中文摘要：

多介质流动问题的求解一般是在结构网格上实现，而三角形网格对于复杂计算区域具有更好的适应性，本文结合rGFM方法，给出三角形网格上多介质流动问题界面处理方法．利用level-set方法跟踪界面，在界面处构造Riemann问题，得到界面处流体准确的流动状态．通过定义界面边界条件，将多介质流动问题转化为单介质流动问题，利用高精度RKDG方法求解．采用多个算例验证该方法的稳健性和有效性，结果表明该方法能准确捕捉界面和激波的位置，保持界面清晰．

英文摘要：

Simulation of multi-medium compressible flows is generally on structured meshes. As triangular meshes provide a flexible way for decomposing a complex domain, we present an interface treating method for multi-medium flows on triangular meshes with a rGFM （real ghost fluid method）. A level set function is used to capture interface. A Riemann problem is constructed at interface to provide fluid states. By defining interface boundary conditions with these states, calculation can be carried out as if in a single medium flow. A high-accuracy RKDG method is then employed to discretizing equations. Several examples are given to test robustness and efficiency of the algorithm. It shows that the method can capture sharp interface and shock wave accurately.