Application of the MCMC Method for the Calibration of DSMC Parameters

A Markov Chain Monte Carlo (MCMC) algorithm was employed to obtain a calibrated distribution for the hard sphere diameter, the VHS reference diameter, and the temperature viscosity exponent of argon, for use in the Direct Simulation Monte Carlo (DSMC) method. Shock-tube experiments from Alsmeyer [1] were used to provide the necessary calibration data for use in the MCMC method. The DSMC method used in this work employs the algorithm of Bird [2], with modifications to allow for the efficient simulation of a 1D shock. When calibrating for the hard sphere diameter (the temperature viscosity exponent is set to 0.5 for the hard sphere method), the results of the MCMC method agree with a simple brute-force method, and a single value for the hard-sphere diameter is obtained. For the VHS method, however, when simultaneously calibrating the VHS reference diameter and the temperature viscosity exponent, we find that normalized density data alone does not provide sufficient information to obtain a single solution for both parameters. Instead we find a band in parameter space where acceptable solutions are obtained.