Uncertainty quantification analysis of point-particle Eulerian-Lagrangian systems with stochastic forcing*

Particle-laden and droplet-laden flows are present in many anthropogenic and natural environments and have been a recurrent interest in the scientific community. Essentially two modeling frameworks can be considered to describe these environments including the Eulerian-Eulerian (EE) frame, which assumes  both phases as a continuum and the Eulerian-Lagrangian (EL) where the particle or dispersed phase is traced along its Lagrangian path and the carrier gas or liquid is modeled in the Eulerian frame. A key element in both modeling frames is the forcing between the phases. Particularly, in reduced models such as the point-particle model, this forcing is not known analytically in general for a wide range of particle conditions and can only be determined empirically or in a data-driven manner within certain confidence bounds. To alleviate this modeling inaccuracy, one must understand the propagation of the uncertainty of the forcing to the solution of the particle-laden flow problem. This can then be applied to multiscale and data-driven models in which uncertainty quantification plays a central role. In this talk, we will discuss a comprehensive analysis of the propagation of a quantified uncertainty in a random particle forcing into an Eulerian-Lagrangian system by developing and comparing the Monte Carlo method, the method of moments and the method of distributions. The Monte Carlo method and the probability density function model that follows from the method of distributions are closed. The method of moments is not and we close it a priori with the Monte Carlo results. The three methods are compared for multiple random forcing distributions and for two one-way coupled canonical problems with carrier flows that include a uniform flow and the stagnation flow.