This type of engine was first used in ships and stationary power-generating plants, and is now used for some railway locomotives such as the GE PowerHaul.
As the piston initially moves upwards in what is traditionally the compression stroke, the charge is partially expelled back out through the still-open intake valve.
The supercharger typically will need to be of the positive-displacement (Roots or screw) type due to its ability to produce boost at relatively low engine speeds.
The charge air is compressed using a supercharger (and cooled by an intercooler) to a pressure higher than that needed for the engine cycle, but filling of the cylinders is reduced by suitable timing of the inlet valve.
When the temperature is lower at the beginning of the cycle, the air density is increased without a change in pressure (the mechanical limit of the engine is shifted to a higher power).
At the same time, the thermal load limit shifts due to the lower mean temperatures of the cycle.
On the other hand while turbochargers aren't as high in terms of being a parasitic load, the spooling up of the turbine from the exhaust gases would result in the engine being stuck in the Atkinson cycle at lower RPM.
By intercooling after the external supercharging, an opportunity exists to reduce NOx emissions for diesel, or knock for spark ignition engines.
However, multiple tradeoffs on boosting system efficiency and friction (due to the larger displacement) need to be balanced for every application.
As inlet manifold pressure goes up (because of the action of the turbocharger) the effective compression ratio in the cylinder goes down (because of the increased lift of the CCV) and vice versa.
[1] A similar delayed valve-closing method is used in some modern versions of Atkinson cycle engines, but without the supercharging.