<p>Challenges faced in computational analysis of aortic-valve to aorta flow include (i) contact between the valve leaflets, which changes the flow-domain topology, (ii) high-resolution boundary-layer representation even with the topology changes, (iii) thin leaflets that generate thin shear layers and associated vortex structures, and (iv) flow driven primarily by pressure differences. In addressing these challenges with the Space–Time Computational Flow Analysis (STCFA), we use the “ST-SI-TC-IGA.” The core component of the ST-SI-TC-IGA is the ST Variational Multiscale (ST-VMS) method, and the other key components are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and the ST Isogeometric Analysis (ST-IGA). The Constrained-Flow-Profile Traction is also a part of the STCFA here, enabling us to use traction boundary condition at the inlet. Furthermore, for more cost-effective mesh refinement near the solid surfaces of the complex geometries involved, we are using a moving T-splines mesh with the product-form T-splines basis functions. This is enabled by the Complex-Geometry T-Splines Mesh Generation method. The mesh motion is enabled by a combination of the Fiber-Reinforced Hyperelasticity Mesh Update Method and the “ST-C,” a method for temporal data representation, relying on IGA basis functions in time. Our objective in the computational flow analysis here is to clarify how the geometric features of the aortic arch influence the flow patterns around the leaflets of a bioprosthetic aortic valve. That will enable a better understanding of (a) the mechanisms by which the aortic curvature and torsion influence the near-leaflet flow patterns, such as flow reversal and vortex dynamics, and (b) the wall shear stress and oscillatory shear index distributions resulting from those flow patterns.</p>