A spatially-correlated random walk model for capturing two-point statistics in turbulent particle-laden flows

We present a modeling framework designed to capture two-point statistics of inertial particles in turbulent flows. Stochastic models are widely used in large-eddy simulations (LES) and Reynolds-averaged Navier-Stokes (RANS) simulations due to their ability in predicting one-point fluid statistics (e.g., velocity variance and autocorrelation) and their insensitivity to grid coarsening. Modeling the subgrid-scale velocity field as an independent stochastic process, however, prevents such models from capturing spatial heterogeneity (e.g., preferential concentration and particle pair dispersion). In this work, a spatially correlated random walk (SCRW) model is proposed based on an Ornstein-Uhlenbeck (OU) process with a spatially varying covariance matrix that embeds two-point particle information. The covariance matrix is quantified from direct numerical simulations of inertial particles in homogeneous isotropic turbulence. Computational and analytical challenges associated with the high dimensionality of the model are addressed and a path forward is presented.