Mechanical and Civil Engineering Seminar

All models have errors arising from their inherent structure ("form") that result in prediction uncertainty. The prevailing approach in model form uncertainty quantification is to calibrate a model "mismatch" or model "inadequacy" term against data, which is then used to determine the prediction uncertainty for a quantity of interest. This data-based approach requires data that may not be available or may not be available over all conditions and fails to take advantage of or even respect the model's underlying physics. In this seminar, an alternative approach to model form uncertainty quantification will be presented that is inherently physics-based. The objective is to translate model assumptions, which ultimately result in model errors, into mathematical statements of uncertainty. Two distinct approaches are considered differentiated by what is explicitly known about the model assumptions. In some situations, model assumptions are only implicitly known due to an ignorance of the underlying physics. In these cases, an equally plausible peer model is proposed, with the difference between the two models serving as an estimate for the model error. In other situations, model assumptions are explicitly known and are usually made for the sake of computational expediency. In these cases, a set of hierarchical models can be constructed with nested assumptions. Physical principles in a higher-fidelity model in the hierarchy can be directly used to identify a "trigger" parameter that indicates when a lower-fidelity model in the hierarchy is expected to have a large error, with a model error parameterized in terms of the "trigger" parameter. These two approaches will be leveraged to estimate the uncertainties arising from different component models in Large Eddy Simulation (LES) of turbulent combustion. The notion of peer models is applied to modeling of unresolved turbulent mixing, and the notion of hierarchical models is applied to the modeling of unresolved combustion processes. In addition, it will be shown how the concept of hierarchical model error estimation can be used to develop an error-adaptive physical model for unresolved combustion processes.