Discontinuous isogeometric analysis methods for the first-order form of the neutron transport equation with discrete ordinate (S) angular discretisation

Owens, A.R.; Welch, J.A.; Kópházi, J.; Eaton, M.D.

doi:10.1016/j.jcp.2016.03.060

Cited by 26 publications

(17 citation statements)

References 13 publications

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“…This ensures that exactly the same solvers and convergence criteria are used for both IGA and FE solutions. Inferno is a first-order neutron transport code with local refinement capabilities [36,37,38]. It is a discontinuous IGA discrete ordinate (S N ) code and is used in this paper to generate reference solutions to a number of nuclear reactor physics verification benchmark test cases.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…B-splines and NURBS of degree p exhibit the same theoretical orders of convergence as FE basis functions of the same order. However, as mentioned earlier, it has been seen that splines of maximal smoothness (C p−1 ) require fewer dof in order to reproduce the same error for neutron diffusion theory [35] and that FE methods require fissile mass preservation techniques in order to match IGA in the case of first-order neutron transport [36]. The increased smoothness and support of spline basis functions leads to complications in other areas: direct solver performance [50], multi-grid methods [51], and domain decomposition algorithms [52] have all required extra study.…”

Section: Nurbs Patchesmentioning

confidence: 92%

“…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%

“…In a neutron transport context, IGA has been applied to the mono-energetic [33] and multigroup [35] neutron diffusion equation, the second-order even-parity equation [34], as well as the first-order neutron transport equation [36,37,38]. Throughout all of this work it has been seen that in terms of accuracy per degree of freedom (dof) an IGA spatial discretisation is as least as good as a FE one.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Numerical Resultsmentioning

confidence: 99%

Section: Nurbs Patchesmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Self Cite

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“…The LDG method [17][18][19][20] means it easy to achieve high accuracy in space and time and provides useful mathematical properties with respect to conservation, stability, and super convergence. In particular, the LDG method can use the mesh with the hanging node [21,22] for calculation, and it is convenient to apply the method for simulating flows in complex geometries. Therefore, the adaptive Cartesian grid is used for future easier engineering applications [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

New Immersed Boundary Method on the Adaptive Cartesian Grid Applied to the Local Discontinuous Galerkin Method

Zhang

Zhu

Yan

et al. 2018

Chin. J. Mech. Eng.

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Currently, many studies on the local discontinuous Galerkin method focus on the Cartesian grid with low computational efficiency and poor adaptability to complex shapes. A new immersed boundary method is presented, and this method employs the adaptive Cartesian grid to improve the adaptability to complex shapes and the immersed boundary to increase computational efficiency. The new immersed boundary method employs different boundary cells (the physical cell and ghost cell) to impose the boundary condition and the reconstruction algorithm of the ghost cell is the key for this method. The classical model elliptic equation is used to test the method. This method is tested and analyzed from the viewpoints of boundary cell type, error distribution and accuracy. The numerical result shows that the presented method has low error and a good rate of the convergence and works well in complex geometries. The method has good prospect for practical application research of the numerical calculation research. which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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An algorithm for accurate modeling and simulating reactor cores with involute‐shaped fuel plates by Monte Carlo

et al. 2021

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Summary A real three‐dimensional representation of reactor core with involute fuel plates via Monte Carlo method is still lacking at the present, and usually equivalent homogeneous models of water coolants and simplified fuel plate shapes have been used. This work proposed an algorithm to simulate the reactor core composed of involute fuel plates with an explicit accurate description of its involute surfaces. The description of involute surfaces is through its governing equations. The mathematical function methods to depict the involute curves and the schemes to compute the distance between any neutron particle and an involute surface along a ray are presented and demonstrated step‐by‐step. The algorithm is realized in the Monte Carlo code and validated by the published data of a high flux isotope reactor. This study definitively provides a method to model the involute fuel plates in the Monte Carlo simulation.

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Discontinuous isogeometric analysis methods for the first-order form of the neutron transport equation with discrete ordinate (S) angular discretisation

Cited by 26 publications

References 13 publications

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

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

New Immersed Boundary Method on the Adaptive Cartesian Grid Applied to the Local Discontinuous Galerkin Method

An algorithm for accurate modeling and simulating reactor cores with involute‐shaped fuel plates by Monte Carlo

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