Uncertainty quantification of shock–bubble interaction simulations

We present a numerical analysis of the shock–bubble interaction with uncertainty in bubble density. We considered a bubble with density uncertainty with a Gaussian distribution, of which effects on the flow structures are analyzed using a stochastic collocation method. The uncertainty is modeled by polynomial chaos, and the effects of the uncertainty are evaluated from the simulation results that are associated with the quadrature points of the bubble density with random fluctuations. Specifically, we focus on the impact of the density uncertainty in a bubble on the flow structures over the entire computational domain. The statistics of the density field, such as mean and standard variance, are investigated. The analysis reveals that the uncertainty of bubble density affects different flow structures with different significance, which provides a global sensitivity map for the whole solution domain. Efforts have been also made to quantify the uncertainties in the motions of different waves and fronts. It is observed that the velocities of different waves/fronts exhibit large differences in the response to the bubble-density uncertainty, which is in accordance with the existing experimental and numerical studies.