Bayesian Calibration of Third Order Transport Coefficients in Reactive Nonequilibrium Flows: A Computational Illustration

This paper presents a computational demonstration of the Bayesian estimation framework developed for third-order extended thermodynamics (ET3) transport coefficients in chemically reactive nonequilibrium flows. The study illustrates how Markov Chain Monte Carlo (MCMC) methods can be employed to infer higher-order transport parameters, including relaxation coefficients, higherorder viscosities, and nonlinear coupling terms, from synthetic observational data consistent with the ET3 governing equations. Bayesian inference combines physically informed prior distributions with likelihood functions derived from theoretical model predictions to obtain posterior probability distributions that quantify parameter uncertainty. Representative MCMC trace plots and posterior distributions demonstrate chain convergence, parameter identifiability, and uncertainty reduction following Bayesian calibration. The inferred posterior distributions are propagated through the ET3 model to assess confidence intervals for key thermodynamic quantities and nonequilibrium transport variables. The computational results illustrate that Bayesian calibration significantly improves parameter estimation while preserving thermodynamic consistency and providing rigorous uncertainty quantification. Although based on synthetic benchmark data, the study demonstrates the practical implementation of the theoretical Bayesian framework and establishes a reproducible methodology for calibrating higher-order transport coefficients in reactive nonequilibrium flows. The proposed approach provides a foundation for future applications involving experimental measurements and high-fidelity numerical simulations in combustion, hypersonic aerothermodynamics, plasma physics, and other high-energy-density flow environments.