Mitigation of pressure pulsations in the exhaust of a pulse detonation combustor is crucial for operation with a downstream turbine. For this purpose, a device termed the shock divider is designed and investigated. The intention of the divider is to split the leading shock wave into two weaker waves that propagate along separated ducts with different cross-sections, allowing the shock waves to travel with different velocities along different paths. The separated shock waves redistribute the energy of the incident shock wave. The shock dynamics inside the divider are investigated using numerical simulations. A second order dimensional split finite volume MUSCL-scheme is used to solve the compressible Euler equations. Furthermore, low-cost simulations are performed using Geometrical Shock Dynamics to predict the shock wave propagation inside the divider. The numerical simulations are compared to high-speed schlieren images and time-resolved total pressure recording. For the latter, a high frequency pressure probe is placed at the divider outlet, which is shown to resolve the transient total pressure during the shock passage. Moreover, the separation of the shock waves is investigated and found to grow as the divider duct width ratio increases. The numerical and experimental results allow for a better understanding of the dynamic evolution of the flow inside the divider and inform its capability to reduce the pressure pulsations at the exhaust of the pulse detonation combustor.