Numerical modeling of neutron diffusion non-stationary problems

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.