### Abstract

The overall goal of this chapter is to highlight the mathematical framework useful to carry out an uncertainty quantification study. The chapter starts with some basic definition of probability, explains non-intrusive Polynomial Chaos methods and, at the end, shows some more advanced techniques used today. The chapter shows an overview of all the most common techniques that have been used in UQ for CFD and there is the presentation of new ideas that will become more common in the coming years. There is a clear trend from bespoke solution towards more automatic UQ methods.

Original language | English |
---|---|

Title of host publication | Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines |

Publisher | Springer International Publishing |

Pages | 67-155 |

Number of pages | 89 |

Edition | 2 |

ISBN (Electronic) | 9783319929439 |

ISBN (Print) | 9783319929422 |

DOIs | |

Publication status | Published - 22 Jun 2018 |

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines*(2 ed., pp. 67-155). Springer International Publishing. https://doi.org/10.1007/978-3-319-92943-9_3

**Mathematical formulation.** / Carnevale, M.; Ahlfeld, R.

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

*Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines.*2 edn, Springer International Publishing, pp. 67-155. https://doi.org/10.1007/978-3-319-92943-9_3

}

TY - CHAP

T1 - Mathematical formulation

AU - Carnevale, M.

AU - Ahlfeld, R.

PY - 2018/6/22

Y1 - 2018/6/22

N2 - The overall goal of this chapter is to highlight the mathematical framework useful to carry out an uncertainty quantification study. The chapter starts with some basic definition of probability, explains non-intrusive Polynomial Chaos methods and, at the end, shows some more advanced techniques used today. The chapter shows an overview of all the most common techniques that have been used in UQ for CFD and there is the presentation of new ideas that will become more common in the coming years. There is a clear trend from bespoke solution towards more automatic UQ methods.

AB - The overall goal of this chapter is to highlight the mathematical framework useful to carry out an uncertainty quantification study. The chapter starts with some basic definition of probability, explains non-intrusive Polynomial Chaos methods and, at the end, shows some more advanced techniques used today. The chapter shows an overview of all the most common techniques that have been used in UQ for CFD and there is the presentation of new ideas that will become more common in the coming years. There is a clear trend from bespoke solution towards more automatic UQ methods.

UR - http://www.scopus.com/inward/record.url?scp=85053996245&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-92943-9_3

DO - 10.1007/978-3-319-92943-9_3

M3 - Chapter

SN - 9783319929422

SP - 67

EP - 155

BT - Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines

PB - Springer International Publishing

ER -