In certain embodiments, there is provided a method of operating a turbocharged system including injecting a first quantity of fuel into an engine cylinder at a first predetermined time during a second half of a compression stroke before a piston of the engine cylinder reaches top dead center of the compression stroke. The method further includes injecting a second quantity of fuel into the engine cylinder at a second predetermined time after the first predetermined time when the piston is advanced by a predetermined advance value before the piston reaches the top dead center of the compression stroke.