A precision benchmark suite for nuclear reactor point kinetics equations via converged accelerated Taylor series (cats)

TL;DR

This paper introduces the CATS benchmark suite using a converged accelerated Taylor series method for highly precise solutions to nuclear reactor point kinetics equations, enabling extreme accuracy in transient simulations.

Contribution

The paper presents a novel high-precision benchmark suite and the CATS algorithm, employing adaptive mesh refinement and convergence acceleration for solving point kinetics equations with unprecedented accuracy.

Findings

Achieved 10-12 digit precision in solutions

Validated results against quadruple precision BEFD algorithm

Established new benchmark cases with complex reactivity insertions

Abstract

Extreme benchmarks of ten or more places for the point kinetics equations for time dependent nuclear reactor power transients are rare. Therefore, to establish an extreme benchmark, we will employ a Taylor series with continuous analytical continuation (CAC) to solve the ordinary differential equations of point kinetics including feedback. Non-linear Wynn-epsilon convergence acceleration confirms the highly precise solutions for neutron and precursor densities. Through adaptive partitioning of time intervals, the proposed Converged Accelerated Taylor Series, or CATS algorithm [1] in double precision, automatically performs successive mesh refinement to obtain high precision initial conditions for each sub-interval, with the intent to reduce propagation error. Confirmation of ten to twelve places comes from comparison to the BEFD (Backward Euler Finite Difference) algorithm [2] in quadruple precision also developed by the author. We report benchmark results for common cases found in the literature including step, ramp, zigzag and sinusoidal prescribed reactivity insertions and insertions with non-linear adiabatic Doppler feedback. We also establish a suite of new prescribed reactivity insertions and insertions with feedback, based on reactivities with Taylor series as suggested by the CATS algorithm.