Three-Dimensional Vortex Methods for Particle-Laden Flows with Two-Way Coupling

This paper presents a three-dimensional viscous vortex method for the simulation of particulate flows with two-way coupling. The flow is computed using Lagrangian vortex elements advected with the local velocity, while their strength is modified to account for viscous diffusion, vortex stretching, and generating vorticity induced by the particles. The solid particles move according to viscous drag and gravity, creating vorticity, which is discretised using vortex elements. This method adaptively tracks the evolution of the vorticity field and the generation of new computational elements to account for the vorticity source term. A key aspect of the present scheme is the remeshing of the computational elements to adaptively accommodate the production of vorticity induced by the solid particles, and to ensure sufficient support for the proper resolution of the diffusion equation. High-order moment-conserving formulas are implemented to maintain the adaptive character of the method while they remain local to minimize the computational cost. These formulas are also implemented in the particle–mesh interpolation of the field and particle quantities in the context of a Vortex-in-Cell algorithm. The method is validated against the results of a related finite-difference study for an axisymmetric swirling flow with particles. The method is then applied to the study of a three-dimensional particle blob falling under the effect of gravity. It is shown that drastically different behaviours are found depending on the presence of an initial vorticity field.
Keyword: Vortex methods,Particle-laden flows,Lagrangian method