Summary In this paper we present an adaptive wavelet method to integrate the velocity-vorticity formulation of the two-dimensional Navier-Stokes equations coupled with a penalisation technique to handle easily solid boundaries of arbitrary shape. The validity of this method, called Coherent Vortex Simulation (CVS), is demonstrated by computing flows past different bluff bodies. Firstly, we show the computation of a flow around an impulsively started cylinder at Reynolds number 3000. The results are compared with those of a DNS using a spectral method and with others computed with two different vortex methods. Secondly, we also present simulations of a flow around a NACA air-foil profile at Reynolds number 1000.