气液两相流动问题广泛出现在国防和民用领域，开展该问题的数值模拟研究具有重要的应用背景。本项目将开展二维和三维气液两相流界面(可压缩不可压缩界面)处理方法及自适应网格技术研究。由于可压缩流体的解在不可压缩极限(马赫数趋于零)下收敛到不可压缩流体的解，因此先考虑液体为可压缩流体，利用可压缩多介质流基于求解Riemann问题的界面处理方法，在界面处构造和求解Riemann问题，在不可压缩极限下，得到气液界面(可压缩不可压缩界面)处的流动状态。考虑到液体的粘性和表面张力作用，分别为气体和液体定义界面边界条件，将两相流问题转化为单相流问题，利用间断伽辽金方法分别求解流体控制方程组和跟踪界面的Level Set方程，得到气液两相流动问题的整体间断伽辽金数值求解方法。将自适应移动网格技术应用于二维和三维气液两相流计算，提高解的分辨率和计算效率，得到清晰界面，不出现混合流体和非物理振荡。

It is very important to develop the numerical simulation of Gas-water two phase flow as the applications of which happens in numerous field. In this project we will develop an interface treating method for two- and three- dimensional compressible-incomoressible two phase flow and the applications of adaptive mesh technique. In this method, we consider the liquid as compressible fluid, then the compressible-incompressible interface states can be obtained by solving the compressible Riemann problems as the compressible solution converges to incompressible solution as the Mach number goes to zero. The real ghost fluid method (rGFM) is employed to define the interface boundary condition, therefore the simulation can be carried out as if for single phase fluid. The Runke-Kutta discontinuous Galerkin (RKDG) method is applied to solve the fluid controlling equation and the level set equation so as to the global RKDG solution is obtained for gas-water two phase flow. The adaptive moving mesh technique is extended to the compressible-incompressible two phase flow to improve the resolution of the solution and the computational efficiency. The method can keep sharp interface with no fluid mixture and unphysical oscillations.