Abatract. I will present a highly parallel domain decomposition algorithm for the simulation of blood flows in human arteries by solving the incompressible Navier-Stokes equations. The system is discretized with a fully implicit finite element method on unstructured moving meshes in 3D and solved by a Newton-Krylov algorithm preconditioned with an overlapping Schwarz method. Several mathematical, bio-mechanical, and supercomputing issues will be discussed in detail, and some numerical experiments for the simulation of blood flows in a full-size human body will be presented. Lastly I will discuss the control of the fluid via the parameters of the Navier-Stokes equations and its connection with healthy living.