A lattice model for the Eulerian description of heavy particle suspensions

TL;DR

This paper introduces a lattice-based numerical method for simulating the dynamics of heavy inertial particles in turbulent flows, effectively capturing particle clustering and dispersion in complex fluid systems.

Contribution

A novel lattice model for Eulerian simulation of heavy particle suspensions that improves accuracy in turbulent flow analysis.

Findings

Good agreement with Lagrangian dynamics in clustering and dispersion

Effective at large Stokes numbers and collision-sensitive scenarios

Applicable to 1D and 2D turbulent flow simulations

Abstract

Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is here introduced for simulating the dynamics of diffusive heavy inertial particles in turbulent flows. The approach is based on the position/velocity phase-space particle distribution. The discretization of velocities is inspired from lattice Boltzmann methods and is chosen to match discrete displacements between two time steps. For each spatial position, the time evolution of particles momentum is approximated by a finite-volume approach. The proposed method is tested for particles experiencing a Stokes viscous drag with a prescribed fluid velocity field in one dimension using a random flow, and in two dimensions with the solution to the forced incompressible Navier-Stokes equations. Results show good agreements between Lagrangian and Eulerian dynamics for both spatial clustering and the dispersion in particle velocities. This demonstrates the suitability of the proposed approach at large Stokes numbers or for situations where details of collision processes are important.