Hierarchical model form uncertainty quantification for turbulent combustion modeling

All models invoke assumptions that result in model errors. The objective of model form uncertainty quantification is to translate these assumptions into mathematical statements of uncertainty. If each assumption in a model can be isolated, then the uncertainties associated with each assumption can be independently assessed. In situations where a series of assumptions leads to a hierarchy of models with nested assumptions, physical principles from a higher-fidelity model can be used to directly estimate a physics-based uncertainty in a lower-fidelity model. Turbulent nonpremixed combustion models fall into a natural hierarchy from the full governing equations to Conditional Moment Closure to “flamelet”-like models to thermodynamic equilibrium, and, at each stage of the hierarchy, a single assumption can be isolated. In this work, estimates are developed for the uncertainties associated with each assumption in the hierarchy; the general method identifies a “trigger” parameter that can be obtained with information only from the lower-fidelity model that is used to estimate the error in the lower-fidelity model using only physical principles from the higher-fidelity model. The approach will be applied with LES and compared to previous estimates of uncertainties associated with other physical models and parameters.