Geodesic
Numerical modeling of neutron diffusion non-stationary problems
Matematičeskoe modelirovanie, Tome 29 (2017) no. 7, pp. 44-62

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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.
Mots-clés : neutron flux equation, multigroup diffusion approximation, implicit scheme, explicit-implicit scheme.
Keywords: spectral problem, regular mode 
@article{MM_2017_29_7_a3,
     author = {A. V. Avvakumov and P. N. Vabishchevich and A. O. Vasilev and V. F. Strizhev},
     title = {Numerical modeling of neutron diffusion non-stationary problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {44--62},
     publisher = {mathdoc},
     volume = {29},
     number = {7},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_7_a3/}
}
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A. V. Avvakumov; P. N. Vabishchevich; A. O. Vasilev; V. F. Strizhev. Numerical modeling of neutron diffusion non-stationary problems. Matematičeskoe modelirovanie, Tome 29 (2017) no. 7, pp. 44-62. http://geodesic.mathdoc.fr/item/MM_2017_29_7_a3/