Uncertainty propagation in CFD using polynomial chaos decomposition

O. M. Knio; O. P. Le Maître

doi:10.1016/j.fluiddyn.2005.12.003

Uncertainty propagation in CFD using polynomial chaos decomposition

O. M. Knio^*, O. P. Le Maître

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

239 Scopus citations

Abstract

Uncertainty quantification in CFD computations is receiving increased interest, due in large part to the increasing complexity of physical models, and the inherent introduction of random model data. This paper focuses on recent application of PC methods for uncertainty representation and propagation in CFD computations. The fundamental concept on which polynomial chaos (PC) representations are based is to regard uncertainty as generating a new set of dimensions, and the solution as being dependent on these dimensions. A spectral decomposition in terms of orthogonal basis functions is used, the evolution of the basis coefficients providing quantitative estimates of the effect of random model data. A general overview of PC applications in CFD is provided, focusing exclusively on applications involving the unreduced Navier-Stokes equations. Included in the present review are an exposition of the mechanics of PC decompositions, an illustration of various means of implementing these representations, and a perspective on the applicability of the corresponding techniques to propagate and quantify uncertainty in Navier-Stokes computations.

Original language	English (US)
Pages (from-to)	616-640
Number of pages	25
Journal	Fluid Dynamics Research
Volume	38
Issue number	9
DOIs	https://doi.org/10.1016/j.fluiddyn.2005.12.003
State	Published - Sep 2006
Externally published	Yes

Bibliographical note

Funding Information:
The authors acknowledge helpful interactions with collaborators, particularly R. Ghanem, H. Najm, B. Debusschere, and M. Reagan. This work was supported by the Laboratory Directed Research and Development Program at Sandia National Laboratories, by the Defense Advanced Research Projects Agency (DARPA) and Air Force Research Laboratory, Air Force Material Command, USAF, under agreement number F30602-00-2-0612. The US government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Computations were performed at the National Center for Supercomputer Applications. O. K. also acknowledges support from the Alexander von Humboldt Foundation.

Keywords

CFD
Navier-Stokes
Numerical method
Polynomial chaos
Uncertainty quantification

ASJC Scopus subject areas

Mechanical Engineering
General Physics and Astronomy
Fluid Flow and Transfer Processes

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10.1016/j.fluiddyn.2005.12.003

Cite this

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title = "Uncertainty propagation in CFD using polynomial chaos decomposition",

abstract = "Uncertainty quantification in CFD computations is receiving increased interest, due in large part to the increasing complexity of physical models, and the inherent introduction of random model data. This paper focuses on recent application of PC methods for uncertainty representation and propagation in CFD computations. The fundamental concept on which polynomial chaos (PC) representations are based is to regard uncertainty as generating a new set of dimensions, and the solution as being dependent on these dimensions. A spectral decomposition in terms of orthogonal basis functions is used, the evolution of the basis coefficients providing quantitative estimates of the effect of random model data. A general overview of PC applications in CFD is provided, focusing exclusively on applications involving the unreduced Navier-Stokes equations. Included in the present review are an exposition of the mechanics of PC decompositions, an illustration of various means of implementing these representations, and a perspective on the applicability of the corresponding techniques to propagate and quantify uncertainty in Navier-Stokes computations.",

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note = "Funding Information: The authors acknowledge helpful interactions with collaborators, particularly R. Ghanem, H. Najm, B. Debusschere, and M. Reagan. This work was supported by the Laboratory Directed Research and Development Program at Sandia National Laboratories, by the Defense Advanced Research Projects Agency (DARPA) and Air Force Research Laboratory, Air Force Material Command, USAF, under agreement number F30602-00-2-0612. The US government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Computations were performed at the National Center for Supercomputer Applications. O. K. also acknowledges support from the Alexander von Humboldt Foundation.",

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N2 - Uncertainty quantification in CFD computations is receiving increased interest, due in large part to the increasing complexity of physical models, and the inherent introduction of random model data. This paper focuses on recent application of PC methods for uncertainty representation and propagation in CFD computations. The fundamental concept on which polynomial chaos (PC) representations are based is to regard uncertainty as generating a new set of dimensions, and the solution as being dependent on these dimensions. A spectral decomposition in terms of orthogonal basis functions is used, the evolution of the basis coefficients providing quantitative estimates of the effect of random model data. A general overview of PC applications in CFD is provided, focusing exclusively on applications involving the unreduced Navier-Stokes equations. Included in the present review are an exposition of the mechanics of PC decompositions, an illustration of various means of implementing these representations, and a perspective on the applicability of the corresponding techniques to propagate and quantify uncertainty in Navier-Stokes computations.

AB - Uncertainty quantification in CFD computations is receiving increased interest, due in large part to the increasing complexity of physical models, and the inherent introduction of random model data. This paper focuses on recent application of PC methods for uncertainty representation and propagation in CFD computations. The fundamental concept on which polynomial chaos (PC) representations are based is to regard uncertainty as generating a new set of dimensions, and the solution as being dependent on these dimensions. A spectral decomposition in terms of orthogonal basis functions is used, the evolution of the basis coefficients providing quantitative estimates of the effect of random model data. A general overview of PC applications in CFD is provided, focusing exclusively on applications involving the unreduced Navier-Stokes equations. Included in the present review are an exposition of the mechanics of PC decompositions, an illustration of various means of implementing these representations, and a perspective on the applicability of the corresponding techniques to propagate and quantify uncertainty in Navier-Stokes computations.

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Uncertainty propagation in CFD using polynomial chaos decomposition

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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