Uncertainty quantification of kinetic models using adjoint-driven active subspace algorithms

Simulations of chemically reacting flows are particularly sensitive to kinetic models, which in turn depend on a large number of parameters. Therefore, quantifying parametric uncertainties is essential in order to assess the applicability and performance of such models. The size of the parameter space renders conventional methods in quantifying uncertainties impractical. The active subspace methodology has proven to be very effective in such applications and has been adopted here to analyze ignition delay time in an isochoric adiabatic reactor. This method has been augmented with an adjoint-based algorithm to provide low-cost access to gradient information, necessary for dimensionality reduction. In addition, the predictions of the active subspace method have been compared to a linear approximation using the adjoint model (LAAM), where depending on the case, a satisfactory estimation is achieved at a fraction of the cost. Moreover, a strategy is presented for constructing a multi-dimensional response surface for cases, where contrary to previous studies, a single dominant direction is insufficient in predicting the corresponding PDF. Finally, the uncertainties with respect to initial conditions are analyzed, highlighting the limitations of the linear approach (LAAM) in cases with strong nonlinearities.