Stability analysis of higher-order neutronics-depletion coupling schemes and Bateman operators

Abstract Previous work has introduced the stability analysis of coupled neutronics-depletion solvers for the standard explicit Euler and predictor-corrector methods. The present work is an extension of this analysis to higher-order schemes that are commonly used, including the LE, LE/LI, LE/QI, and their implicit versions where such a method exists. Substepping, extrapolation, and linear and quadratic interpolation are investigated, and their effects on numerical stability are discussed. A realistic, numerically-stiff depletion system is considered by applying automatic differentiation to the Chebyshev rational approximation method; accounting for initial nonlinear behaviour, the predictions from the stability analysis match the outcomes of simulation.