Uncertainty quantification in reacting flow modeling.

Uncertainty quantification (UQ) in the computational modeling of physical systems is important for scientific investigation, engineering design, and model validation. In this work we develop techniques for UQ based on spectral and pseudo-spectral polynomial chaos (PC) expansions, and we apply these constructions in computations of reacting flow. We develop and compare both intrusive and non-intrusive spectral PC techniques. In the intrusive construction, the deterministic model equations are reformulated using Galerkin projection into a set of equations for the time evolution of the field variable PC expansion mode strengths. The mode strengths relate specific parametric uncertainties to their effects on model outputs. The non-intrusive construction uses sampling of many realizations of the original deterministic model, and projects the resulting statistics onto the PC modes, arriving at the PC expansions of the model outputs. We investigate and discuss the strengths and weaknesses of each approach, and identify their utility under different conditions. We also outline areas where ongoing and future research are needed to address challenges with both approaches.