Point-cloud Subgrid Particle-Averaged Reynolds Stress Equivalent (SPARSE) method for particle-laden flows with stochastic forcing

For process scale problems in particle-laden flows described with Eulerian-Lagrangian (EL) formulations where the Particle-Source-In-Cell (PSIC) method is used, it is often needed to compute millions to billions of particles where a reduced modeling is needed. The point-particle assumption considers particles as single points and models the momentum and energy exchanged between phases because their analytical descriptions are only available in scarce physical situations. The forcing of the particle phase is thus corrected with empirical and/or data-driven correlations that introduce uncertainty, rendering the particle equations stochastic. The double purpose of alleviating the computational cost and including the stochastic character of the forcing is addressed here using the Subgrid Particle-Averaged Reynolds Stress Equivalent (SPARSE) method. The point-cloud SPARSE method averages the dispersed phase in Lagrangian form, leading to a closed set of equations to describe the first two moments of stochastically forced particle clouds. The resulting formulation is scalable to three-dimensional complex flows. We test the SPARSE formulation in elementary analytical flows and with an isotropic turbulence case computed with a DNS solver.