Single-particle sedimentation in viscous fluids: an Eulerian approach

This study presents a simplified Eulerian numerical model for efficiently simulating particle sedimentation, including translational and rotational dynamics, in viscous fluids. Unlike conventional hybrid Eulerian–Lagrangian methods, the proposed approach eliminates the need for a moving mesh by partitioning particle geometry directly within a fixed Eulerian framework. Particle motion and orientation are represented through time-dependent inlet boundary conditions, accounting for local hydrodynamic forces and torques explicitly calculated on particle surfaces. The method is validated against analytical, numerical, and experimental benchmarks, demonstrating its accuracy for spheres and elliptical particles. Additionally, the model successfully captures particle–wall interactions at the bottom virtual wall via prescribed lubrication forces. Simulations for various shapes, including spheres, elliptical particles, flat disks, and cylinders, highlight the model's versatility, and computational efficiency within its stated limitations of single-particle, low Reynolds number laminar flow conditions.