Abstract: Based on detailed hydrogen and oxygen chemical kinetics model, the multi-species reactive Euler equations were established to describe the hydrogen and oxygen detonation. Using third-order Additive Runge-Kutta methods in time discretization, using fifth-order weighted essentially non-oscillatory (WENO) scheme in spatial discretization, a high-solution large-scale program was developed. It was verified that the program could solve stiff source term caused by multispecies chemical reaction, which could also save computation time and computation memory. With this program, the process of detonation initiation with convergence of shock waves was numerically simulated for 3 types of concave cavity, hemispherical concave cavity, semi-ellipsoidal concave cavity and conical concave cavity. The simulation results show the characteristic of detonation initiation in different types of concave cavity.