## 3 Analysis of the Transition between Shock Reflections
### Position (a)  
Figure 9 shows the result of applying 107.5 m) of energy upstream of the wedges (point (a) in Figure 8). The shock wave structure from the upper wedge collapses due to the blast wave that is generated by the energy deposition and the disturbance is also propagated in a part of the oblique shock wave that is generated from the lower wedge. At this time (T = 40 \(\upmu\)s), the Mach reflections temporarily disappear due to the interaction between the oblique shock wave and the blast wave and then the disturbance from the energy deposition passes the computational domain (T = 120 \(\upmu\)s). The blast wave that is caused by the energy deposition temporarily changes the symmetric shock structure into an asymmetric one. At 100 \(\upmu\)s, two slip lines are observed: an upper slip line that meets the blast wave through the oblique shock from the lower wedge and a lower slip line from the Mach reflection that is generated by the interaction with the blast wave and the lower oblique shock. The Mach reflection that is generated by the interaction between the blast wave and the oblique shock has the form of a right running shock. The behavior of the blast wave propagating along with the upper wedge from 100 to 240 \(\upmu\)s was examined in detail. The wave from the deposition initially propagates upstream and then downstream along with the flow over time and intersects with the flow of the preceding blast wave. This wave passes through Mach reflections between 200 and 240 \(\upmu\)s, which creates a temporary shock wave structure that is similar to the one that developed when the angle of the upper wedge decreased. According to a previous study [4], to induce a transition from Mach reflection to regular reflection in a steady flow, it is necessary to generate conditions in which the Mach reflection is not maintained, such as by reducing the wedge angle or increasing the freestream Mach number. In this study, the wedge is symmetrical, but the wave structure is temporarily asymmetrical due to the energy deposition. Thus, when the overall Mach reflection (oMR) changes to an overall regular reflection (oRR), there should be a moment when there are direct Mach reflection (DiMR) and inversed Mach reflection (InMR) structures (right or left running shocks) [31; 32]. The definition of the oMR, oRR, DiMR, and InMR are described by [PERSON] et al. [33]. Figure 8: Location of energy deposition. Although this study was performed with an unsteady flow, the results show that a transition occurs under similar conditions. The preceding blast waves interacted with the oblique shock that is generated  
Figure 9: Interaction between blast wave and oblique shock, deposition upstream of the wedges. Energy: 107.5 mJ. from the lower wedge and produced temporarily asymmetric Mach reflections. The subsequent blast wave induces a transition by generating a shock structure, which is similar to the structure that could be generated by installing a wedge with a smaller angle than the one suggested in the von Neumann criteria. It is assumed that the transition is terminated after about 600 us, however unlike in Figure 5 (left), a slip line was observed after the reflection point, which suggests that little disturbance remains. Figure 10 shows the results from when the deposition energy is increased to 215 mJ at the same location (position (a)). Even though the energy level was increased, the phenomena are almost the same, including the collapse of the Mach reflection, regeneration, and the transition. In this case, as the deposited energy increases, the velocity of the blast wave increases, so the collapse of the reflected shock structure begins earlier than in the previous conditions. However, the last interaction between the blast wave and the Mach reflection occurs at 200 to 240 us, which is nearly the same as in Figure 9. Distortion of the reflected shock is also observed.