Variable coefficient depletion equations – Reference solution based on Rational Approximation Methods

Abstract

High order neutronic-depletion coupling strategies achieve better simulation performance against traditional strategies, at the cost of demanding variable coefficient depletion equations rather than constant ones to be solved. Through results comparisons of Rational Approximation solvers with various settings, different types of errors are explicitly separated and analyzed. In particular, sub-step errors of most nuclides are found to suffer from slow convergent problem; method intrinsic errors of the 14-order Chebyshev Rational Approximation Method are found to be large enough to interrupt convergence processes of sub-step errors prematurely. In addition, the fading behavior of the sub-step errors is captured and explained, and it leads to the optimal sub-step division appears to have moderate decreasing sub-step sizes; also, numerical truncation errors are shown to be dominated by method intrinsic errors. Accordingly, the extended precision 64-order Quadrature Rational Approximation Method and the Richardson Extrapolation technique are combined to obtain reference solutions.