The present paper describes an overview of mathematical modeling of the glass melting process inside an open-top skull furnace having DC plasma discharge as the primary energy source. This melting system has been developed by Plasmelt Glass Technologies LLC (Boulder, CO, USA). A mathematical model of intensive glass melting, which is a non-stationary state process, and corresponding software have been developed by modeling team of Laboratory of Glass Properties LLC (LGP). This mathematical model has been created in parallel with the development of the melting process itself. Having a fully operational pilot unit available the Plasmelt team had the possibility to compare behavior of a real melting system with that calculated by the model. Special attention was paid to accuracy of input data on both physical properties of glass and processing parameters. The influence of absorption of radiation in short- and near- IR ranges (0.6 – 2.6 µm) by the molten glass on some key process parameters (throughput and outflow molten glass temperature) has been studied. This work has become possible because of intensive work of the joint team: Ron Gonterman and Mike Weinstein (Plasmelt), Scott Parker (University of Colorado), Oleg Prokhorenko, Sergey Tarakanov, Sergey Chivilikhin, Marina Chistokolova and Roman Eroshkin (LGP) on task formulation, experimental runs, model development, testing and verification, and physical properties studies.