Confirmation of accuracy of generalized power series method for the solution of point kinetics equations with feedback

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• 作者：Yasser Mohamed Hamada ; ^{hoooorgrk@yahoo.com}
• 关键词：Point kinetics equations ; Feedback reactivity ; Generalized power series method ; Step size control ; Convergence ; Numerical solutions
• 刊名：Annals of Nuclear Energy
• 出版年：2013
• 出版时间：May, 2013
• 年：2013
• 卷：55
• 期：Complete
• 页码：184-193
• 全文大小：421 K

文摘

In this paper, generalized power series method (GPWS) is developed to obtain approximate solutions to point kinetics equations with feedback. The stiffness of the kinetics equations restricts the time interval to a small increment, which in turn restricts the traditional power series method (PWS) within a very small constant step size especially when the generation times are very small. The GPWS method has introduced time intervals that are much longer than time intervals used in the conventional numerical integrations like Generalized Runge-Kutta or power series methods, and it is thus useful in reducing computing time. Convergence of both the power series and the partial sums are discussed and the time step has been restricted within a circle of convergence by using the convergence conditions. Local truncation errors and some other constraints are used to produce the largest step size allowable at each step while keeping the error within a specific tolerance. The accuracy of the method is examined using five different cases of temperature reactivity feedback for step and ramp impressive reactivities with one and six groups of delayed neutrons. Supercritical (prompt and delayed) processes of a nuclear reactor with temperature feedback are discussed while inserting large and small reactivities. Results obtained by GPWS method attest the effectiveness the theoretical analysis, they demonstrate that the convergence of the iteration scheme can be controllable. The proposed method is accurate when compared to the analytical and numerical methods.