The evolution of main shock waves generated by multiple finite-energy blast sources with time-delayed energy release is investigated. We demonstrate that a merged shock wave forms when the individual blasts interact within a critical interval of delay times. This interval is determined principally by the initial sound speed ratio between the compressed gas of the blasts and the ambient medium. Numerical simulations confirm both the existence and the boundaries of this merging regime. Extending the analysis to the strong-shock stage, we derive an asymptotic solution that incorporates an equivalent energy release and a temporal scaling for the dual-source system, thereby describing the propagation of the merged shock front. These results provide a foundational model for multiple blast–shock processes, with potential applications to astrophysical phenomena, intense laser–matter interactions, and blast-wave dynamics in general.
Ma et al. (2026) studied this question.