Simulation of Three-dimensional Internal Flows by the Random Vortex and Boundary Element Methods

A vortex boundary element method is developed for the grid-free simulation of time-dependent , incompressible, viscous ow in three-dimensional conngurations. The numerical scheme is based on a combination of the Lagrangian vortex method to capture the convection and stretch of the vortical eld, the random walk method to describe the diiusion process, and the boundary element method to impose the normal ux boundary condition on the boundary surfaces. The no-slip boundary condition is satissed by an extended vortex tile generation mechanism. A new boundary condition is devised to impose the fully developed ow properties at the exit plane. The formulation of the numerical scheme is presented, followed by a parametric study of the accuracy of the method using the model problem of ow in a duct with square cross-section at Re = 100. Additionally, results from an example of piston driven ow in a cylinder with square cross-section and an ooset port at Re = 350 (based on the piston side and maximum speed) are presented.