A series of fluid-structure interaction (FSI) simulation models of the opening and closing of a leaflet heart valve has been developed in COMSOL Multiphysics. These models can be used to perform in silico experiments for quantifying and improving the performance of prosthetic heart valves. Model input parameters include geometry dimensions and elastic properties of the leaflets. Performance can be interrogated by probing blood flow field predictions around the leaflets, for example, looking for regions of high shear stress that could imply blood clotting and cell damage. The predicted shape of the valves is also important for determining how completely the valves are able to open and close. A simplified 2D model was used as a proof of concept for the implementation of the physical equations, boundary conditions, and meshing strategy. 3D models of both tricuspid and bicuspid configurations were then constructed representing realistic prosthetic valves attached within an aorta section. Blood flow within the aorta is driven by either transient pressure or velocity flow curves representing realistic in vivo conditions on the inlet side. The highly flexible polymer valve membranes are represented by a hyperelastic material model which captures the large-displacement fluctuations during the transitions between closed and open positions. The intimately coupled fluid-structure equations are solved using the COMSOL Multiphysics segregated solver approach at each time step with customized Jacobian update settings for additional robustness within the nonlinear solver. An automatic remeshing framework is needed to avoid excessive mesh distortion in the blood flow regions. A special weak contribution technique was used to obtain the converged solution. The weak contribution customization represents an additional numerical diffusion term added to the flow continuity equation to improve numerical stability and speed up solution time at the cost of slightly smoothed flow field results. Predicted results are consistent with expected behavior showing the arresting of blood flow with the closing of the valve as well as peak flow rate prediction as being in the forward, open valve condition.