The paper considers the problem of thermal convection in the melt zone during unidirectional crystallization of a metal axisymmetric sample with a free surface boundary (liquid bridge) under microgravity. The mathematical problem includes a system of Navier-Stokes equations in the Boussinesq approximation with an equation for the mass transfer of impurity particles in a liquid, as well as equations for the motion of the liquid free surface.
A numerical algorithm for solving the problem based on the vortex and current function method, linearization of the problem, and finite-difference approximation using the variable direction method to solve the difference system of linear equations is developed. The physical parameters of thermal convection processes in the melt zone are calculated. It is shown that taking into account the motion of the free boundary near the crystallizing liquid phase leads to a change in the distribution of impurities near the curing surface, which in turn causes a change in the characteristics of the cured material.
Димитриенко Ю.И., Леонтьева С.В. Моделирование термоконвективных процессов при однонаправленной кристаллизации сплавов с учетом движения свободных границ. Математическое моделирование и численные методы. 2018. № 4. с. 3–24.