Uncertainty propagation using Wiener-Haar expansions


Journal Article

An uncertainty quantification scheme is constructed based on generalized Polynomial Chaos (PC) representations. Two such representations are considered, based on the orthogonal projection of uncertain data and solution variables using either a Haar or a Legendre basis. Governing equations for the unknown coefficients in the resulting representations are derived using a Galerkin procedure and then integrated in order to determine the behavior of the stochastic process. The schemes are applied to a model problem involving a simplified dynamical system and to the classical problem of Rayleigh-Bénard instability. For situations involving random parameters close to a critical point, the computational implementations show that the Wiener Haar (WHa) representation provides more robust predictions that those based on a Wiener-Legendre (WLe) decomposition. However, when the solution depends smoothly on the random data, the WLe scheme exhibits superior convergence. Suggestions regarding future extensions are finally drawn based on these experiences. © 2004 Elsevier Inc. All rights reserved.

Full Text

Cited Authors

  • Le Mat╠ére, OP; Knio, OM; Najm, HN; Ghanem, RG

Published Date

  • June 10, 2004

Published In

Volume / Issue

  • 197 / 1

Start / End Page

  • 28 - 57

International Standard Serial Number (ISSN)

  • 0021-9991

Digital Object Identifier (DOI)

  • 10.1016/j.jcp.2003.11.033

Citation Source

  • Scopus