The hybrid detonation formulation of three-dimensional condensed phase explosives is presented based on the multiphase compressible fluid equation and the reaction rate equation. The iteration method of thermodynamic equilibrium for the multiphase detonation mixed reaction zone is built and an efficient detonation parallel software is developed. The feasibility of the physical model, the numerical method and the program module are verified by comparative experiments. We focus on the wave front structure, the coupling of flow fields and chemical reactions and the secondary initiation mechanism of condensed phase explosives by numerical simulations of the detonation process at various corners. The numerical results show that the diffraction area of a corner of 135°is larger than that of 90°of PBX9404 explosive, and the wave front structure is affected by the local flow field velocity. The temporary "death zone" is formed because the chemical reactions are decoupled from the leading shock wave when the detonation wave passes the corner. As the corner angle increases, the dead zone of the corner is expanded. The key of secondary initiation in the dead zone is that the acting time of back-detonation wave should be longer than the critical induction time of explosives in the corner zone.