Simulation of three-dimensional internal flows by the random vortex and boundary element methods

Abstract
A vortex boundary element method is developed for the grid-free simulation of time-dependent, incompressible, viscous flow in three dimensional configurations. The numerical scheme is based on a combination of the Lagrangian vortex method to capture the convection and stretch of the vortical field, the random walk method to describe the diffusion process, and the boundary element method to impose the normal flux boundary condition on the boundary surfaces. The no-slip boundary condition is satisfied by an extended vortex tile generation mechanism. A new boundary condition is devised to impose the fully developed flow 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 flow in a duct with square cross-section at Re=100. Additionally, results from an example of piston driven flow in a cylinder with square cross-section and an offset port at Re=350 (based on the piston side and maximum speed) are presented.