Injecting frozen hydrogen pellets has been proposed as a method of efficiently refueling Tokamak fusion reactors. The intense heat of the reactor causes the pellet to lose mass in a process called ablation. This process creates a cloud-like area around the pellet which partially shields it from further ablation. We are interested in modelling the behavior of the pellet and the resulting flow numerically. We will present the effect of physical parameters such as magnetic field strength, pellet rotation, and pellet surface conditions on the rate of pellet ablation. Improvements made to older models will be discussed. Data and conclusion will be presented for the one-dimensional and two-dimensional case. Areas of further research will be explained.