Application of Bayesian Statistical Methods for the Analysis of DSMC Simulations of Hypersonic Shocks

Abstract

This research centers on laying the groundwork for the application of Bayesian statistical methods for the calibration of parameters relevant to modeling a hypersonic shock layer with the Direct Simulation Monte Carlo (DSMC) method. The DSMC method used in this work employs the algorithm of Bird (1994), with modifications to allow for the efficient simulation of a 1D hypersonic shock. The Larsen-Borgnakke model is employed to handle the exchange of energy between translational, rotational, and vibrational modes, and the TCE model was used to convert Arrhenius-form reaction rate constants into reaction crosssections, after modification to allow the code to accurately model reactions with arbitrarily large rates relative to the VHS collision rate. The DSMC code was written and optimized with shock tube simulations in mind. Two global, Monte Carlo based sensitivity analyses were performed to determine which reaction rates most affect the simulation results for the case of a hypersonic shock in five-species air. The square of the Pearson correlation coefficient was used as the measure for sensitivity in the first of the analyses, and the mutual information was used as the measure in the second. The reaction rates with the highest sensitivities have been identified for two different quantities of interest (QoIs). For a shock speed of ~8000 m/s (M ∞ ≈ 23), both sensitivity analysis methods agree that the reaction rate