### 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 |

State | Published - Dec 1 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 |

### Publication series

Name | American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009 |
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Volume | 3 |

### 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 |

### Keywords

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

### ASJC Scopus subject areas

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

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## Cite this

Ganapol, B. D., & Hadad, K. (2009). The converged Sn algorithm for nuclear criticality. In

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