Book Description

Vortex methods are a powerful method for simulating incompressible flows at high Reynolds number. This work extends the basic method to include viscous effects in the presence of solid boundaries. The combination of a fully viscous vortex method with a fast parallel algorithm is used to simulate the flow past an impulsively started cylinder. Experiments have shown that this flow is characterized by the presence of secondary eddies within the main recirculating region. The numerical simulations successfully reproduced these secondary structures over a wide range of Reynolds number (Re=550 to 9500). It was observed that the secondary phenomenon can lead to a major flow reorganization by drastically altering the transport of vorticity. At Re=550, the vortex sheet smoothly rolls up into the primary vortex. For Re=3000 and 9500, however, secondary eddies interfere with that process and the flux of vorticity is redirected toward the cylinder where it accumulates into a new vortical structure. The impulsive start is followed by a 1/(square root of t) singularity in the drag coefficients. The numerical simulations captured this behavior and the computed drag history for short times is in close agreement with the one predicted by a matched asymptotics analysis.