Variable coefficient depletion equations – Efficient calculation method. (1st June 2020) - Huang, Kai; Cao, Liangzhi; Wu, Hongchun; Fu, Xuedong; Ying, Yangjun; Zhu, Shengdong
Highlights: The coefficient averaging sub-step division is optimized by a dimensionless analysis. An efficient two-stage method that combine CRAM and Gauss-Legendre Method is proposed. A sub-step division scheme is constructed to overcome the method discontinuity issue. Abstract: Neutron flux field changes in terms of intensity and spectrum from time to time in nuclear reactors. Considering this effect more faithfully, high order neutronic-depletion coupling strategies were shown to be advantageous over traditional ones. While the variable coefficient depletion equations rather than the constant ones are meant to be solved. Through exploiting characteristics of depletion problems, a two-stage method that combines Chebyshev Rational Approximation Method (CRAM) and Gauss-Legendre Method is proposed, and its implementation details are tuned to overcome the method discontinuity problem. At the same time, the regular coefficient averaging sub-step division scheme is optimized by taking advantage of the fading behavior of sub-step errors. Test problems with varying properties are formulated and calculated. Numerical results showed that the sub-step division optimization could improve calculation efficiency for about one order of magnitude, meanwhile the two-stage method offers additionally 2–10 times of efficiency gain.