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Modelling of processes of formation of steel ingots is carried out on the basis of solutions of multidimensional nonlinear differential equations. The process of the formation of ingots accompanied by complex turbulent processes. Therefore, this scientific papaer is devoted to describing the equations, boundary conditions, the choice of the mathematical model for the simulation of hydrodynamic processes and heat and mass transfer in the formation ingot. Much attention is paid to the software implementation and visualization of mathematical models