We focus on the arterial fluid mechanics of patient-specific computer modeling of blood flow in the human aorta. The core computational technology is the space–time variational multiscale (ST-VMS) formulation of incompressible flows, and in conjunction with that we use a number of special techniques targeting arterial fluid mechanics. The special techniques include a mapping technique for the non-circular inflow boundaries, mesh generation techniques for both the unstructured tetrahedral and structured hexahedral aortic meshes, techniques for generating refined layers of mesh near the arterial surfaces, and a technique for calculating the oscillatory shear index (OSI). We compute the unsteady flow patterns in eight different aortas and visually investigate how in each case the geometry influences the wall shear stress, the OSI, and the flow patterns at different instants during the cardiac cycle.