The flow dynamics through the peripheral and hinge regions of a bi-leaflet mechanical heart valve are complex and result in abnormally high shear stresses particularly during the closing phase of the valve function. It has been observed that, the late stages of closure is more significant in the dynamics of platelet activation; therefore, the later stages of closure is simulated by solving the two-dimensional Navier-Stokes equations using an Eulerian Levelset based sharp interface Cartesian grid method. Using a fixed Cartesian mesh incorporating local mesh refinement for solution accuracy and efficiency, the flow through and within a recessed hinge design and an open pivot hinge design is compared. Platelets are modelled as point particles by Lagrangian particle tracking algorithm with one way coupling. A dilute particle flow is assumed and particle-particle interactions are neglected. It was observed that the hinge region of the open pivot valve indicated a lower potential for activation of platelets compared to that in valves with a recessed hinge design.