A numerical investigation of the head-on collision of two equal-sized alumina droplets has been conducted. Direct numerical simulations were performed by employing a volume of fluid method for tracking the interface and an adaptive mesh for improving the calculation efficiency. First, simulations of the head-on collision of tetradecane droplets in nitrogen were carried out, and three different outcomes of collision were captured: bouncing, coalescence after substantial deformation, and reflexive separation. These outcomes are in good agreement with the experiments. The numerical critical Weber numbers between the different regimes are also in good agreement with their experimental values. Next, the head-on collision of alumina droplets was investigated at various Weber numbers (1-800) and at one Ohnesorge number (0.1151). In addition to the three outcomes captured earlier, coalescence after a long extension between reflexive separation without satellite and reflexive separation with one satellite is observed. Furthermore, the numerical critical Weber numbers between these distinct regimes were obtained, and the numerical critical Weber number between coalescences after substantial deformation and reflexive separation agrees well with its theoretical value. Finally, collision models of alumina droplets are presented by modifying current droplet collision models.