The solution of the point kinetics equations via converged accelerated Taylor series (CATS)

B. Ganapol, P. Picca, A. Previti, D. Mostacci

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

This paper deals with finding accurate solutions of the point kinetics equations including non-linear feedback, in a fast, efficient and straightforward way. A truncated Taylor series is coupled to continuous analytical continuation to provide the recurrence relations to solve the ordinary differential equations of point kinetics. Non-linear (Wynn-epsilon) and linear (Romberg) convergence accelerations are employed to provide highly accurate results for the evaluation of Taylor series expansions and extrapolated values of neutron and precursor densities at desired edits. The proposed Converged Accelerated Taylor Series, or CATS, algorithm automatically performs successive mesh refinements until the desired accuracy is obtained, making use of the intermediate results for converged initial values at each interval. Numerical performance is evaluated using case studies available from the literature. Nearly perfect agreement is found with the literature results generally considered most accurate. Benchmark quality results are reported for several cases of interest including step, ramp, zigzag and sinusoidal prescribed insertions and insertions with adiabatic Doppler feedback. A larger than usual (9) number of digits is included to encourage honest benchmarking. The benchmark is then applied to the enhanced piecewise constant algorithm (EPCA) currently being developed by the second author.

Original languageEnglish (US)
Title of host publicationInternational Conference on the Physics of Reactors 2012, PHYSOR 2012
Subtitle of host publicationAdvances in Reactor Physics
Pages3391-3409
Number of pages19
StatePublished - Dec 6 2012
EventInternational Conference on the Physics of Reactors 2012: Advances in Reactor Physics, PHYSOR 2012 - Knoxville, TN, United States
Duration: Apr 15 2012Apr 20 2012

Publication series

NameInternational Conference on the Physics of Reactors 2012, PHYSOR 2012: Advances in Reactor Physics
Volume4

Other

OtherInternational Conference on the Physics of Reactors 2012: Advances in Reactor Physics, PHYSOR 2012
CountryUnited States
CityKnoxville, TN
Period4/15/124/20/12

Keywords

  • Convergence acceleration
  • Extraordinary accuracy
  • Point kinetics
  • Taylor series

ASJC Scopus subject areas

  • Nuclear Energy and Engineering

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    Ganapol, B., Picca, P., Previti, A., & Mostacci, D. (2012). The solution of the point kinetics equations via converged accelerated Taylor series (CATS). In International Conference on the Physics of Reactors 2012, PHYSOR 2012: Advances in Reactor Physics (pp. 3391-3409). (International Conference on the Physics of Reactors 2012, PHYSOR 2012: Advances in Reactor Physics; Vol. 4).