2016
DOI: 10.13182/nse16-4
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Calculation of Higher-Order Fluxes in Symmetric Cores—I: Theory

Abstract: 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 c… Show more

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Cited by 5 publications
(3 citation statements)
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“…, to obtain a biorthonormal basis. For reactors with radial symmetry, it can be proved (see (Tommasi et al, 2016)) that degenerated eigenvalues (i.e. eigenvalues with multiplicity greater than 1) can appear and consequently the adjoint modes computed are not directly biorthogonal.…”
Section: Eigenvalue Computations 100mentioning
confidence: 99%
“…, to obtain a biorthonormal basis. For reactors with radial symmetry, it can be proved (see (Tommasi et al, 2016)) that degenerated eigenvalues (i.e. eigenvalues with multiplicity greater than 1) can appear and consequently the adjoint modes computed are not directly biorthogonal.…”
Section: Eigenvalue Computations 100mentioning
confidence: 99%
“…It means that the spectrum of these modes is very clustered. The third and fourth eigenvalue are equal since they are degenerate due to the reactor radial symmetry (for more details, see (Tommasi et al, 2016) 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 First, we study the performance of the block inverse-free preconditioner Arnoldi method (BIFPAM). Table 2, shows a comparison of the number of iterations (Iterations) and CPU time needed to solve the problem with the BIFPAM using different dimensions, m, of the Krylov subspace without preconditioner, with the ILU preconditioner and with the geometric multigrid preconditioner (GMG).…”
Section: Cuboid Reactormentioning
confidence: 99%
“…The innovative boundary conditions described in the companion paper 10 were implemented in an Sn solver and 2-D Cartesian diffusion solver. Advantage was taken from the currently implemented boundary conditions (reflective, periodic) so that only a few changes were needed (except for the coupled problem).…”
Section: Iid Conclusion Of the Verification Workmentioning
confidence: 99%