Aortic stenosis caused by valve calcification is a major cause of death around the world. Hemodynamic factors have been suggested to be major players in the development of valve calcification, yet a detailed knowledge of the blood flow dynamics as experienced by endothelial cells on valve surfaces is still lacking. In this study we carry out high-resolution numerical simulations of the blood flow through a polymeric trileaflet valve in order to elucidate the differential flow dynamics on the aortic and ventricular sides of the valve leaflets. Limiting streamlines and surface shear stress contours are used to probe and quantify the blood flows on its side. Complicated flow patterns were only observed on the aortic side of the valve near the region where focalized distribution of valve calcification is typically observed.