## 4 Discussion  
In this study, numerical studies on the transition characteristics with energy deposition were performed to avoid Mach reflections in the dual solution domain. A two-dimensional unsteady analysis was performed to efficiently simulate the flow around a symmetric geometry. In comparison with the experiment results using a hemisphere model, the proposed numerical method showed good agreement in the flow structures, such as the shock and blast wave propagation and reflections. In addition, the conditions under which Mach or regular reflection occurred in the dual solution domain were in good agreement with the theoretical study.  
The computational results show that it is possible to transition from Mach reflections to regular reflections through energy deposition at an asymmetric location. The preceding blast waves that were generated by the energy deposition interacted with the oblique shock from the wedge and disrupted the Mach reflections. During the regeneration of the shock waves, the blast wave induces regular reflection, which has a similar effect to changing the wedge angle to below the von Neumann criteria through several additional interactions. The results showed that the transition occurred faster as the focus moved into the contraction zone when the same energy was deposited.  
However, when more energy was deposited, the shock wave structure collapsed sooner, but the total time that was required for flow stabilization was increased due to the generation of a strong blast wave. As the level of energy increased further, the transition did not occur. The entire disruption of the shock system by strong blast waves prevented the local shock angle variation in the regeneration process. The results suggest that the expansion wave also plays a role in the transition. This tendency is maintained for different focal locations. However, when the focus of energy deposition lies on the symmetry axis, no transition occurs regardless of the energy level because the shock system is not changed to an asymmetric configuration by a disturbance.  
These results suggest that the shock wave transition phenomena in the dual solution domain are affected by both the amount and the location of the energy. It is also expected that there is an optimal location for energy deposition that depends on the operating conditions and the shape of the structure. However, this study mainly focused on the feasibility of the proposed technique and the investigation of the transient shock wave characteristics by laser energy deposition. Thus, the effect of various parameters needs further investigation, including the freestream conditions, the length of the wedge, asymmetric arrangements, and three-dimensional effects.  
Conceptualization, S.K. and H.J.L.; methodology, S.K. and H.J.L.; software, S.K. and Y.K.; validation, S.K., Y.K., and H.J.L.; formal analysis, S.K.; investigation, S.K. and H.J.L.; resources, H.J.L.; data curation, S.K. and Y.K.; writing--original draft preparation, S.K. and Y.K.; writing--review and editing, H.J.L.; visualization, S.K. and Y.K.; supervision, H.J.L.; project administration, H.J.L.; funding acquisition, H.J.L.  
**Funding:** This work was supported by the National Research Foundation of Korea (NRF) Grant, which is funded by the Government of Korea (MIST) (2017R1C1B5076748).  
**Conflicts of Interest:** The authors declare no conflict of interest.