  In this work, numerical solutions of the two dimensional time dependent
incompressible flow, in a driven cavity at high Reynolds number Re, are
presented. At high Re, there is a controversy. Some studies predicted that the
flow is steady, others found time dependent non-steady flow, either periodic or
aperiodic. In this study, the driven lid cavity is successfully solved using a
very fine grid mesh, for Re up to $30 000$. We discretize the Vorticity-Stream
formulation of the Navier-Stokes equation with the SSPRK(5,4) scheme in a
$1024\times1024$ grid. Using this very fine grid, the results obtained converge
to a stationary solution. Detailed results for Re between $5 000$ and $30 000$
are presented. The driven lid cavity problem is solved with a NVIDIA GPU using
the CUDA programming environment with double precision.
