The occurrence of aircraft icing can significantly affect flight performance. One of the most important aspects in the study of anti-icing technology for aircraft is the distribution of overflow water. Owing to the external airflow pressure, shear stress, and surface tension, the water film breaks up to form steady rivulets. Experiments on NACA0012 airfoil surfaces were conducted based on an open straight-flow and low-speed wind tunnel. Simultaneously, an engineered three-dimensional rivulet model considering the surface roughness was established based on the energy-minimum principle. A comparison between the simulation and experimental results shows that the errors in the water film breakup location and the flow velocity of rivulets are less than 20%, and the errors in the spacing and width of rivulets are less than 40%. In addition, the effects of surface temperature and uniform roughness on water film breakup were investigated. Furthermore, the rivulet model was applied to the numerical calculation of the thermal performance of hot-air anti-icing systems. The simulations reveal that the uniform roughness of the wing surface causes the water film to break earlier. As the surface roughness increases, the thickness, spacing, and width of the rivulets increase, and the rivulet flow velocity decreases.