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**Harvard**

Zinzani, F., Demazière, C. och Sunde, C. (2008) *Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities*.

** BibTeX **

@article{

Zinzani2008,

author={Zinzani, Filippo and Demazière, Christophe and Sunde, Carl},

title={Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities},

journal={Annals of Nuclear Energy},

issn={0306-4549},

volume={35},

issue={11},

pages={2109-2125},

abstract={In this paper, numerical methods aiming at determining the eigenfunctions, their adjoint and the corresponding eigenvalues of the two-group neutron diffusion equations representing any heterogeneous system are investigated. First, the classical power iteration method is modified so that the calculation of modes higher than the fundamental mode is possible. Thereafter, the explicitly-restarted Arnoldi method, belonging to the class of Krylov subspace methods, is touched upon. Although the modified power iteration method is a computationally-expensive algorithm, its main advantage is its robustness, i.e. the method always converges to the desired eigenfunctions without any need from the user to set up any parameter in the algorithm. On the other hand, the Arnoldi method, which requires some parameters to be defined by the user, is a very efficient method for calculating eigenfunctions of large sparse system of equations with a minimum computational effort. These methods are thereafter used for off-line analysis of the stability of boiling water reactors in a two-dimensional representation of the core. Since several oscillation modes are usually excited (global and regional oscillations) when unstable conditions are encountered, the characterization of the stability of the reactor using for instance the Decay Ratio as a stability indicator might be difficult if the contribution from each of the modes are not separated from each other. Such a modal decomposition is applied to a stability test performed at the Swedish Ringhals-1 unit in September 2002, after the use of the Arnoldi method for pre-calculating the different eigenmodes of the neutron flux throughout the reactor. The modal decomposition clearly demonstrates the excitation of both the global and regional oscillations. Furthermore, such oscillations are found to be intermittent with a time-varying phase shift between the first and second azimuthal modes.},

year={2008},

keywords={Code development, diffusion equation, eigenfunction, BWR instabilities},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 87865

A1 Zinzani, Filippo

A1 Demazière, Christophe

A1 Sunde, Carl

T1 Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities

YR 2008

JF Annals of Nuclear Energy

SN 0306-4549

VO 35

IS 11

SP 2109

OP 2125

AB In this paper, numerical methods aiming at determining the eigenfunctions, their adjoint and the corresponding eigenvalues of the two-group neutron diffusion equations representing any heterogeneous system are investigated. First, the classical power iteration method is modified so that the calculation of modes higher than the fundamental mode is possible. Thereafter, the explicitly-restarted Arnoldi method, belonging to the class of Krylov subspace methods, is touched upon. Although the modified power iteration method is a computationally-expensive algorithm, its main advantage is its robustness, i.e. the method always converges to the desired eigenfunctions without any need from the user to set up any parameter in the algorithm. On the other hand, the Arnoldi method, which requires some parameters to be defined by the user, is a very efficient method for calculating eigenfunctions of large sparse system of equations with a minimum computational effort. These methods are thereafter used for off-line analysis of the stability of boiling water reactors in a two-dimensional representation of the core. Since several oscillation modes are usually excited (global and regional oscillations) when unstable conditions are encountered, the characterization of the stability of the reactor using for instance the Decay Ratio as a stability indicator might be difficult if the contribution from each of the modes are not separated from each other. Such a modal decomposition is applied to a stability test performed at the Swedish Ringhals-1 unit in September 2002, after the use of the Arnoldi method for pre-calculating the different eigenmodes of the neutron flux throughout the reactor. The modal decomposition clearly demonstrates the excitation of both the global and regional oscillations. Furthermore, such oscillations are found to be intermittent with a time-varying phase shift between the first and second azimuthal modes.

LA eng

DO 10.1016/j.anucene.2008.05.004

LK http://dx.doi.org/10.1016/j.anucene.2008.05.004

OL 30