Model Error Quantification in Non-Equilibrium Flows

In computational fluid dynamics simulations for reentry space vehicles, reduced-order models for thermochemical nonequilibrium are commonly employed due to their computational efficiency. However, it is crucial to assess the inadequacies of these models, as their predictions directly impact the design of the thermal protection system. In this study, we enhance the multi-temperature model, obtained through a coarse-graining strategy, by introducing stochastic model error terms to account for inaccuracies arising in simulations of reentry flow over a blunt body. The Lagrangian approach is employed to solve for the evolution of species mole fractions across various realizations of the stochastic model error terms. Utilizing Karhunen-Loeve Expansion and Polynomial Chaos Expansions, we create an efficient surrogate from the obtained realizations. This surrogate is then applied in Bayesian inference to determine the posteriors of the stochastic model error terms. When these posteriors are forward propagated through the model, they yield probabilistic predictions of the low-fidelity model that effectively capture the high-fidelity model output, which was used as data in the calibration procedure.