engine with moving valves and a piston, where the meshing process must be repeated each timestep. In addition, due A hybrid random vortex-boundary element method is developed for the solution of time-dependent incompressible three-dimen-to the Lagrangian nature of the method, convection is sional internal flow problems. The numerical scheme is grid-free approximated with minimal numerical diffusion, making within the flow domain and is based on a combination of the Lagranthe scheme an excellent tool for analyzing high Reynolds gian vortex method to capture the convection and stretch of the number flows. Vortex methods are also self-adaptive and, vortical field, the random walk method to describe the diffusion hence, are capable of dynamically concentrating computaprocess, and the boundary element method to superimpose a potential flow on the vortical field such that the normal flux boundary tional elements where significant velocity gradients evolve, condition is satisfied. The no-slip boundary condition is satisfied such as in regions with high recirculation or in shear layers. by generating vorticity tiles on solid boundaries, which are subse-Furthermore, vortex methods readily facilitate an intuitive quently diffused and convected into the flow interior. Additionally, a and quantitative tool for interrogating ''three-dimensionalboundary condition is devised for the application of fully developed ity effects'' in the flow by monitoring vorticity stretch in flow properties at the exit plane. In this paper, the formulation and the numerical scheme are presented, followed by a parametric study the field. This is an immediate consequence of representing of the accuracy of the method using the model problem of the flow the Navier-Stokes equations in the velocity-vorticity forin a duct with square cross section at R e ฯญ 100. We show that the mulation, where the three-dimensional equations are dismethod converges to the analytical solution of the problem as the tinguished from their two-dimensional counterpart by the resolution of the time integration and the discretization are imextra vorticity stretch term. Finally, vortex methods are proved, and we discuss the impact of each resolution parameter on the accuracy. In addition, selected results from the simulation naturally adaptable to massively parallel computing, which of an impulsively started flow over a cube at R e ฯญ 100 are presented. can be exploited to solve large-scale problems efficiently.
We use the results of this test case to demonstrate that the method Currently, three-dimensional vortex methods display a captures the effect of sharp edges, parallel and normal to the streamfew computational difficulties which need to be resolved wise flow direction, on the flow dynamics. แฎ 1997 Academic Press with more vigor. First, the computational cost for evaluating the vortex element velocities using traditional summation techniques grows quadratically with the number of 75