A unified approach for numerical calculation of space-dependent kinetic equation

作者：Ban Yuichiro^*; Endo Tomohiro; Yamamoto Akio

来源：Journal of Nuclear Science and Technology, 2012, 49(5): 496-515.

DOI：10.1080/00223131.2012.677126

• space-dependent kinetics
• transient
• multigrid amplitude function method
• Theta method
• frequency transform method
• improved quasi-static method
• auto time-step control
• analytical polynomial nodal method

A unified numerical method based on the factorization approach is developed to solve the space-dependent neutron kinetic equation. Various numerical methods for solving the space-dependent kinetic equation have been developed so far. These methods can be classified into two categories, i.e., the direct and the factorization methods. The factorization method is known as an effective numerical method. In the present study, a new factorization method named the multigrid amplitude MAF) method is developed. Unlike the improved quasi-static (IQS) method, an independent amplitude function is assigned for each spatial region and energy group in the MAF method. The MAF method is a generalization of conventional methods, e. g., the frequency transform, IQS, and Theta methods. To evaluate the amplitude function in the MAF method, the time-dependent coarse-mesh finite difference (TCMFD) method is developed. The MAF method is implemented into a space-dependent kinetic code on the basis of the analytical polynomial nodal method. In order to verify the effectiveness of the MAF method, the TWIGL, Langenbuch, Maurer, and Werner (LMW), and Laboratorium fur Reaktorregelung and Anlagensicherung (LRA) benchmark problems are analyzed. The calculation results show the effectiveness of the present method.

• 出版日期2012-5