A numerical solution to the point kinetic equations using Taylor–Lie series combined with a scaling and squaring technique

Abstract

A system of differential equations is derived to model the dynamics of neutron density and the delayed neutron precursors within a point kinetics equation modeling framework for a nuclear reactor. The point kinetic equations are mathematically characterized as stiff, occasionally nonlinear, ordinary differential equations, posing significant challenges when numerical solutions are sought, and traditionally resulting in the need for smaller time step intervals within various computational schemes. In light of the above realization, the present paper proposes a new discretization/simulation method that is: (i) conceptually inspired by system-theoretic notions used in the analysis of sampled-date system dynamics (discrete-time system dynamics) under potentially irreducible large sampling periods/time steps, and (ii) technically based on Taylor–Lie series and the zero-order hold (ZOH). Within the proposed time discretization framework, the sampled-data representation of the original point kinetic system of equations is derived for an arbitrary size of the time-step used. Furthermore, within the context of the proposed approach, the integration of a scaling-and-squaring technique is pursued for the attainment of further performance enhancement of the proposed simulation technique. The performance of the proposed approach is evaluated in several case studies involving step and ramp-like reactivity profiles as well as multiple input examples that simultaneously account for variations in reactivity and neutron source function profiles. In particular, it is demonstrated, that by applying the proposed method, the inherent stiffness problem associated with the simulation challenges of the point kinetic equations can be adequately addressed within a wide range of reactor operating conditions, including large sampling periods dictated by physical and/or technical limitations associated with the current state of sensor and digital reactor control system technology.