VELOCITY-VORTICITY FORMULATION WITH VORTEX PARTICLE-IN-CELL METHOD FOR INCOMPRESSIBLE VISCOUS FLOW SIMULATION, PART I: FORMULATION AND VALIDATION

Abstract

A new velocity-vorticity formulation along with a vortex particle-in-cell method (PIC) is developed to solve the incompressible viscous steady and unsteady flow problems for a closed domain. The article demonstrates that the vortex PIC method has some of the advantages of Lagrangian particle methods for computing convection, while the use of a Eulerian grid to compute the diffusion enables viscous flows to be computed. The solution procedure that is described takes advantage of fast Poisson solvers for computational efficiency. Two-dimensional driven cavity flows with impulsively started and oscillating lids are chosen to test the method. The computation results are in good agreement with those of the numerical literature.