Numerical modeling of neutron diffusion non-stationary problems

A. V. Avvakumov ; P. N. Vabishchevich ; A. O. Vasilev ; V. F. Strizhev

Matematičeskoe modelirovanie, Tome 29 (2017) no. 7, pp. 44-62.

Résumé

As a rule, mathematical modeling of transient processes in nuclear reactors is considered in the multigroup diffusion approximation. In this approach, the basic model involves a multidimensional system of coupled equations of the parabolic type. Similarly to common thermal phenomema, it is possible here to separate a regular mode of nuclear reactor operation that is associated with a selfsimilar behaviour of a neutron flux at large times. In this case, the main feature of dynamic processes is a fundamental eigenvalue of the corresponding spectral problem. To solve approximately time-dependent problems, we employ the fully implicit scheme of the first-order approximation and symmetric second-order scheme. Separately, we investigate the explicit-implicit scheme that greatly simplifies the transition to a new time level. An approximation in space is constructed using standard finite elements with polynomials of various degree. Numerical simulation of the regular mode was performed for the reactor VVER-1000 test problem in the two-group approximation.

Détail

Mots-clés : neutron flux equation, multigroup diffusion approximation, implicit scheme, explicit-implicit scheme.
Keywords: spectral problem, regular mode

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