The subject of the present work is the start-up vortex issuing from a sharp trailing edge accelerated from rest in still air. A numerical simulation of the flow has been performed in the case of a semi-infinite at plate by solving the Navier–Stokes equations in the ψ_ω formulation. The numerical algorithm is based on a fast multigrid implicit integration of the difference equations in an unstructured mesh that is dynamically built to minimize the computational costs. A local refinement of the mesh near the edge of the plate increases the accuracy of the simulation. The results show that the asymptotic stage of the vortex evolution is self-similar in the mean, but the appearance of instabilities produces a time-dependent flow which is not instantaneously self-similar.