Abstract In Japan, it is planned to use vitrification to immobilize high level radioactive liquid waste (HLLW) obtained from the nuclear reprocessing process. In the vitrification process, the HLLW will be mixed with molten glass in a joule-heated glass melter. The molten glass is then poured into a canister through a nozzle at the bottom of the melter. When some abnormalities occurred, feature of the discharged flow become different from that in normal conditions. We cannot observe the state of the molten glass inside the melter directly because of the severe environment. Accordingly, we cannot investigate the cause when the abnormalities occurred. Hence, numerical simulation of the discharged flow becomes important to understand and recover from operational problems or abnormalities with the glass melter. However, existing numerical models of the glass melter do not really simulate the discharged glass flow. In the present study, we introduce a new algorithm into an existing Lagrangian approach to efficiently simulate the discharged glass flow. To verify the model, 3D simulations were performed on a real scale system and got compared with the results of experimental validation tests. The simulation results show good agreement with the experimental results. Consequently, the new Lagrangian approach accurately simulates the molten glass flow.