Natural convection in a closed cavity under stochastic non-boussinesq conditions

Olivier Le Maître*, M. T. Reagan, B. Debusschere, H. N. Najm, R. G. Ghanem, O. M. Knio

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


A stochastic projection method (SPM) is developed for quantitative propagation of uncertainty in compressible zero-Mach-number flows. The formulation is based on a spectral representation of uncertainty using the polynomial chaos (PC) system, and on a Galerkin approach to determining the PC coefficients. Governing equations for the stochastic modes are solved using a mass-conservative projection method. The formulation incorporates a specially tailored stochastic inverse procedure for exactly satisfying the mass-conservation divergence constraints. A brief validation of the zero-Mach-number solver is first performed, based on simulations of natural convection in a closed cavity. The SPM is then applied to analyze the steady-state behavior of the heat transfer and of the velocity and temperature fields under stochastic non-Boussinesq conditions.

Original languageEnglish (US)
Pages (from-to)375-394
Number of pages20
JournalSIAM Journal on Scientific Computing
Issue number2
StatePublished - 2005
Externally publishedYes


  • Karhunen-Loève
  • Natural convection
  • Navier-Stokes
  • Polynomial chaos
  • Stochastic
  • Uncertainty

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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