In the past 60 years, the replacement of the aortic valve by a prosthesis has become a routine treatment for severe aortic valve failure. Several valve prostheses have been developed of which the bileaflet mechanical heart valves (BMHVs) are widely preferred. However, current BMHVs still induce thromboembolism, among other undesired side effects, which is believed to be due to non-physiological flow generated by the leaflets. Insights into the dynamics of a BMHV can be provided by numerical methods. In this study, the dynamics of the BMHV are calculated by a strong fluid-structure interaction (FSI) coupling algorithm and the aortic BMHV is simulated under realistic, patient-specific boundary conditions. Upstream of the valve, a model of the left ventricle is constructed. The geometry downstream of the valve consists of a patient-specific aorta with patient-specific flow rates and physiological pressure profiles at its endings. To the best of our knowledge, this is the first 3D numerical simulation of an aortic BMHV that combines upstream and downstream anatomical boundary conditions with a strongly coupled solution of the valve leaflet movement. The results give insights into realistic flow fields and leaflet kinematics. Clinical performance parameters are calculated, such as the amount of back flow and the drop in flow potential energy.