Numerical simulation of 3D incompressible flows around large scale objects at high Reynolds number using the unsteady Navier-Stokes equations is challenging. In order to obtain accurate simulations, very fine meshes are necessary, and such simulations are increasingly important for modern engineering practices, such as understanding the flow behavior around high speed trains, cars and wind turbines, which can reduce the need for building physical models and wind-tunnel experiments. The computation for this kind of simulations is very challenging because of the large fluids domain, the complex geometry, the moving boundary, and the high Reynolds number; thus the use of massively parallel computers and scalable parallel algorithms has become indispensable. In this talk, we introduce a Newton-Krylov-Schwarz based fully implicit method for the 3D unsteady incompressible Navier-Stokes equations discretized with a stabilized finite element method on very fine unstructured meshes. We test the algorithm for some 3D complex unsteady flows, including flows passing a high speed train, a car, and a wind turbine with realistic geometries, realistic Reynolds numbers, and realistic wind speed, on a supercomputer with thousands of processors. Numerical experiments show that the algorithm has almost linear scalability with over three thousand processors for problems with tens of millions of unknowns.