Shock wave focusing is considered a new type of initiation method that does not require external ignition devices. For this method, understanding the shock wave/flame interaction accurately is one of the critical issues for revealing the ignition and triggering mechanisms during shock wave focusing processes. In this study, numerical simulations was carried out to investigate the detailed flow field evolution of the focusing process with kerosene as fuel. Two detonation initiation modes were found during the shock wave focusing processes, which were the direct initiation mode and the reflected shock wave collision initiation mode, respectively. At the detonation wave propagation stage, the primary detonation wave decouples and fails to propagate out of the cavity. The multiple initiation phenomenon occurs in the cavity and it dominated detonation waves to propagate outside of the cavity to accomplish one thermal cycle. There is no positive correlation between jet temperature and detonation wave propagation velocity. When the jet temperature is low, the detonation wave velocity dominated by multiple initiation mode is the fastest. The analysis of the shock wave focusing process under different jet velocities showed that when the jet velocity was lower than 2Ma, the decoupling of the primary detonation wave failed to induce multiple detonation waves. Driven by the vortex in the semicircular cavity, the flame is almost stationary, which means the failure of the detonation wave propagation process.