本项目主要针对多介质可压缩流体力学问题，特别是区域为复杂几何边界，动边界等特点的实际问题，在二维结构和非结构网格上开展高阶精度及高分辨率的ALE间断Petrov-Galerkin方法研究。研究内容包括三个方面。首先是针对欧拉坐标系下可压缩流体力学气动方程组，开展间断Petrov-Galerkin方法研究；其次是针对Lagrange坐标系下多介质可压缩流体力学气动方程组，构造间断Petrov-Galerkin拉氏格式；最后是开展适用于多介质可压缩流问题的高精度ALE间断Petrov-Galerkin方法研究。项目研究可以充分发挥间断Petrov-Galerkin方法和ALE方法的优势，构造出适用于多介质流和大变形问题数值模拟的算法并研制出相应的计算程序。研究成果可以为内爆动力学、惯性约束聚变和高速碰撞等问题的数值模拟提供可靠的计算方法和程序。

In this project, some high order and high resolution ALE discontinuous Petrov- Galerkin methods on two-dimensional structured and unstructured mesh are constructed for solving multi-medium compressible flows, especially for problems with complex geometric boundary, moving boundary. The research is consisted of three parts. The first one is developing the discontinuous Petrov-Galerkin algorithm for solving compressible gas dynamic equations in Eulerian coordinate; The second one is concerning about the lagrangian algorithm for solving compressible gas dynamic equations; At last, we begin the research on ALE method for solving multi-medium compressible flows problems. The research can develop the algorithm and corresponding programm for multi-medium and large deform problem by combining the advantages of discontinuous finite element method, Petrov-Galerkin method and ALE method. The research can be used in dynamic of interior explosion, inertial confinement fusion and the high velocity impact.