A new uncoupled algorithm of simulating chemical non-equilibrium flow originally realized by finite difference method was extended to the unstructured finite volume method, which makes the simulation of reaction flow in complex configurations possible. The H₂/Air shock-induced oscillating combustion experiment conducted by Lehr was simulated, and the computed oscillating frequencies conformed well with the ones acquired by experiment, which indicates that the present method is temporally and spatially second order accurate. It is also demonstrated that geometrical configuration plays a definitive role in the combustion regime. If the truncated angle is less or equal to 15 degrees, high frequency oscillating combustion in regular regime occurs, while if the angle is larger or equal to 20 degrees, low frequency oscillating combustion in large-disturbance regime is observed.