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 journalArticlepeer-review

311 Scopus citations


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 languageEnglish (US)
Pages (from-to)9-44
Number of pages36
JournalJournal of Computational Physics
Issue number1
StatePublished - Sep 1 2002
Externally publishedYes


  • 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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