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Emission in many astrophysical transients originates from a shocked fluid. Acentral engine typically produces an outflow with varying speeds, leading tointernal collisions within the outflow at finite distances from the source.Each such collision produces a pair of forward and reverse shocks with the twoshocked regions separated by a contact discontinuity (CD). As a usefulapproximation, we consider the head-on collision between two cold and uniformshells (a slower leading shell and a faster trailing shell) of finite radialwidth, and study the dynamics of shock propagation in planar geometry. We findsignificant differences between the forward and reverse shocks, in terms oftheir strength, internal energy production efficiency, and the time it takesfor the shocks to sweep through the respective shells. We consider thesubsequent propagation of rarefaction waves in the shocked regions and explorethe cases where these waves can catch up with the shock fronts and therebylimit the internal energy dissipation. We demonstrate the importance of energytransfer from the trailing to leading shell through $pdV$ work across the CD.We outline the parameter space regions relevant for models of differenttransients,e.g., Gamma-ray burst (GRB) internal shock model, fast radio burst(FRB) blastwave model, Giant flare due to magnetars, and superluminoussupernovae (SLSN) ejecta. We find that the reverse shock likely dominates theinternal energy production for many astrophysical transients.

Internal Shocks Hydrodynamics: the Collision of Two Cold Shells in Detail