Comparison of multipoint kinetic with methods of the direct solution of diffusion equation and conventional point kinetic for investigation of nuclear reactors transient

One of the most important aspects in design and operation of a nuclear reactor is investigation of the reactor during transient and non-steady conditions. For this purpose, different methods are presented for transient analysis. The direct solution of space-time dependent neutron diffusion equation with delayed neutron precursor equation is one of the most accurate and computationally expensive method. Use of this method in power control system design results in complex controller that its implementation encounters difficulties. Therefore, the point kinetic equation is used in design of nuclear reactor power control system by losing of the neutron flux shape variations. Recently, the multipoint kinetic equations are presented to decrease this limitation. This paper investigates the solution of multipoint kinetic in nuclear reactors and compares its results to conventional point kinetic equation and time-dependent solution of neutron diffusion equation for different benchmarks. The multipoint kinetic equations are derived via two group diffusion equations and are solved with forth order Runge-Kutta method. The results indicate that the deviation of the power level by use of multipoint kinetic method is lower than the conventional single point method in contrast to time-dependent solution of neutron diffusion equation. The deviation of power level is getting bigger in large reactivity insertion/withdraw that small reactivity perturbation. Therefore, multipoint kinetic method is more recommended for small reactivity change.