The flow inside a lid-driven square cavity have been imposed a wide controversy during these last decades.Multiple studies found to exist in the literature included this case, which is widely used for benchmarking in computational fluid dynamic due to the simplicity of geometry. some classes of studies have investigated the existence of steady flow in the driven cavity, they found a steady 2D numérical solution until 35000 value of Reynolds number.However, other classes of studies have stated that the flow in driven cavity submitted to a hydrodynamic instability and they illustrated a continuation méthode to locate the point at which a Hopf bifurcation occurs leading to a transition from a steady flow to unsteady.In the shade of these studies and with this uncertainty surrounding this subject we wanted to get more clarification especially for steady flow solutions.The present study represents a numerical computation for steady flow inside a lid-driven square cavity, the governing equation is solved using a finite volume method based on second order scheme of accuracy. Steady solutions are obtained for Reynolds numbers ascending from 100 to 50000, using a resolution of 1024 x1024 grid point. A good agreement with previous results in the literature, the work was done in this paper including proprieties of flow in the center of primary and secondary vortices, velocity components and numérical values for stream function and vorticity which assure a good example for benchmarking purposes
