A computational technique for evaluating eigenfunctions of symmetrical nuclear systems

Bruna, G.B.; Sargeni, A.

doi:10.1016/0306-4549(94)90023-x

Cited by 6 publications

(2 citation statements)

References 9 publications

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“…In a more radical way, and to avoid possible convergence problems, all existing symmetries can be broken using small localized perturbations of the material distribution within the reactor and then the k-eigenfunctions of the asymmetric perturbed system may be used as an expansion basis to approximate the eigenfunctions of the symmetric system. 31 Real-life reactors, once burnup occurs or control rods are inserted at different heights, no longer exhibit global material arrangement symmetries, but start-of-life designed industrial reactor cores most often do. Moreover, critical experiments in zero-power reactors are often, at least in a first approximation, designed as presenting material symmetries.…”

Section: Id Materials Symmetries Eigenvalue Degeneracies and Problmentioning

confidence: 99%

Calculation of Higher-Order Fluxes in Symmetric Cores—I: Theory

Tommasi

Maillot

Rimpault

2016

Nuclear Science and Engineering

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In neutron chain systems with material symmetries, various k-eigenvalues of the neutron balance equation beyond the dominant one may be degenerate. Eigenfunctions can be partitioned into several classes according to their invariance properties with respect to the symmetry operations (mirror symmetries and rotations) keeping the material distribution in the system unchanged. Their calculation can be limited to a fraction of the system (sector) provided that innovative boundary conditions matching the symmetry classes are used, and whole-system eigenfunctions can then be unfolded from the solutions obtained over the sector. With power iteration as the method for searching k-eigenvalues, this use of the material symmetries to split the global problem into a variety of smaller-sized problems has several computational advantages: lower computation times and memory requirements, increased dominance ratios, lowered possible degeneracies in each subproblem, and possible parallel (separated) treatment of the subproblems. The implementation is discussed in a companion paper using diffusion and transport theories.

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Section: Id Materials Symmetries Eigenvalue Degeneracies and Problmentioning

confidence: 99%

Calculation of Higher-Order Fluxes in Symmetric Cores—I: Theory

Tommasi

Maillot

Rimpault

2016

Nuclear Science and Engineering

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“…This method has been extended to access highorder eigenfunctions and eigenvalues, taking advantage of the F-orthogonality properties of eigenfunctions associated with distinct eigenvalues. 1,2 This is called the filtering technique. However, some differences between the fundamental mode (always positive) and the harmonics may lead usual iterative solvers to fail.…”

Section: Ia Overview Of Some Matters Using Traditional Filtering Tementioning

confidence: 99%

Calculation of Higher-Order Fluxes in Symmetric Cores—II: Implementation

Maillot

Tommasi

Rimpault

2016

Nuclear Science and Engineering

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In neutron chain systems with material symmetries, various k-eigenvalues of the neutron balance equation beyond the dominant one may be degenerated. As shown in a companion paper, the power iteration method can be used to compute higher eigenfunctions in symmetric systems, provided that the global problem is partitioned into symmetry class-related lower-sized problems with appropriate boundary conditions. Those boundary conditions have been implemented in the diffusion solver of the ERANOS code system in rectangular geometry and within the framework of a discontinuous Galerkin spatial approximation of the multigroup discrete ordinates transport equation in the SNATCH solver. Numerical results in homogeneous geometry are provided for verification purposes, as well as the first eigenfunctions of the Takeda benchmarks. Finally, the transport effect on the first flux harmonics for an industrial-sized reactor ZPPR-18 is discussed.

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