Mathematical modeling of thermal behavior for additive manufacturing with metal powder injection

A mathematical model of the processes taking place in laser melting with injection of metal powders is suggested. The model involves the self-consistent equations for the dynamics of the free surface, the temperature, the concentration of components and the melt flow velocities. The paper presents the algorithm of its numerical realization, as well as the results of test calculation of the temperature fields, the structure of the melt convective flows, the solute distribution and the geometric characteristics of the object to be formed.