In-flight icing usually occurs when supercooled droplets impact on the cold surface of an aircraft, which should be concerned for its adverse effects on aerodynamic performance. To fundamentally elucidate the detailed mechanism of aircraft icing, a mathematical model on the impingement dynamics and solidification of a supercooled water droplet was developed and further validated with previous experimental results. Considering the effects of surface tension, wall adhesion and contact line dynamics, the coupled volume of fluid and level-set method was used to track the air-water interface, with the solidification issue solved by the enthalpy-porosity method. The temporal evolutions of the water phase, flow velocity, temperature and heat flux distributions were tracked and analyzed after the phase transition of supercooled water occurred. High impact velocities and millimeter-sized droplets were considered in this study to make the results more applicable to in-flight icing. As concluded, the spreading ratios of the droplets mainly distribute in the range of 0.8 +/- 0.1 corresponding to LWC = 1.0 g/m(3). Besides, the transient heat transfer between the solid surface and droplets could be fitted by a logarithmic function after appropriate dimensionless processing, which was proportional to the 1.5th power of the liquid fraction. Contributions of this work could be an effort to understand the microphysical phenomenon in the aerodynamic icing process. (C) 2019 Elsevier Ltd. All rights reserved.