Intrusive uncertainty quantification of relevant multiphase flows: assessment of the multiUQ framework

Current direct numerical simulations of the Navier-Stokes equations for multiphase flow assume known initial and boundary conditions. However, due to potential variability in boundary conditions and measurement error in fluid characteristics, this assumption results in a simplification of the problem. Uncertainty quantification (UQ) is a tool that measures how input uncertainty propagates through a system and manifests in output. Extracting statistical information from a UQ solver offers greater understanding of how variables interact in a non-linear fluid system, potentially improving engineering designs. Monte-Carlo sampling is a common form of non-intrusive UQ, which is straight-forward to implement. Intrusive UQ methods exist, including those used in the multiUQ framework, which are more computationally efficient. In this work, details of an intrusive multiphase UQ method are provided which require including uncertain variables in the governing equations and rewriting numerical methods. Computational cost of the method is compared to Monte-Carlo. The method is applied to an oscillating droplet, falling water droplet, and an atomizing jet to demonstrate the usefulness of the technique and assess the sensitivity of outputs to multiple input uncertainties using Sobol indices.