SUMMARYAn algorithm for a time accurate incompressible Navier-Stokes solver on an unstructured grid is presented. The algorithm uses a second order, three-point, backward di erence formula for the physical time marching. For each time step, a divergence free ow 每eld is obtained based on an arti每cial compressibility method. An implicit method with a local time step is used to accelerate the convergence for the pseudotime iteration. To validate the code, an unsteady laminar ow over a circular cylinder at a Reynolds number of 200 is calculated. The results are compared with available experimental and numerical data and good agreements are achieved.Using the developed unsteady code, an interaction of a Karman vortex street with an elliptical leading edge is simulated. The incident Karman vortex street is generated by a circular cylinder located upstream. A clustering to the path of the vortices is achieved easily due to exibility of an unstructured grid. Details of the interaction mechanism are analysed by investigating evolutions of vortices. Characteristics of the interactions are compared for large-and small-scale vortex streets. Di erent patterns of the interaction are observed for those two vortex streets and the observation is in agreement with experiment.