete ordinate (SN) angular discretisation

Latimer

Kópházi

Eaton

et al. 2020

Annals of Nuclear Energy

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This paper presents the application of isogeometric analysis (IGA) to the spatial discretisation of the multi-group, self-adjoint angular flux (SAAF) form of the neutron transport equation with a discrete ordinate (S N) angular discretisation. The IGA spatial discretisation is based upon non-uniform rational B-spline (NURBS) basis functions for both the test and trial functions. In addition a source iteration compatible maximum principle is used to derive the IGA spatially discretised SAAF equation. It is demonstrated that this maximum principle is mathematically equivalent to the weak form of the SAAF equation. The rate of convergence of the IGA spatial discretisation of the SAAF equation is analysed using a method of manufactured solutions (MMS) verification test case. The results of several nuclear reactor physics verification benchmark test cases are analysed. This analysis demonstrates that for higher-order basis functions, and for the same number of degrees of freedom, the FE based spatial discretisation methods are numerically less accurate than IGA methods. The difference in numerical accuracy between the IGA and FE methods is shown to be because of the higher-order continuity of NURBS basis functions within a NURBS patch as well as the preservation of both the volume and surface area throughout the solution domain within the IGA spatial discretisation. Finally, the numerical results of applying the IGA SAAF method to the OECD/NEA, seven-group, two-dimensional C5G7 quarter core nuclear reactor physics verification benchmark test case are presented. The results, from this verification benchmark test case, are shown to be in good agreement with solutions of the first-order form as well as the second-order even-parity form of the neutron transport equation for the same order of discrete ordinate (S N) angular approximation.

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“…As a result, numerical and approximation methods are often applied. A large collection of numerical methods were developed, this include: the discrete ordinate method (DOM) [1], finite element method (FEM) [2], finite volume method (FVM) [3], monte carlo method (MCM) [4], spectral element method [5], discrete spherical harmonics method [6] an so on. More informations on this can be found in [7].…”

Section: Introductionmentioning

confidence: 99%

Solution of the one-speed neutron transport equation in anisotropic scattering medium with a Pomraning-Eddington approximation approach

et al. 2019

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In this work, a combined modified K-integral approach and Pomraning-Eddington approximation to solve the neutron transport equation for general anisotropic scattering law is presented. This combined approach leads to the establishment of general expressions of the even e(x, μ) and odd o(x, μ) functions of the angular variable μ. Both functions are slowly varying in x. Furthermore, these expressions can be reduced to those reported in literature. In addition, the parameters such as OPEN ACCESS RECEIVED

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The spectral element method for static neutron transport in AN approximation. Part I

Cited by 9 publications

References 8 publications

Integral Methods in Science and Engineering

Integral Methods in Science and Engineering

A geometry conforming isogeometric method for the self-adjoint angular flux (SAAF) form of the neutron transport equation with a discrete ordinate (SN) angular discretisation

Solution of the one-speed neutron transport equation in anisotropic scattering medium with a Pomraning-Eddington approximation approach

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