3-DIMENSIONAL VORTEX SIMULATION OF TIME-DEPENDENT INCOMPRESSIBLE INTERNAL VISCOUS FLOWS

A hybrid random vortex-boundary element method is developed for the so lution of time-dependent incompressible three-dimensional internal flo w problems. The numerical scheme is grid-free within the flow domain a nd is based on a combination of the Lagrangian vortex method to captur e the convection and stretch of the vortical field, the random walk me thod to describe the diffusion process, and the boundary element metho d to superimpose a potential flow on the vortical field such that the normal flux boundary condition is satisfied. The no-slip boundary cond ition is satisfied by generating vorticity tiles on solid boundaries, which are subsequently diffused and convected into the flow interior. Additionally, a boundary condition is devised for the application of f ully developed flow properties at the exit plane. In this paper, the f ormulation and the numerical scheme are presented, followed by a param etric study of the accuracy of the method using the model problem of t he flow in a duct with square cross section at R-e = 100. We show that the method converges to the analytical solution of the problem as the resolution of the time integration and the discretization are improve d, and we discuss the impact of each resolution parameter on the accur acy. In addition, selected results from the simulation of an impulsive ly started flow over a cube at R-e = 100 are presented. We use the res ults of this test case to demonstrate that the method captures the eff ect of sharp edges, parallel and normal to the streamwise flow directi on, on the flow dynamics. (C) 1997 Academic Press.