The flow and morphological characteristics of liquid water on the icing and anti-icing surfaces of aircraft are closely related to the icing characteristics and anti-icing surface temperature distribution. To predict the flow and breakup characteristics of a water film, a 3D model of continuous water film flow and a model of water film breakup into rivulets on an anti-icing surface were constructed based on the icing model, and the corresponding methods for solving the models were developed. Using the NACA0012 airfoil as a simulation object, the changing characteristics of height and velocity for a continuous water film with time and the morphological characteristics of rivulets formed from the breakup of a continuous water film were simulated numerically. The results indicate that, with an increase in inflow velocity, the time required for the water film to completely cover the surface and reach stability decreases. Downstream in the water droplet impact zone, the calculated values of continuous water film height align well with experiments, as well as the stream height at the continuous water film rupture location with the experimental values. With the reasonable contact angle, the calculation error of the stream width is within 10%.