The ability to perform device-to-device (D2D) communication in Long Term Evolution (LTE)-based cellular networks became possible with the introduction of Proximity Services (ProSe) functionalities in the 3rd Generation Partnership Program (3GPP) specifications. In this paper, we provide a description of the ProSe implementation that extends the LTE model already available in ns-3. Our model contains key features defined in LTE Release 12 and further enhanced in LTE Release 13 related to synchronization, discovery, and communication. We also provide validation of each feature by comparing simulation results with analytical models developed as part of our work on D2D communication.