I'm reading about how the stator vanes are diffusors, which diffuse the air flow in a axial compressor to a larger flow area to build up pressure BUT at the same time the compressor shows its overall flow area getting REDUCED at the same place. So, how does that work out? Or in other words: What is the causal chain between the air getting a higher velocity in the rotor blades and the higher pressure in the exhaust port?
The device has to be designed so that each stage does its job.
The stator reduces the high velocity out put of a stage to a lower velocity, increasing the pressure. But the subsequent rotary section needs a smaller area because the higher pressure gas takes up less volume. So the two have to be designed in tandem. This is really advanced flow design. My guess is that most of these design parameters have been arrived at emperically, not via math. I would expect gas turbine manufactureres to have some really advanced modeling software, but with the equations being developed emperically.