A generalized correction scheme for two-way coupled particle-laden Euler–Lagrange simulations

A two-way coupled, $3D$, Euler–Lagrange point particle formulation is proposed that takes into consideration the disturbance in the flow caused by the dispersed particles to obtain the undisturbed fluid flow field essential for the accurate computation of force closure models. Specifically, an advection–diffusion–reaction (ADR) equation for Stokes flow developed by Pakseresht and Apte (Pakseresht and Apte, 2021) for obtaining the disturbance flow field created by the particle is extended to non-Stokesian flow conditions. Using the solution for flow over a cylinder, an ADR equation for obtaining the disturbance flow field created by a particle in pseudo-$2D$ flows is derived. The present technique for non-Stokesian flows performs significantly better than the existing Stokesian correction scheme, especially for higher particle Stokes numbers and particle-to-grid spacing ratios. The extension of the present technique to the porous particles is examined using two test cases, namely, the settling of porous particles under gravity in a quiescent fluid and porous particles subjected to the oscillating body force field. The present technique is straightforward to implement in all existing Euler–Lagrange solvers based on either ADR or zonal-advection–diffusion–reaction (Zonal-ADR) model.