Abstract: A new upwind scheme is presented for solving the N S equations on unstructured grid. Spatial discretion is based on flux splitting of Roe. It can capture the strong shock and discontinuity. Solutions are advanced in time by Runge Kutta time stepping scheme and implicit Gauss Seidel relaxation procedure. The adaptive techniques is given. The numerical experiments for flow in tunnel with step, reflection of shock on a flat and flow in cascades demonstrate the flexibility of the present method.