### Abstract

A new discrete ordinates algorithm to determine the multiplication factor of a 1D nuclear reactor, based on Bengt Carlson's S _{n} method, is presented. The algorithm applies the Romberg and Wynn-epsilon accelerators to accelerate a 1D, one-group S _{n} solution to its asymptotic limit. We demonstrate the feasibility of the Converged Sn (CSn) solution on several one-group criticality benchmark compilations. The new formulation is especially convenient since it enables highly accurate critical fluxes and eigenvalues using the most fundamental transport algorithm.

Original language | English (US) |
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Title of host publication | American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009 |

Pages | 1713-1729 |

Number of pages | 17 |

Volume | 3 |

State | Published - 2009 |

Event | International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009 - Saratoga Springs, NY, United States Duration: May 3 2009 → May 7 2009 |

### Other

Other | International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009 |
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Country | United States |

City | Saratoga Springs, NY |

Period | 5/3/09 → 5/7/09 |

### Fingerprint

### Keywords

- Criticality
- Discrete ordinates
- Multiplication factor
- One-group

### ASJC Scopus subject areas

- Nuclear Energy and Engineering
- Computational Mathematics
- Nuclear and High Energy Physics

### Cite this

*American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009*(Vol. 3, pp. 1713-1729)

**The converged Sn algorithm for nuclear criticality.** / Ganapol, Barry D; Hadad, K.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009.*vol. 3, pp. 1713-1729, International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009, Saratoga Springs, NY, United States, 5/3/09.

}

TY - GEN

T1 - The converged Sn algorithm for nuclear criticality

AU - Ganapol, Barry D

AU - Hadad, K.

PY - 2009

Y1 - 2009

N2 - A new discrete ordinates algorithm to determine the multiplication factor of a 1D nuclear reactor, based on Bengt Carlson's S n method, is presented. The algorithm applies the Romberg and Wynn-epsilon accelerators to accelerate a 1D, one-group S n solution to its asymptotic limit. We demonstrate the feasibility of the Converged Sn (CSn) solution on several one-group criticality benchmark compilations. The new formulation is especially convenient since it enables highly accurate critical fluxes and eigenvalues using the most fundamental transport algorithm.

AB - A new discrete ordinates algorithm to determine the multiplication factor of a 1D nuclear reactor, based on Bengt Carlson's S n method, is presented. The algorithm applies the Romberg and Wynn-epsilon accelerators to accelerate a 1D, one-group S n solution to its asymptotic limit. We demonstrate the feasibility of the Converged Sn (CSn) solution on several one-group criticality benchmark compilations. The new formulation is especially convenient since it enables highly accurate critical fluxes and eigenvalues using the most fundamental transport algorithm.

KW - Criticality

KW - Discrete ordinates

KW - Multiplication factor

KW - One-group

UR - http://www.scopus.com/inward/record.url?scp=74549225044&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74549225044&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:74549225044

SN - 9781615673490

VL - 3

SP - 1713

EP - 1729

BT - American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009

ER -