The solution of the point kinetics equations via converged accelerated Taylor series (CATS)
- Dept. of Aerospace and Mechanical Engineering, Univ. of Arizona (United States)
- Laboratorio di Montecuccolino, Alma Mater Studiorum - Universita di Bologna (Italy)
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. (authors)
- Research Organization:
- American Nuclear Society, Inc., 555 N. Kensington Avenue, La Grange Park, Illinois 60526 (United States)
- OSTI ID:
- 22105820
- Resource Relation:
- Conference: PHYSOR 2012: Conference on Advances in Reactor Physics - Linking Research, Industry, and Education, Knoxville, TN (United States), 15-20 Apr 2012; Other Information: Country of input: France; 28 refs.
- Country of Publication:
- United States
- Language:
- English
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