Numerical simulations are conducted to study pressure gain combustion in a linear channel with discrete injection slots. The mechanism involves generating transverse combustion waves that continuously shuttle across the linear channel to facilitate rapid energy release from premixed reactant injected at a prescribed total pressure. Simulation results reveal that the transverse wave mode depends strongly on the relative amount of oxygen and nitrogen in the oxidizer. A higher injection total pressure is required to establish transverse waves with greater volume fraction of nitrogen. However, the transverse wave is difficult to be continuously sustained in such scenario, and the combustion has a tendency to revert back to the deflagration mode. From time to time, the phenomenon of flash back then transit to detonation can be observed to re-establish the transverse waves. Strong blast waves emanating from the injection plane at high injection total pressure are found to interfere with the transverse waves. Consequently, pressure gain combustion using premixed ethylene/air as the reactant in a linear channel geometry involves highly unsteady wave dynamics.