A computer model has been developed to investigate the processes of heat and mass transfer under the influence of concentrated energy sources on materials with specified thermophysical characteristics, including temperature-dependent ones. The model is based on the application of the volume of fluid (VOF) method and finite-difference approximation of the Navier–Stokes differential equations formulated for a viscous incompressible medium. The “predictor-corrector” method has been used for the coordinated determination of the pressure field which corresponds to the continuity condition and the velocity field. The modeling technique of the free liquid surface and boundary conditions has been described. The method of calculating surface tension forces and vapor recoil pressure has been presented. The algorithm structure is given, the individual modules of which are currently implemented in the Microsoft Visual Studio environment. The model can be applied for studying the metal transfer during the deposition processes, including the processes with electron beam spatial oscillation. The model was validated by comparing the results of computational experiments and images obtained by a high-speed camera.

The relevance of creating specialized computer programs that convert a virtual 3D model of an object into machine code (G-code) for controlling the process of 3D printing products from wire raw materials is substantiated. It is shown that for wire-based additive technologies, a fundamentally important requirement is to ensure the continuity of the surfacing trajectory within one section. A method for determining a continuous surfacing trajectory is proposed, the implementation of which requires two stages: performing a numerical analysis of a two-dimensional region with boundary conditions describing this section; and running a heuristic algorithm for the movement of the surfacing head, in which the direction of movement is selected based on the results of the analysis. The procedure for setting boundary conditions and an algorithm for numerically solving the boundary value problem of determining the field of the “height” function for each section are described. The principles of operation of the heuristic algorithm for selecting the direction of head movement based on the calculated height field and continuous determination of the proximity of adjacent layers and section boundaries are disclosed. An analysis of the algorithm operation is carried out using a section with holes as an example, and the potential of using numerical methods to calculate the change in the temperature field during the surfacing process is shown.