In this paper, the flattening and the simultaneous solidification of a liquid particle when it hits a solid surface are described mathematically and numerically simulated in cylindrical coordinates on the basis of the Navier-Stokes equations. The heat transfer in the particle and in the substrate is simulated by solving the 2-D heat conduction problem, whereby hydrodynamic processes in the melted particle as well as pressure forces are taken into account. The particle solidification is investigated using the one-dimensional Stefan problem, taking into account the contact heat conduction at the boundary between particle and substrate. For numerical calculations, computational algorithms were created on the basis of the difference method, which were implemented in the form of an applied program complex. Paper includes a German-language abstract.