Spectral Analysis of Computational Stability Conditions of Some Schemes for Solving Spatial Kinetics of Nuclear Reactor

Algorithms are obtained to compute spatial kinetics of nuclear reactor in diffusion multi-group approximation with allowance made for delayed neutrons. The final system of equations is brought to the standard form of evolution system. This system is demonstrated to be stiff. Four computational schemes to realize these algorithms are considered: one scheme is purely explicit; two schemes are semi implicit; and the last one is fully implicit. For the each of considered schemes conditions of computational stability of these algorithms are written in a generalized form. Conclusions are derived about complexity to realize these schemes as computer codes. The found stability conditions are studied extensively in numerical experiment to compute spatial kinetics of homogeneous zone with neutron physical properties typical for VVER reactors. Numerical analysis of eigenvalue spectra allowed to formulate recommendations on choosing varying time steps to find solution with a given precision in a so called boundary layer and in asymptotic case.