### Abstract

A novel methodology for the solution of non-linear point kinetic (PK) equations is proposed. The technique, based on a piecewise constant approximation (Kinard and Allen, 2004), is enhanced by explicitly accounting for the feedback and the reactivity variation within a time step through an iterative cycle. High accuracy is achieved by introducing a sub-mesh for the numerical evaluation of integrals involved and by correcting the source term to include the non-linear effect on a finer time scale. The resulting Enhanced Piecewise Constant Approximation (EPCA) is tested on a set of classical linear problems with several types of reactivity insertions (step, linear, sinusoidal, zig-zag) and shows extreme accuracy (to 9 digits) even when large time steps are considered (i.e., 100 times the neutron mean life). Non-linear reactor kinetics is then considered and compared to highly accurate results obtained via convergence acceleration. Its accuracy and the fast convergence make the EPCA algorithm particularly attractive for applications.

Original language | English (US) |
---|---|

Pages (from-to) | 43-53 |

Number of pages | 11 |

Journal | Annals of Nuclear Energy |

Volume | 58 |

DOIs | |

State | Published - 2013 |

### Fingerprint

### Keywords

- Benchmarking
- Non-linear neutron kinetics
- Reactor equations

### ASJC Scopus subject areas

- Nuclear Energy and Engineering

### Cite this

**A highly accurate technique for the solution of the non-linear point kinetics equations.** / Picca, Paolo; Furfaro, Roberto; Ganapol, Barry D.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - A highly accurate technique for the solution of the non-linear point kinetics equations

AU - Picca, Paolo

AU - Furfaro, Roberto

AU - Ganapol, Barry D

PY - 2013

Y1 - 2013

N2 - A novel methodology for the solution of non-linear point kinetic (PK) equations is proposed. The technique, based on a piecewise constant approximation (Kinard and Allen, 2004), is enhanced by explicitly accounting for the feedback and the reactivity variation within a time step through an iterative cycle. High accuracy is achieved by introducing a sub-mesh for the numerical evaluation of integrals involved and by correcting the source term to include the non-linear effect on a finer time scale. The resulting Enhanced Piecewise Constant Approximation (EPCA) is tested on a set of classical linear problems with several types of reactivity insertions (step, linear, sinusoidal, zig-zag) and shows extreme accuracy (to 9 digits) even when large time steps are considered (i.e., 100 times the neutron mean life). Non-linear reactor kinetics is then considered and compared to highly accurate results obtained via convergence acceleration. Its accuracy and the fast convergence make the EPCA algorithm particularly attractive for applications.

AB - A novel methodology for the solution of non-linear point kinetic (PK) equations is proposed. The technique, based on a piecewise constant approximation (Kinard and Allen, 2004), is enhanced by explicitly accounting for the feedback and the reactivity variation within a time step through an iterative cycle. High accuracy is achieved by introducing a sub-mesh for the numerical evaluation of integrals involved and by correcting the source term to include the non-linear effect on a finer time scale. The resulting Enhanced Piecewise Constant Approximation (EPCA) is tested on a set of classical linear problems with several types of reactivity insertions (step, linear, sinusoidal, zig-zag) and shows extreme accuracy (to 9 digits) even when large time steps are considered (i.e., 100 times the neutron mean life). Non-linear reactor kinetics is then considered and compared to highly accurate results obtained via convergence acceleration. Its accuracy and the fast convergence make the EPCA algorithm particularly attractive for applications.

KW - Benchmarking

KW - Non-linear neutron kinetics

KW - Reactor equations

UR - http://www.scopus.com/inward/record.url?scp=84875826585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875826585&partnerID=8YFLogxK

U2 - 10.1016/j.anucene.2013.03.004

DO - 10.1016/j.anucene.2013.03.004

M3 - Article

AN - SCOPUS:84875826585

VL - 58

SP - 43

EP - 53

JO - Annals of Nuclear Energy

JF - Annals of Nuclear Energy

SN - 0306-4549

ER -