Optimal fidelity multi-level Monte Carlo for quantification of uncertainty in simulations of cloud cavitation collapse

TL;DR

This paper develops an optimal fidelity multi-level Monte Carlo method to efficiently quantify uncertainties in cloud cavitation collapse simulations, revealing significant variability in pressure peaks and their correlation with cloud structure.

Contribution

It introduces novel optimal control variate coefficients for MLMC, achieving over two orders of magnitude speedup in uncertainty quantification of cavitation collapse.

Findings

Large uncertainties in peak pressure location and magnitude.

Significant correlations between cloud structure and pressure uncertainties.

Optimal MLMC method greatly reduces computational cost.

Abstract

We quantify uncertainties in the location and magnitude of extreme pressure spots revealed from large scale multi-phase flow simulations of cloud cavitation collapse. We examine clouds containing 500 cavities and quantify uncertainties related to their initial spatial arrangement. The resulting 2000-dimensional space is sampled using a non-intrusive and computationally efficient Multi-Level Monte Carlo (MLMC) methodology. We introduce novel optimal control variate coefficients to enhance the variance reduction in MLMC. The proposed optimal fidelity MLMC leads to more than two orders of magnitude speedup when compared to standard Monte Carlo methods. We identify large uncertainties in the location and magnitude of the peak pressure pulse and present its statistical correlations and joint probability density functions with the geometrical characteristics of the cloud. Characteristic properties of spatial cloud structure are identified as potential causes of significant uncertainties in exerted collapse pressures.