We have performed high-resolution fluid-structure interaction simulations of physiologic pulsatile flow through a bi-leaflet mechanical heart valve (BMHV) in an anatomically realistic aorta. The results are compared with numerical simulations of the flow through an identical BMHV implanted in a straight aorta. The comparisons show that although some of the salient features of the flow remain the same, the aorta geometry can have a major effect on both the flow patterns and the motion of the valve leaflets. For the studied configuration, for instance, the BMHV leaflets in the anatomic aorta open much faster and undergo a greater rebound during closing than the same valve in the straight axisymmetric aorta. Even though the characteristic triple-jet structure does emerge downstream of the leaflets for both cases, for the anatomic case the leaflet jets spread laterally and diffuse much faster than in the straight aorta due to the aortic curvature and complex shape of the anatomic sinus. Consequently the leaflet shear layers in the anatomic case remain laminar and organized for a larger portion of the accelerating phase as compared to the shear layers in the straight aorta, which begin to undergo laminar instabilities well before peak systole is reached. For both cases, however, the flow undergoes a very similar explosive transition to the small-scale, turbulent-like state just prior to reaching peak systole. The local maximum shear stress is used as a metric to characterize the mechanical environment experienced by blood cells. Pockets of high local maximum shear are found to be significantly more widespread in the anatomic aorta than in the straight aorta throughout the cardiac cycle. Pockets of high local maximum shear were located near the leaflets and in the aortic arc region. This work clearly demonstrates the importance of the aortic geometry on the flow phenomena in a BMHV and demonstrates the potential of our computational method to carry out image-based patient-specific simulations for clinically relevant studies of heart valve hemodynamics.