Computational Challenges in Sampling and Representation of Uncertain Reaction Kinetics in Large Dimensions

Overview

Abstract

Constructing functional representations of the key quantities of interest (QoIs), the ignition delay time (τ_ign), of an uncertain ignition reaction in high dimension is our main goal. First, attention is focused on the ignition delay time of an iso-octane air mixture, using a detailed chemical mechanism with 3,811 elementary reactions. Uncertainty in all reaction rates is directly accounted for using associated uncertainty factors, assuming independent log uniform priors. A Latin hypercube sample (LHS) of the ignition delay times was first generated, and the resulting database was then exploited to assess the possibility of constructing polynomial chaos (PC) representations in terms of the canonical random variables parameterizing the uncertain rates. We explored two avenues, namely sparse regression (SR) using LASSO, and a coordinate transform (CT) approach. Preconditioned variants of both approaches were also considered, namely using the logarithm of the ignition delay time as QoI. A global sensitivity analysis is performed using the representations constructed by SR and CT.

Next, the tangent linear approximation is developed to estimate the sensitivity of the ignition delay time with respect to individual rate parameters in a detailed chemical mechanism. Attention is focused on a gas mixture reacting under adiabatic, constant-volume conditions. The approach is based on integrating the linearized system of equations governing the evolution of the partial derivatives of the state vector with respect to individual random variables, and a linearized approximation is developed to relate the ignition delay sensitivity to the scaled partial derivatives of temperature. In particular, the computations indicate that for detailed reaction mechanisms the TLA leads to robust local sensitivity predictions at a computational cost that is order-of magnitude smaller than that incurred by finite-difference approaches based on one-at-a-time rate parameters perturbations.

In the last part, we explore the potential of utilizing TLA-based sensitivities to identify active subspace and to construct suitable representations. Performance is assessed based contrasting experiences with CT-based machinery developed earlier. 

Brief Biography

Saja Almohammadi received the B.S. degree in mathematic from the King Abdulaziz University  in 2009, and the M.S. degree from the Department of Applied Math, King Abdullah University of Science and Technology, in 2014, where she is currently pursuing the Ph.D. degree. Her research interests include working on Uncertainty Quantification (UQ) on chemical system. Development of methods for forward UQ as applied to chemical kinetic application.