Native aortic valve cusps are composed of collagen fibers embedded in their layers. Each valve cusp has its own distinctive fiber alignment with varying orientations and sizes of its fiber bundles. However, prior mechanical behavior models have not been able to account for the valve-specific collagen fiber networks (CFN) or for their differences between the cusps. This study investigates the influence of this asymmetry on the hemodynamics by employing two fully coupled fluid-structure interaction (FSI) models, one with asymmetric-mapped CFN from measurements of porcine valve and the other with simplified-symmetric CFN. The FSI models are based on coupled structural and fluid dynamic solvers. The partitioned solver has nonconformal meshes and the flow is modeled by employing the Eulerian approach. The collagen in the CFNs, the surrounding elastin matrix, and the aortic sinus tissues have hyperelastic mechanical behavior. The coaptation is modeled with a master-slave contact algorithm. A full cardiac cycle is simulated by imposing the same physiological blood pressure at the upstream and downstream boundaries for both models. The mapped case showed highly asymmetric valve kinematics and hemodynamics even though there were only small differences between the opening areas and cardiac outputs of the two cases. The regions with a less dense fiber network are more prone to damage since they are subjected to higher principal stress in the tissues and a higher level of flow shear stress. This asymmetric flow leeward of the valve might damage not only the valve itself but also the ascending aorta.