The lecture is focused on high order compact schemes for direct numerical simulation (DNS) and large eddy simulation (LES) for flow separation, transition, tip vortex, and flow control. Discussion will be given for several fundamental issues such as high quality grid generation, high order schemes for curvilinear coordinates, the CFL condition for complex geometry, and high-order weighted compact schemes for shock capturing and shock-vortex interaction. The computation examples include DNS for flow transition, DNS for flow separation and transition around an airfoil with attack angle, control of flow separation by using pulsed jets and vortex generator, and LES simulation for a tip vortex behind a 3-D airfoil. The computation also shows an almost linear growth in efficiency obtained by using multiple processors.