Nuclear Techniques ›› 2018, Vol. 41 ›› Issue (3): 30501-030501.doi: 10.11889/j.0253-3219.2018.hjs.41.030501


Comparison and analysis of several typical algorithms in solving depletion equations

TAN Jie, ZHANG Peng   

  1. Hydraulic Machinery Transients Key Laboratory of Ministry of Education. Wuhan University;, Wuhan 430072, China
  • Received:2017-08-21 Revised:2017-09-28 Online:2018-03-10 Published:2018-03-14
  • Supported by:
    Supported by National Natural Science Foundation of China (No.11305036)

Abstract: [Background] It is very important to trace fuel concentration changing with high precision and efficiency in the current core simulation calculations, where an essential part is to solve depletion equations precisely. [Purpose] This study aims to solve point-core depletion equations in different sizes with various methods and find out the characteristics of these methods by a self-programming burnup module. [Methods] Four methods including Chebyshev rational approximation method (CRAM), Padé approximation method, Krylov Subspace method and transmutation trajectory analysis (TTA) were used to realize burnup calculations and comparative analysis with the results by CRAM with 16 orders in high precision for different-scale burnup systems. [Results] The results suggested that CRAM could provide very accurate solutions in a very short computing time, and the higher the coefficient order, the higher the precision and step stability. Padé approximation method could get accurate results affected marginally by step length with double precision in small and medium systems quickly, but high precision computation should be adopted for large systems while little affected by step length. Krylov Subspace method had accurate solutions in small and medium systems with double floats. However, it can't be applied to large cases. TTA was applicable to burnup equations at any scale with a weak accuracy and a slower speed because of linear chain simplification. [Conclusion] The four methods can be adapted to the depletion calculations of the cores in different cases, and the responding results can be treated as reference for the development and application of different burnup calculation systems.

Key words: Depletion, CRAM, Padé approximation method, Krylov Subspace method, TTA

CLC Number: 

  • TL329.2