Three-dimensional Vortex methods for particle-laden flows with two-way coupling

This paper presents a three-dimensional viscous vortex method for the simul ation of particulate flows with two-way coupling, The flow is computed usin g Lagrangian vortex elements advected with the local velocity, while their strength is modified to account for viscous diffusion, vortex stretching, a nd generating vorticity induced by the particles. The solid particles move according to viscous drag and gravity, creating vorticity, which is discret ised using vortex elements. This method adaptively tracks the evolution of the vorticity field and the generation of new computational elements to acc ount for the vorticity source term. A key aspect of the present scheme is t he remeshing of the computational elements to adaptively accommodate the pr oduction of vorticity induced by the solid particles, and to ensure suffici ent support for the proper resolution of the diffusion equation. High-order moment-conserving formulas are implemented to maintain the adaptive charac ter of the method while they remain local to minimize the computational cos t. These formulas are also implemented in the particle-mesh interpolation o f the field and particle quantities in the context of a Vortex-in-Cell algo rithm, The method is validated against the results of a related finite-diff erence study for an axisymmetric swirling flow with particles, The method i s then applied to the study of a three-dimensional particle blob falling un der the effect of gravity, It is shown that drastically different behaviour s are found depending on the presence of an initial vorticity field. (C) 20 01 Academic Press.