热毛细流是流体力学一个重要基础问题，亦是微重力流体物理研究的一个重点问题。耦合自由表面动态变形的热毛细流的数值模拟是计算流体力学的一个重要挑战。前期由于数值技术的局限，文献中关于自由表面动态变形对热毛细流失稳及其随后三维演化的影响缺乏相应数值模拟研究。本项目利用微重力环境下的提拉法晶体生长简化模型，发展基于动态网格谱元法的线性稳定性分析程序研究自由液面动态变形对热毛细流失稳的影响；同时发展引入相场法和连续表面力模型的有限体积法，研究热毛细流失稳后的三维演化与自由液面动态变形的关系；最后研究旋转磁场与液封技术手段对热毛细流和自由表面（液封是液-液界面）动态变形的控制作用。本项目工作不但旨在揭示自由表面动态变形对热毛细流失稳及其随后三维演化的影响，而且同时发展耦合自由表面动态变形的热毛细流数值模拟计算技术，为解决大量相关流体动力学问题奠定基础。

Thermocapillary flow is an important fundamental problem of fluid dynamics, and thermocapillary flow is also a key problem in microgravity fluid physics. It is a challenge to simulate thermocapillary flow coupling with the dynamic deformation of fee surface. Because of the limitation of numerical simulating technique, there is no report about the effect of the free-surface dynamical deformation on the stability of thermocapillary flow and also its three-dimensional convection evolution. In this proposal, we plan to develop a linear stability analysis method based on the spectral element method with dynamical mesh to investigate the effect of the free-surface dynamic deformation on the onset of thermocapillary flow instability in the simplified configuration of Czochralski crystal growth under microgravity. In the meantime, we also develop the finite volume method incorporating the phase field theory and the continuum surface force (CSF) model to investigate the correlation between the three-dimensional oscillating thermocapillary flow and the dynamic deformation of free surface. Finally, we investigate the effect of the rotating magnetic field and also the liquid encapsulant on the thermocapillary flow and its free-surface dynamic deformation. In this research, not only we intend to reveal the effect of free-surface dynamic deformation on the stability of thermocapillary flow and its three-dimensional convection evolution, but also we develop the numerical technique to simulate thermocapillary flow with dynamic interface deformation, and in future, we expect to solve a large number of the relating fluid dynamics problems with the developed numerical technique in this work.