Abstract The article presents a finite volume method for the numerical study of solution crystal growth. The mathematical model is based on the time-dependent Navier-Stokes equations in the stream function/vorticity form, energy and mass transfer equations in solid and liquid phases, and thermodynamics equilibrium conditions at the phase transition interface. The problem is axisymmetric and studied in a cylindrical body-fitted coordinate system. The equations for temperature and composition in the solid and liquid phases, and interface velocity are solved simultaneously. The approach ensures global conservation of kinetic and thermal energy and conservation of the solute. The proposed strategy allows performing a full-scale numerical simulation of a variety of technological regimes with a reversal in the crystal dissolution and growth. Sample calculations are reported for prototypes of liquid phase diffusion growth process and Bridgman-Stockbarger method.

中文翻译：

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用于研究溶液晶体生长技术的保守有限体积策略

摘要 本文提出了一种用于溶液晶体生长数值研究的有限体积法。数学模型基于流函数/涡度形式的瞬态 Navier-Stokes 方程、固相和液相中的能量和传质方程以及相变界面处的热力学平衡条件。该问题是轴对称的，并在圆柱体拟合坐标系中进行研究。同时求解固相和液相中的温度和成分以及界面速度方程。该方法确保了动能和热能的全局守恒以及溶质的守恒。所提出的策略允许对各种技术方案进行全面的数值模拟，并在晶体溶解和生长方面进行逆转。