Abstract
The urgency of the development of mathematical modeling tools that allow calculating the shape of free surface of the melt during the analysis of surfacing processes, introduced in additive production, is shown. A mathematical formulation of the problem is presented, which corresponds to Lagrangian description of liquid medium. It includes equation of motion and energy equation. A numerical algorithm for solving this problem is described, based on Smoothed Particle Hydrodynamics method, and the corresponding equations are given. The analysis of the results of solution of test problems is carried out and comparison of experimental results of the process with well-known data and physical representations is given. The conclusion is made about the possibility of applying this modeling method for development of additive production and creation of automatic control systems for the processes of shaping.
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