In this paper, we study the Mach reflection phenomenon in inviscid flows using a higher order discontinuous Galerkin method and overset grids. We use the shock capturing procedure proposed in Siva Prasad Kochi et al. using overset grids to capture the discontinuities occurring in the supersonic flow over a wedge accurately. In this procedure, we obtain a coarse grid solution first and using the troubled cell data, we construct an overset grid which is approximately aligned to all the discontinuities. We rerun the solver with the coarse grid solution as the initial condition while using the troubled cell indicator and the limiter only on the overset grid. This allows us to capture the discontinuities accurately. Using this procedure, we have obtained the solution for Mach $3.0$ and $4.0$ flow over a wedge for various wedge angles and determined the detachment criterion and the Von Neumann condition accurately. We have also determined the Mach stem height for various wedge angles for these Mach numbers. We have also demonstrated the hysteresis that occurs in the transition from regular reflection to Mach reflection.

翻译：在本文中,我们使用高顺序不连续的 Galerkin 法和高置网格来研究静脉流中的马赫反射现象。我们使用Siva Prasad Kochi等人建议的休克捕捉程序,使用高置网格来精确地捕捉超声流在网格上发生的不连续现象。在这个程序中,我们首先获得粗粗格网格解决方案,然后使用麻烦的单元格数据,我们建造一个与所有不连续状态大致一致的超置网格。我们用粗粗格网格解决方案作为初始状态重新运行,同时使用麻烦的细胞指标和限制器仅在高置网格上进行。这使我们能够准确地捕捉不连续现象。我们利用这个程序获得了马赫3.0美元和4.0美元流的解决方案,用于各种边缘角度,确定了隔离标准以及Von Neumann条件。我们还确定了这些马赫数字的各种网格角度的马赫干高度。我们还演示了从正常反射到马赫反射过程中发生的螺旋。