New semi-analytical algorithm for solving PKEs based on Euler-Maclaurin approximation. (15th June 2020) - Xiao, Yunlong; Gu, Zhixing; Zhang, Qingxian; Ge, Liangquan; Zeng, Guoqiang; Li, Fei
Abstract: Point kinetics equations (PKEs) is an significant model used to describe dynamic behaviors of neutron in nuclear reactors. How to cope with its stiffness problems is very important to solve PKEs accurately and efficiently. In this paper, a new semi-analytical algorithm based on Euler-Maclaurin Approximation (SAEMA) is developed to solve PKEs. SAEMA algorithm is applied and tested in different reactors with three typical reactivity insertion cases, including step, ramp and sinusoidal insertions. Firstly, the investigations on the computational stability are performed under different time step sizes. Secondly, the performances on computational accuracy are evaluated by comparing the results by SAEMA algorithm with the ones by analytical method and excellent CATS algorithm. Finally, by comparing the CPU time consumed by SAEMA algorithm with the physical time, the studies on the computational efficiency are also carried out. Just as results shows, SAEMA algorithm is reasonably an attractive way to solve the PKEs.