  An uncertainty quantification framework is developed for Eulerian-Lagrangian
models of particle-laden flows, where the fluid is modeled through a system of
partial differential equations in the Eulerian frame and inertial particles are
traced as points in the Lagrangian frame. The source of uncertainty in such
problems is the particle forcing, which is determined empirically or
computationally with high-fidelity methods (data-driven). The framework relies
on the averaging of the deterministic governing equations with the stochastic
forcing and allows for an estimation of the first and second moment of the
quantities of interest. Via comparison with Monte Carlo simulations, it is
demonstrated that the moment equations accurately predict the uncertainty for
problems whose Eulerian dynamics are either governed by the linear advection
equation or the compressible Euler equations. In areas of singular particle
interfaces and shock singularities significant uncertainty is generated. An
investigation into the effect of the numerical methods shows that
low-dissipative higher-order methods are necessary to capture numerical
singularities (shock discontinuities, singular source terms, particle
clustering) with low diffusion in the propagation of uncertainty.
