多相流自由界面的不稳定性问题是多相流中的重要问题，与液滴破碎、燃料输运、水下爆炸、喷流、惯性局限融合等许多问题紧密关联。在一些复杂的系统中，更是存在多种不稳定性机制相互竞争。通过研究这类问题，在科学上可以帮助人们理解许多现象背后的物理机制，在工程上可以帮助发展相关设计和工艺。本课题拟在一种既有可压缩多相流计算流体力学算法体系基础上继续发展，并应用其更深入的研究多相流自由界面的不稳定性问题。从一些基本的Rayleigh-Taylor、Kelvin-Helmholtz和Richtmyer-Meshkov不稳定性问题出发，在线性阶段与理论解进行对比，在包括非线性阶段的更完整的过程中和实验结果进行对比。一方面完善算法体系，一方面研究探讨物理过程。在此基础上，进一步研究包括高速气流中的液滴破碎这样的更复杂的系统，研究其中各种不稳定性各种模式的相互竞争，探讨不同流体属性和不同的流场对不稳定性的影响。

Interfacial instability in multi-fluid system is very important in the study of multi-phase flows. Many phenomena, including drop aerobreakup, fuel transportation, under-water explosion, jet, and inertial confinement fusion are closely related to it. In some complex systems, several different instabilities compete with each other. With the study on this kind of problems, people can get better understanding about the inside physics mechanisms, and can get more ideas to improve designs and techniques. In this project, we plan to continue the development of a compressible multi-phase computational fluid dynamics algorithm system，and apply it to study the multi-fluid interfacial instability problems. We plan to start from some basic instabilities, including Rayleigh-Taylor, Kelvin-Helmholtz and Richtmyer-Meshkov. In the linear region, we can compare with some existing theoretical solutions; in the bigger region, including the nonlinear region, we can compare with some experimental results. In this way, we can improve the algorithm system and study the physics process. Upon these, we plan to continue to study more complex systems, like drop aerobreakup. The competition of different instabilities and different modes, the effects of different fluid properties and different flow fields will be studied.