A stochastic projection method for fluid flow. II. Random process

Olivier P. Le Matre; Matthew T. Reagan; Habib N. Najm; Roger G. Ghanem; Omar M. Knio

doi:10.1006/jcph.2002.7104

A stochastic projection method for fluid flow. II. Random process

Olivier P. Le Matre, Matthew T. Reagan, Habib N. Najm, Roger G. Ghanem, Omar M. Knio^*

^*Corresponding author for this work

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

314 Scopus citations

Abstract

An uncertainty quantification scheme is developed for the simulation of stochastic thermofluid processes. The scheme relies on spectral representation of uncertainty using the polynomial chaos (PC) system. The solver combines a Galerkin procedure for the determination of PC coefficients with a projection method for efficiently simulating the resulting system of coupled transport equations. Implementation of the numerical scheme is illustrated through simulations of natural convection in a 2D square cavity with stochastic temperature distribution at the cold wall. The properties of the uncertainty representation scheme are analyzed, and the predictions are contrasted with results obtained using a Monte Carlo approach.

Original language	English (US)
Pages (from-to)	9-44
Number of pages	36
Journal	Journal of Computational Physics
Volume	181
Issue number	1
DOIs	https://doi.org/10.1006/jcph.2002.7104
State	Published - Sep 1 2002
Externally published	Yes

Keywords

Karhune-Loève
Natural convection
Navier-Stokes
Polynomial chaos
Stochastic
Uncertainty

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1006/jcph.2002.7104

Cite this

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title = "A stochastic projection method for fluid flow. II. Random process",

abstract = "An uncertainty quantification scheme is developed for the simulation of stochastic thermofluid processes. The scheme relies on spectral representation of uncertainty using the polynomial chaos (PC) system. The solver combines a Galerkin procedure for the determination of PC coefficients with a projection method for efficiently simulating the resulting system of coupled transport equations. Implementation of the numerical scheme is illustrated through simulations of natural convection in a 2D square cavity with stochastic temperature distribution at the cold wall. The properties of the uncertainty representation scheme are analyzed, and the predictions are contrasted with results obtained using a Monte Carlo approach.",

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AU - Le Matre, Olivier P.

AU - Reagan, Matthew T.

AU - Najm, Habib N.

AU - Ghanem, Roger G.

AU - Knio, Omar M.

PY - 2002/9/1

Y1 - 2002/9/1

N2 - An uncertainty quantification scheme is developed for the simulation of stochastic thermofluid processes. The scheme relies on spectral representation of uncertainty using the polynomial chaos (PC) system. The solver combines a Galerkin procedure for the determination of PC coefficients with a projection method for efficiently simulating the resulting system of coupled transport equations. Implementation of the numerical scheme is illustrated through simulations of natural convection in a 2D square cavity with stochastic temperature distribution at the cold wall. The properties of the uncertainty representation scheme are analyzed, and the predictions are contrasted with results obtained using a Monte Carlo approach.

AB - An uncertainty quantification scheme is developed for the simulation of stochastic thermofluid processes. The scheme relies on spectral representation of uncertainty using the polynomial chaos (PC) system. The solver combines a Galerkin procedure for the determination of PC coefficients with a projection method for efficiently simulating the resulting system of coupled transport equations. Implementation of the numerical scheme is illustrated through simulations of natural convection in a 2D square cavity with stochastic temperature distribution at the cold wall. The properties of the uncertainty representation scheme are analyzed, and the predictions are contrasted with results obtained using a Monte Carlo approach.

KW - Karhune-Loève

KW - Natural convection

KW - Navier-Stokes

KW - Polynomial chaos

KW - Stochastic

KW - Uncertainty

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EP - 44

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

A stochastic projection method for fluid flow. II. Random process

Abstract

Keywords

ASJC Scopus subject areas

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