A refined way of solving reactor point kinetics equations for imposed reactivity insertions

• Main Author: Ganapol Barry D.
• Format: Article
• Language: English
• Published: VINCA Institute of Nuclear Sciences 2009-01-01
• Series: Nuclear Technology and Radiation Protection
• Subjects: nuclear reactor kinetics; Romberg extrapolation; reactivity insertion; thermal reactor; fast reactor
• Online Access: http://www.doiserbia.nb.rs/img/doi/1451-3994/2009/1451-39940903157G.pdf

We apply the concept of convergence acceleration, also known as extrapolation, to find the solution of the reactor kinetics equations (RKEs). The method features simplicity in that an approximate finite difference formulation is constructed and converged to high accuracy from knowledge of the error term. Through the Romberg extrapolation, we demonstrate its high accuracy for a variety of imposed reactivity insertions found in the literature. The unique feature of the proposed algorithm, called RKE/R(omberg), is that no special attention is given to the stiffness of the RKEs. Finally, because of its simplicity and accuracy, the RKE/R algorithm is arguably the most efficient numerical solution of the RKEs developed to date.