Existing three-dimensional modeling approaches to single-screw extrusion can be classified according to the process sections. The discrete element method (DEM) allows describing solids transport in the feed section. The melt flow in the melt section can be calculated by means of computational fluid dynamics (CFD). However, the current state of the art only allows a separate consideration of the respective sections. A joint examination of the process sections still remains challenging. In this study, a novel modeling approach is presented, allowing a joint consideration of solids and melt transport and, beyond that, the formation of melt. For this purpose, the phase transition from the solid to liquid states is modeled for the first time within the framework CFDEMCoupling®, combining CFD and DEM by a novel melting model implemented in this study. In addition, a melting apparatus for the validation of the novel melting model is set up and put into operation. CFD-DEM simulations are carried out in order to calculate the melting rate and are compared to experimental results. A good agreement between the simulation and experimental results is found. From the findings, it can be assumed that the CFD-DEM simulation of single-screw extruder with a joint consideration of the feed and melt section is feasible.