Apparatus and methods for combustion of fuel. Some embodiments of the inventions include a fuel nozzle which injects fuel into a combustion channel of a wave rotor combustor or a pulse detonation combustor In some embodiments the combustion process includes a backward-propagating detonation wave within a substantially closed channel which compresses discrete quantities of combustible and noncombustible mixture. Yet other embodiments include a precombustion chamber integrated into the wave rotor, the outlet stator or both.