Spectral stochastic uncertainty quantification in chemical systems

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

98 Scopus citations


Uncertainty quantification (UQ) in the computational modelling of physical systems is important for scientific investigation, engineering design, and model validation. We have implemented an 'intrusive' UQ technique in which (1) model parameters and field variables are modelled as stochastic quantities, and are represented using polynomial chaos (PC) expansions in terms of Hermite polynomial functions of Gaussian random variables, and (2) the deterministic model equations are reformulated using Galerkin projection into a set of equations for the time evolution of the field variable PC mode strengths. The mode strengths relate specific parametric uncertainties to their effects on model outputs. In this work, the intrusive reformulation is applied to homogeneous ignition using a detailed chemistry model through the development of a reformulated pseudospectral chemical source term. We present results analysing the growth of uncertainty during the ignition process. We also discuss numerical issues pertaining to the accurate representation of uncertainty with truncated PC expansions, and ensuing stability of the time integration of the chemical system.

Original languageEnglish (US)
Pages (from-to)607-632
Number of pages26
JournalCombustion Theory and Modelling
Issue number3
StatePublished - Sep 2004
Externally publishedYes

ASJC Scopus subject areas

  • General Chemistry
  • General Chemical Engineering
  • Modeling and Simulation
  • Fuel Technology
  • Energy Engineering and Power Technology
  • General Physics and Astronomy


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