Artificial intelligence

Abstract: Thermophysical processes accompanied by substance phase transitions are studied in the work. These processes are described by the mathematical model, in which the temperature of each phase satisfies the heat-transfer equation with its thermophysical coefficients. In boundary of phase division, both temperatures are constant and equal to the temperature of a phase transition. On the set parts of boundary, certain schedule is supported. The surface of phase division (“free boundary”) is unknown and Stephan condition is additionally set for its determination. This condition turns mathematical model into nonlinear problem of large difficulty. The Navier-Stokes equations are used to describe velocity fields in liquid phase. To solve the task, the method of small parameter is offered.

Keywords: differential equation, free boundary, numerical algorithms, functional, optimization

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