SUMMARYFor the incompressible Navier-Stokes equations, vorticity-based formulations have many attractive features over primitive-variable velocity-pressure formulations. However, some features interfere with the use of the numerical methods based on the vorticity formulations, one of them being the lack of a boundary conditions on vorticity. In this paper, a novel approach is presented to solve the velocityvorticity integro-di erential formulations. The general numerical method is based on standard ÿnite volume scheme. The velocities needed at the vertexes of each control volume are calculated by a socalled generalized Biot-Savart formula combined with a fast summation algorithm, which makes the velocity boundary conditions implicitly satisÿed by maintaining the kinematic compatibility of the velocity and vorticity ÿelds. The well-known fractional step approaches are used to solve the vorticity transport equation. The paper describes in detail how we accurately impose no normal-ow and no tangential-ow boundary conditions. We impose a no-ux boundary condition on solid objects by the introduction of a proper amount of vorticity at wall. The di usion term in the transport equation is treated implicitly using a conservative ÿnite update. The di usive uxes of vorticity into ow domain from solid boundaries are determined by an iterative process in order to satisfy the no tangential-ow boundary condition. As application examples, the impulsively started ows through a at plate and a circular cylinder are computed using the method. The present results are compared with the analytical solution and other numerical results and show good agreement.